--- slug: the-sixty-fifth-distance passed: 2026-10-08 by: the assay line (research/assay-line/unit-distance-1009/), Codex fixer directed by claude-answering-alexeev-u22 (the unit-distance wave supervisor, who decided every finding after re-reading each WRONG source); source record by Codex (gpt-6.1-sol), checked by Codex checked: 343 confirmed: 313 wrong: 2 unverifiable: 0 observed: 28 stale: 0 --- Count notes: confirmed: 313 (309 CONFIRMED plus four true-page MINOR source-record repairs); wrong: 2 (one WRONG prose claim plus one MINOR runtime readout). This pass implements the directing instance's six-item triage for the-sixty-fifth-distance at 5a634e5551, using the requested pass date of 2026-10-08. The fixer re-read the pinned evidence for every item before editing: four repairs correct citations for true page claims, one narrows a false geometric sentence to four-cycles, and one labels the hypothetical target correctly. The 309 CONFIRMED and 28 OBSERVED lines retain Codex N2's source-by-source checks in research/assay-line/unit-distance-1009/the-sixty-fifth-distance/N2-codex.md; they are not presented as a new exhaustive assay by the fixer. The archived enumeration was not re-run, and retained observations remain observations. ## Claims - CONFIRMED | Unit distances on 23 points: why the maximum is 64 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [seo-result] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Unit distances, settled / a finite case | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [finite-case-label] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | 64 distances you can touch. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [hero-line-1] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | One more that cannot exist. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [hero-line-2] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Among 23 distinct points in the plane, the maximum number of unit pairs is 64. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [maximum-23] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | A known arrangement attains it | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/configuration.json ; git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt | [known-attainment] The retained transcript says "23 distinct points, 253 exact pair tests, 64 unit pairs". Independent multiplication and the actual app reproduce 64 with no colliding points. - OBSERVED | the Artificial Wasteland's exhaustive graph enumeration left 1 survivor with 65 edges, refuted by a 15-node certificate of rhombus and triangle moves. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [enumeration-survivor] Matching excerpt: "**What the search found.** Exactly one graph reached (23,65), in slice 50, and it survived every pruning rule. An exact refutation certificate (a proof tree of 15 nodes over an explicit algebraic number field) shows it is not a unit-distance graph. Nothing [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - CONFIRMED | Move the exact drawing, search the 398 small obstructions, and walk the proof. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [instruments-in-dek] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Computer-assisted, resting on the project's u(22) = 60, and not yet refereed outside the project. | git show 5a634e5551:research/the-sixty-fifth-distance/README.md | [scope-in-dek] Matching excerpt: "This is the reproducibility packet for the standalone u(23) page. The browser checks the 23-point drawing in exact arithmetic, searches the frozen forbidden list when requested, and verifies the whole survivor certificate. Its enumeration funnel and large-run [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | u(23) = 64 One exact drawing. One exhausted search. One short contradiction. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [result-equation] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | One exact drawing. One exhausted search. One short contradiction. | git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt | [single-proof-chain] Matching excerpt: "Independent geometry: 23 distinct points, 253 exact pair tests, 64 unit pairs; 18 integer unit directions. Certificate: 65 edges; 57 rhombi, rank 18; 15 nodes, 7 splits, 8 leaves. Blind Python ACCEPT. Archived rows: 11 levels; 1920 slices, 1955 copies; 1 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Place 23 points and count pairs exactly one unit apart: the maximum is 64. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [plain-1] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Move the points, check the lone candidate for 65, and follow its contradiction. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [plain-2] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Your browser checks the drawing and certificate, but does not repeat the entire archived search. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [plain-3] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | In 1946, Paul Erdős asked: among n distinct points in the plane, how many pairs can be exactly one unit apart? | https://users.renyi.hu/~p_erdos/1946-03.pdf | [erdos-question-1946] Matching excerpt: "3. The function g(n ; r). Denoting by g(n ; r) the maximum number of times a given distance r can occur among n points of a plane we establish" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Write u(n) for the largest count over all arrangements. | https://arxiv.org/html/2412.11914v2 | [definition-un] Matching excerpt: "A unit-distance graph is a simple graph G G for which there exists an injection f : V ⁡ ( G ) → ℝ 2 f\colon V(G)\to\mathbb{R}^{2} such that { u , v } ∈ E ⁡ ( G ) \{u,v\}\in E(G) implies ‖ f ⁡ ( u ) − f ⁡ ( v ) ‖ = 1 \|f(u)-f(v)\|=1 . Let U ⁡ ( n ) U(n) denote [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Alexeev, Mixon and Parshall settled the exact values through 21 points in 2024 | https://arxiv.org/abs/2412.11914v1 | [amp-exact-through21] Matching excerpt: "[Submitted on 16 Dec 2024 (this version), latest version 12 Feb 2025 ( v2 )] [...] Authors: Boris Alexeev , Dustin G. Mixon , Hans Parshall [...] Abstract: We improve the best known upper bound on the number of edges in a unit-distance graph on $n$ vertices [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | this project then established u(22) = 60. | git show 5a634e5551:research/unit-distance-22/RESULT-u22.md | [project-u22] Matching excerpt: "**Theorem.** No unit-distance graph on 22 vertices has 61 edges. Hence u(22) = 60." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | This page gives u(23) = 64 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [this-page-u23] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | u(24) = 68 comes next. | git show 5a634e5551:src/content/strata/the-sixty-ninth-distance.md | [following-u24] Matching excerpt: "dek: "Among 24 distinct points in the plane, the maximum number of unit pairs is 68. A known arrangement attains it; the Artificial Wasteland's exhaustive graph enumeration left one 69-edge survivor, excluded by a contained eleven-vertex graph and an exact [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | An exact small value concerns a fixed point count; the asymptotic question is how u(n) grows as n increases. | https://arxiv.org/html/2412.11914v2 | [fixed-versus-asymptotic] Matching excerpt: "A unit-distance graph is a simple graph G G for which there exists an injection f : V ⁡ ( G ) → ℝ 2 f\colon V(G)\to\mathbb{R}^{2} such that { u , v } ∈ E ⁡ ( G ) \{u,v\}\in E(G) implies ‖ f ⁡ ( u ) − f ⁡ ( v ) ‖ = 1 \|f(u)-f(v)\|=1 . Let U ⁡ ( n ) U(n) denote [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Erdős's conjecture fell in May 2026 | https://arxiv.org/abs/2605.20695v1 | [may-2026-disproof] Matching excerpt: "[Submitted on 20 May 2026] [...] We present a short, digested, human-verified version of the recent OpenAI-generated counterexample to the Erdős unit distance conjecture, and a sequence of reflections on it." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | with more than n^1.014 unit pairs for arbitrarily large n | https://arxiv.org/abs/2605.20579v1 | [explicit-power] Matching excerpt: "We show that there are sets of $n$ points in the plane with $n$ arbitrarily large that contain more than $n^{1.014}$ pairs of points separated by a distance exactly $1$." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | the upper bound O(n^(4/3)) has stood since 1984. | https://arxiv.org/html/2605.20695v1 | [upper-bound-since1984] Matching excerpt: "Let U ⁡ ( n ) U(n) denote the maximum possible number of unit distances determined by n n points in the Euclidean plane. Erdős proved that U ⁡ ( n ) ≥ n 1 + Ω ⁡ ( 1 / log ⁡ log ​ n ) U(n)\geq n^{1+\Omega(1/\log\log n)} , and the best known upper bound is U ⁡ [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Each line joins a pair exactly one unit apart. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [lower-copy-1] Matching excerpt: "export function measure(points) { const edges=[], collisions=[]; for (let u=0;ux===0n)) collisions.push([u,v]); if (isUnit(d)) edges.push([u,v]); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | There are 23 distinct points; the browser tests all 253 pairs, using fractions and square roots rather than a tolerance. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [lower-copy-2] Matching excerpt: "export function measure(points) { const edges=[], collisions=[]; for (let u=0;ux===0n)) collisions.push([u,v]); if (isUnit(d)) edges.push([u,v]); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The starting configuration has 64 unit distances. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/configuration.json | [lower-caption-1] N1's excerpt contains only the source label. The full file also has ""claimedEdges": 64"; all 253 pairs were independently squared and give 64. - CONFIRMED | Its coordinates come from Engel and colleagues' dataset; the count is recomputed here. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/configuration.json ; git show 5a634e5551:research/the-sixty-fifth-distance/tools/densest.py ; git show 5a634e5551:research/the-sixty-fifth-distance/README.md | [lower-caption-2] The source labels the coordinates "Engel et al., run 0; frozen densest.json key 23". The retained extraction program and packet provenance describe that extraction. The coordinates match the frozen 23-point record, and the count is independently recomputed. - CONFIRMED | w₁ = 1/2 + i√3/2; w₃ = 5/6 + i√11/6; z = a + b·w₁ + c·w₃ + d·w₁w₃. | https://arxiv.org/html/2406.15317v3 | [basis-formula] Matching excerpt: "Notation 2.1 . For a positive integer t ∈ ℤ > 0 t\in\mathbb{Z}_{>0} , we let ω t = exp ⁡ ( i ⋅ arccos ⁡ ( 1 − 1 / 2 ​ t ) ) . \omega_{t}=\exp(i\cdot\arccos(1-1/2t)). [...] Definition 2.2 . The Moser lattice, denoted as M L M_{L} , is defined as the additive [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | |z|² = r + s√33; unit exactly when r = 1 and s = 0. | https://arxiv.org/html/2406.15317v3 | [squared-modulus-formula] Matching excerpt: "= ( a 2 + a ​ b + 5 3 ​ a ​ c + 5 6 ​ a ​ d + b 2 + 5 6 ​ b ​ c + 5 3 ​ b ​ d + c 2 + c ​ d + d 2 ) + ( b ​ c − a ​ d ) ​ 33 6 . [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Dragging rounds two basis coefficients to fractions with denominator 120. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [quantization-copy-1] Matching excerpt: "export function snappedDelta(x,y) { return [BigInt(Math.round((x-y/Math.sqrt(3))*Number(denominator))), BigInt(Math.round(2*y/Math.sqrt(3)*Number(denominator))),0n,0n]; }" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The arithmetic checks those snapped coordinates exactly; the screen is approximate. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [quantization-copy-2] Matching excerpt: "export function snappedDelta(x,y) { return [BigInt(Math.round((x-y/Math.sqrt(3))*Number(denominator))), BigInt(Math.round(2*y/Math.sqrt(3)*Number(denominator))),0n,0n]; }" Read against the full pinned source or fetched primary document; its scope supports the claim. - MINOR | Arrow keys move the selected point by one such step. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs ; public/strata/the-sixty-fifth-distance/lattice.mjs | [X1; quantization-copy-3] The page claim is true. The old source record quoted snappedDelta, which handles dragging. The keyboard handler is keyDeltas and move in app.mjs:31-33; its integer numerator changes operate on the denominator-120 grid. The source, excerpt and locator now name that handler. Counted as a confirmed MINOR source-record repair. - CONFIRMED | The integer Moser lattice has 18 unit directions. | https://arxiv.org/html/2406.15317v3 | [18-unit-directions] Matching excerpt: "Theorem 2.5 . In the Moser lattice, there are 18 unit vectors in total." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Choose a point and an anchor, then test every landing one unit from that anchor. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [landing-scope-0] Matching excerpt: "export function landings(points,moving,anchor) { if(moving===anchor) throw new Error('Choose different points.'); return unitDirections().map(direction=> { const p=points.map(x=>x.slice()); p[moving]=points[anchor].map((x,i)=>x+direction[i]*denominator); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | This is a restricted experiment, not a search of all possible plane drawings. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [landing-scope-1] Matching excerpt: "export function landings(points,moving,anchor) { if(moving===anchor) throw new Error('Choose different points.'); return unitDirections().map(direction=> { const p=points.map(x=>x.slice()); p[moving]=points[anchor].map((x,i)=>x+direction[i]*denominator); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Deleting a vertex removes its incident edges. | https://arxiv.org/html/2412.11914v2 | [schade-copy-1] Matching excerpt: "Lemma 2 . A simple graph with n ≥ 1 n\geq 1 vertices and m m edges contains an induced subgraph with n − 1 n-1 vertices and at least ⌈ m ⋅ n − 2 n ⌉ \lceil m\cdot\frac{n-2}{n}\rceil edges." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Schade's averaging bound and u(22) = 60 leave u(23) ≤ floor(23 × 60 / 21) = 65. | https://arxiv.org/html/2412.11914v2#S2 ; git show 5a634e5551:research/unit-distance-22/RESULT-u22.md | [schade-copy-2] AMP Lemma 2 gives ceil(m(n-2)/n) edges after a deletion. With the separately cited project dependency 60, floor(23*60/21) = floor(1380/21) = 65. AMP does not itself establish the project's u(22)=60. - CONFIRMED | The only case above the drawing is therefore 65. | https://arxiv.org/html/2412.11914v2 | [schade-copy-3] Matching excerpt: "Lemma 2 . A simple graph with n ≥ 1 n\geq 1 vertices and m m edges contains an induced subgraph with n − 1 n-1 vertices and at least ⌈ m ⋅ n − 2 n ⌉ \lceil m\cdot\frac{n-2}{n}\rceil edges." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | With 66 edges, some deletion leaves at least ceil(66 × 21 / 23) = 61 edges. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [schade-example-1] Matching excerpt: "Why 65 is the only case: by Schade's lemma (AMP's Lemma), a graph with n vertices and m edges has an induced subgraph on n - 1 vertices with at least ceil(m(n-2)/n) edges. For (23, 66) that is 61 > u(22) = 60, so u(23) <= 65. A graph with more than 65 edges [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | That exceeds the permitted 60. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [schade-example-2] Matching excerpt: "Why 65 is the only case: by Schade's lemma (AMP's Lemma), a graph with n vertices and m edges has an induced subgraph on n - 1 vertices with at least ceil(m(n-2)/n) edges. For (23, 66) that is 61 > u(22) = 60, so u(23) <= 65. A graph with more than 65 edges [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Minimum degree exactly 5: every degree is at least 65 − 60 = 5, while the average degree is 130/23, less than 6. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [degree-copy-1] The source says "so d >= 5; and 2 x 65 / 23 < 6." Recomputed: 65-60=5 and 130/23 is approximately 5.65217, forcing minimum degree exactly 5. - CONFIRMED | No copy of any of the 398 forbidden graphs: all those obstructions remain impossible inside a larger unit-distance graph. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [forbidden-copy-0] Matching excerpt: "A (23,65) unit-distance graph G would have to satisfy all of the following (`CONTRACT.md` Sections 0 to 3 and amendments 1 to 4; `research/unit-distance-22/enum/PRUNING.md`; `RHOMBUS-SPEC.md`; `research/unit-distance-22/check/PROOFS.md`): - **Minimum degree [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The live search below checks this condition. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [forbidden-copy-1] Matching excerpt: "export function checkMapping(pattern,host,map) { return Array.isArray(map)&&map.length===pattern.n&&new Set(map).size===map.length&&map.every(v=>Number.isInteger(v)&&v>=0&&vhost.adj[map[u]][map[v]]); }" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | No forced extra unit pair in an induced ancestor: the 6 TU gadgets and their linear consequences force a missing pair to be unit. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [tu-copy-1] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | A saturated 65-edge graph could not have that extra pair. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [tu-copy-2] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Every canonical ancestor stays below its u(j). | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [ancestry-copy-1] Matching excerpt: "The search enumerates every graph that could be such an ancestor: canonical augmentation by minimum-degree deletion, from the level-10 seeds to 23 vertices (`enum/udenum`, driven by `enum/run-dag2.py`), each graph excluded only by a proved structural rule or [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Repeatedly delete a minimum-degree vertex; use a canonical labelling to assign one parent, then grow back through every allowed extension. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [ancestry-copy-2] Matching excerpt: "The search enumerates every graph that could be such an ancestor: canonical augmentation by minimum-degree deletion, from the level-10 seeds to 23 vertices (`enum/udenum`, driven by `enum/run-dag2.py`), each graph excluded only by a proved structural rule or [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The run starts at order 10 and splits by a hash at order 12. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [ancestry-copy-3] Matching excerpt: "The search enumerates every graph that could be such an ancestor: canonical augmentation by minimum-degree deletion, from the level-10 seeds to 23 vertices (`enum/udenum`, driven by `enum/run-dag2.py`), each graph excluded only by a proved structural rule or [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - OBSERVED | Recorded enumeration, orders 13 through 23. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [funnel-copy-1] Matching excerpt: "- The coverage audit (`verify-chain.py --summary-only`, pinned to target (23, 65), seed level 10 and slices (12, 1920) (level, count), requiring g4, hashes; branch `claude/answering-alexeev-u22-g5` at `34f0dcb9ba`): 1955 slice result directories from 101 [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | These are sums of the frozen cell rows across 1,920 slices, not counts of drawings made in this browser. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [funnel-copy-2] Matching excerpt: "- The coverage audit (`verify-chain.py --summary-only`, pinned to target (23, 65), seed level 10 and slices (12, 1920) (level, count), requiring g4, hashes; branch `claude/answering-alexeev-u22-g5` at `34f0dcb9ba`): 1955 slice result directories from 101 [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - CONFIRMED | At the target: 1 graph kept in slice 50. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [funnel-end-1] Matching excerpt: "**What the search found.** Exactly one graph reached (23,65), in slice 50, and it survived every pruning rule. An exact refutation certificate (a proof tree of 15 nodes over an explicit algebraic number field) shows it is not a unit-distance graph. Nothing [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Kept means not yet ruled out. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [funnel-end-2] Matching excerpt: "**What the search found.** Exactly one graph reached (23,65), in slice 50, and it survived every pruning rule. An exact refutation certificate (a proof tree of 15 nodes over an explicit algebraic number field) shows it is not a unit-distance graph. Nothing [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Checking its separate certificate leaves 0 possible survivors. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [funnel-end-3] Matching excerpt: "**What the search found.** Exactly one graph reached (23,65), in slice 50, and it survived every pruning rule. An exact refutation certificate (a proof tree of 15 nodes over an explicit algebraic number field) shows it is not a unit-distance graph. Nothing [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | 23 vertices, 65 edges. | git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt | [survivor-copy-1] Matching excerpt: "Independent geometry: 23 distinct points, 253 exact pair tests, 64 unit pairs; 18 integer unit directions. Certificate: 65 edges; 57 rhombi, rank 18; 15 nodes, 7 splits, 8 leaves. Blind Python ACCEPT. Archived rows: 11 levels; 1920 slices, 1955 copies; 1 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | This diagram is a graph layout, not a unit-distance drawing. | git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt | [survivor-copy-2] Matching excerpt: "Independent geometry: 23 distinct points, 253 exact pair tests, 64 unit pairs; 18 integer unit directions. Certificate: 65 edges; 57 rhombi, rank 18; 15 nodes, 7 splits, 8 leaves. Blind Python ACCEPT. Archived rows: 11 levels; 1920 slices, 1955 copies; 1 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Passing the forbidden-subgraph filter does not supply coordinates. | git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt | [survivor-copy-3] Matching excerpt: "Independent geometry: 23 distinct points, 253 exact pair tests, 64 unit pairs; 18 integer unit directions. Certificate: 65 edges; 57 rhombi, rank 18; 15 nodes, 7 splits, 8 leaves. Blind Python ACCEPT. Archived rows: 11 levels; 1920 slices, 1955 copies; 1 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The certificate has 15 nodes: 7 two-way splits and 8 contradiction leaves. | git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt ; git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [tree-copy-1] The transcript says "15 nodes, 7 splits, 8 leaves." Both exact implementations and the actual app reproduce it. A full binary tree with 7 splits has 8 leaves and 15 total nodes. - CONFIRMED | The checker reconstructs the 57 rhombus equations, of rank 18, from the graph itself. | git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt | [tree-copy-2] Matching excerpt: "Independent geometry: 23 distinct points, 253 exact pair tests, 64 unit pairs; 18 integer unit directions. Certificate: 65 edges; 57 rhombi, rank 18; 15 nodes, 7 splits, 8 leaves. Blind Python ACCEPT. Archived rows: 11 levels; 1920 slices, 1955 copies; 1 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | For unit displacements x, y, z with ax + by + cz = 0, put A = |a|², B = |b|², C = |c|², q = A + B − C and Δ = 4AB − q². A split checks d² = Δ and covers both rows (q ± id)ax + 2Aby = 0. | https://arxiv.org/html/2412.11914v2 | [heron-rule] Matching excerpt: "Lemma 4 . Given a , b , c , x , y , z ∈ ℂ a,b,c,x,y,z\in\mathbb{C} such that a ​ x + b ​ y + c ​ z = 0 ax+by+cz=0 , | x | = 1 |x|=1 , | y | = 1 |y|=1 , and | z | = 1 |z|=1 , then ( x , y ) (x,y) necessarily satisfies ( | a | 2 + | b | 2 − | c | 2 + d ​ i ) ​ [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | At a leaf, two graph edges obey x = ωy. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [leaf-copy-1] Matching excerpt: "if(m.kind==='L1b'){ keys(m,['kind','edges','omega'],path+'.move');const p=pairs(m,2,path),omega=f.complex(m.omega); need(contains(basis,relation(p,[f.co,f.cn(omega)]),f),`${path}: x = omega*y is not forced`); const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Their unit lengths would require |ω|² = 1. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [leaf-copy-2] Matching excerpt: "if(m.kind==='L1b'){ keys(m,['kind','edges','omega'],path+'.move');const p=pairs(m,2,path),omega=f.complex(m.omega); need(contains(basis,relation(p,[f.co,f.cn(omega)]),f),`${path}: x = omega*y is not forced`); const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The checker proves this relation and computes a different exact squared modulus, so the branch is impossible. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [leaf-copy-3] Matching excerpt: "if(m.kind==='L1b'){ keys(m,['kind','edges','omega'],path+'.move');const p=pairs(m,2,path),omega=f.complex(m.omega); need(contains(basis,relation(p,[f.co,f.cn(omega)]),f),`${path}: x = omega*y is not forced`); const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The certificate works in a real field of degree 4. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-README.txt | [field-copy-1] Matching excerpt: "- The field's minimal polynomial `81t^4 - 684t^2 + 256` is irreducible (an exhaustive Kronecker search), and the interval isolates one real root (Sturm)." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Exact polynomial reduction and rational root isolation certify one selected root; decimals below are display approximations. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-README.txt | [field-copy-2] Matching excerpt: "- The field's minimal polynomial `81t^4 - 684t^2 + 256` is irreducible (an exhaustive Kronecker search), and the interval isolates one real root (Sturm)." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | This result rests on our u(22) = 60, AMP's values through order 21, the 398 forbidden graphs, the 6 TU gadgets, and the rhombus and triangle lemmas R and T. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [dependency-copy-1] Matching excerpt: "A (23,65) unit-distance graph G would have to satisfy all of the following (`CONTRACT.md` Sections 0 to 3 and amendments 1 to 4; `research/unit-distance-22/enum/PRUNING.md`; `RHOMBUS-SPEC.md`; `research/unit-distance-22/check/PROOFS.md`): - **Minimum degree [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - OBSERVED | Recorded VERIFY-ALL: 1,920/1,920 slices re-run, in 48 tasks. 48 first slices were checked whole; the remaining prefixes were compared with a whole check. 6 heavy slices used the memory-bounded checker. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/verify-all.txt | [rerun-copy-1] Matching excerpt: "VERIFY-ALL OK: 1920 of 1920 slices re-run and verified (48 tasks; 48 first slices checked whole, the rest from level 13 with the prefix compared; every prefix the prefix of a whole check; 6 by the memory-bounded verify-chain-lean.py after the G5 check was [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Recorded empty-tree control (22,61): 1,920/1,920 slices complete, 0 distinct graphs kept. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/control22-check.txt | [control-copy-1] Matching excerpt: "TARGET-CHECK OK: (22,61): 1920 of 1920 slices complete, G4 PASS 1920; 0 failing, 0 missing; kept at (22,61): 0 distinct graph(s)" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | A tree known to be impossible came back empty. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/control22-check.txt | [control-copy-2] Matching excerpt: "TARGET-CHECK OK: (22,61): 1920 of 1920 slices complete, G4 PASS 1920; 0 failing, 0 missing; kept at (22,61): 0 distinct graph(s)" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Recorded calibration (21,57): 1,920/1,920 slices complete, 10 distinct graphs kept, including 5/5 known graphs. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/calib2157-check.txt | [calibration-copy-1] Matching excerpt: "TARGET-CHECK OK: (21,57): 1920 of 1920 slices complete, G4 PASS 1920; 0 failing, 0 missing; kept at (21,57): 10 distinct graph(s); known: 5 of 5 kept" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | The filter kept possibilities it could not decide. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/calib2157-check.txt | [calibration-copy-2] Matching excerpt: "TARGET-CHECK OK: (21,57): 1920 of 1920 slices complete, G4 PASS 1920; 0 failing, 0 missing; kept at (21,57): 10 distinct graph(s); known: 5 of 5 kept" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Recorded known-graph control at order 22: 14/14 eligible dataset graphs were found. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/level22-control.txt | [level22-copy-1] Matching excerpt: "LEVEL-22 CONTROL OK: 14 of 14 required graphs found" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Eligibility uses the ancestor degree threshold, not every graph in the dataset. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/level22-control.txt | [level22-copy-2] Matching excerpt: "LEVEL-22 CONTROL OK: 14 of 14 required graphs found" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Recorded blind check: 1/1 certificates accepted, 7/7 tampered inputs rejected. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/blind-check.txt | [blind-copy-1] Matching excerpt: "BLIND-CHECK OK: 1 of 1 top-level certificates accepted by the blind verifier (verify_tree.py sha256 1bafc054ee736f4c); 7 of 7 tampered inputs rejected" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | The two earlier acceptance lines are wrappers around one implementation; this Python verifier was written separately from the format and lemmas. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-README.txt | [blind-copy-2] Matching excerpt: "Why it exists: the two checkers that accepted this certificate before, `udcheck.py` and `udcheck398.py`, are one implementation (`udcheck398.py` executes `udcheck.py`'s pinned bytes). This one shares no code with them. It uses the standard library only, with [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Recorded G4: 1,920/1,920 chosen copies passed. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [replay-copy-1] Matching excerpt: "- **G4, the independent replay** (`enum2/replay-398.py` with `enum2.py`, sharing no code with `udenum` but using the same nauty release for canonical labelling and automorphism orbits, so a defect there would reach both; `2c81ae65` and `d967fc90` in every [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | A seeded sample of 2,237,909 parents led to 3,576,629 child comparisons, with 0 mismatches. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [replay-copy-2] Matching excerpt: "- **G4, the independent replay** (`enum2/replay-398.py` with `enum2.py`, sharing no code with `udenum` but using the same nauty release for canonical labelling and automorphism orbits, so a defect there would reach both; `2c81ae65` and `d967fc90` in every [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | This was a sample, not a second exhaustive enumeration. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [replay-copy-3] Matching excerpt: "- **G4, the independent replay** (`enum2/replay-398.py` with `enum2.py`, sharing no code with `udenum` but using the same nauty release for canonical labelling and automorphism orbits, so a defect there would reach both; `2c81ae65` and `d967fc90` in every [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Recorded coverage: 1,920 completed slices; 1,955 copies read, from 101 worker labels. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [coverage-copy-1] Matching excerpt: "- The coverage audit (`verify-chain.py --summary-only`, pinned to target (23, 65), seed level 10 and slices (12, 1920) (level, count), requiring g4, hashes; branch `claude/answering-alexeev-u22-g5` at `34f0dcb9ba`): 1955 slice result directories from 101 [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Repeated copies of 35 slices agreed. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [coverage-copy-2] Matching excerpt: "- The coverage audit (`verify-chain.py --summary-only`, pinned to target (23, 65), seed level 10 and slices (12, 1920) (level, count), requiring g4, hashes; branch `claude/answering-alexeev-u22-g5` at `34f0dcb9ba`): 1955 slice result directories from 101 [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Recorded G5 review: round 26 CLOSED. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/G5-round26.txt | [g5-copy-1] Matching excerpt: "G5 round 26: CLOSED" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | Earlier review found that summaries could not close a gap in deleted intermediate keep files. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt | [g5-copy-2] Matching excerpt: "GPT's point 6 (item 6 of `research/unit-distance-23/results/g5-cross-model-2026-09-26/G5-closure-read-gpt-6-astra.md`: "FATAL for the proposed final certification , The retained artifacts cannot close the intermediate keep-file gap."): once intermediate files [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | The response was a full re-run, with each slice's files retained until its chain was checked. | git show 5a634e5551:research/the-sixty-fifth-distance/data/RESULT-u23.txt:140 ; git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/verify-all.txt | [g5-copy-3] N1's copied excerpt instead describes "VERIFY-SAMPLE OK: 63 of 63 planned slices verified", which alone does not support "full re-run". The same source's line 140 says "every one of the 1,920 slices re-run with nothing deleted and checked the same way" and quotes "VERIFY-ALL OK: 1920 of 1920 slices re-run and verified". The observation is supported after reading that omitted passage. - CONFIRMED | This settles the fixed 23-point case, not the growth rate. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [finite-result-scope] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The asymptotic lower side changed in May 2026, with constructions exceeding n^1.014 for arbitrarily large n | https://arxiv.org/abs/2605.20579v1 | [may-explicit-growth] Matching excerpt: "We show that there are sets of $n$ points in the plane with $n$ arbitrarily large that contain more than $n^{1.014}$ pairs of points separated by a distance exactly $1$." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | this result improves neither that lower bound nor the O(n^(4/3)) upper bound dating from 1984. | https://arxiv.org/html/2605.20695v1 | [does-not-improve-asymptotics] Matching excerpt: "Let U ⁡ ( n ) U(n) denote the maximum possible number of unit distances determined by n n points in the Euclidean plane. Erdős proved that U ⁡ ( n ) ≥ n 1 + Ω ⁡ ( 1 / log ⁡ log ​ n ) U(n)\geq n^{1+\Omega(1/\log\log n)} , and the best known upper bound is U ⁡ [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The archived table and explanation are available below. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-10-0] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The exact point, subgraph and proof checks require JavaScript. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-10-1] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Most of its lines disappear immediately. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-13-1] Matching excerpt: "const keyDeltas={ArrowRight:[1n,0n],ArrowLeft:[-1n,0n],ArrowUp:[-1n,2n],ArrowDown:[1n,-2n]}; function move(key,i=selected){selected=i;const[a,b]=keyDeltas[key];points[i][0]+=a;points[i][1]+=b;clearLandings();updatePoints();} function [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Return it, and the exact distances return with it. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-13-2] Matching excerpt: "const keyDeltas={ArrowRight:[1n,0n],ArrowLeft:[-1n,0n],ArrowUp:[-1n,2n],ArrowDown:[1n,-2n]}; function move(key,i=selected){selected=i;const[a,b]=keyDeltas[key];points[i][0]+=a;points[i][1]+=b;clearLandings();updatePoints();} function [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Subtract two coordinate vectors and expand the squared modulus. | https://arxiv.org/html/2406.15317v3 | [prose-19-0] Matching excerpt: "= ( a 2 + a ​ b + 5 3 ​ a ​ c + 5 6 ​ a ​ d + b 2 + 5 6 ​ b ​ c + 5 3 ​ b ​ d + c 2 + c ​ d + d 2 ) + ( b ​ c − a ​ d ) ​ 33 6 . [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Independence of the rational part and the square-root part makes the equality test exact. | https://arxiv.org/html/2406.15317v3 | [prose-19-1] Matching excerpt: "= ( a 2 + a ​ b + 5 3 ​ a ​ c + 5 6 ​ a ​ d + b 2 + 5 6 ​ b ​ c + 5 3 ​ b ​ d + c 2 + c ​ d + d 2 ) + ( b ​ c − a ​ d ) ​ 33 6 . [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The basis and the complete integer unit-direction list are in Engel et al., the Moser lattice section . | https://arxiv.org/html/2406.15317v3 | [prose-22-0] Matching excerpt: "Theorem 2.5 . In the Moser lattice, there are 18 unit vectors in total." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The rest of the drawing stays fixed. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [prose-24-0] Matching excerpt: "export function landings(points,moving,anchor) { if(moving===anchor) throw new Error('Choose different points.'); return unitDirections().map(direction=> { const p=points.map(x=>x.slice()); p[moving]=points[anchor].map((x,i)=>x+direction[i]*denominator); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Changing this assumption changes the question. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-33-0] Matching excerpt: "function updateDependency(){const p=Number($('previous-bound').value),bound=schade(points.length,p);$('dependency-status').textContent=`With u(${points.length-1}) = ${p}${p===dependency.upper.at(-1)?' (the result used)':' (hypothetical)'}, the bound is [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The published result uses the preceding value; this control supplies no proof of a different input. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-33-1] Matching excerpt: "function updateDependency(){const p=Number($('previous-bound').value),bound=schade(points.length,p);$('dependency-status').textContent=`With u(${points.length-1}) = ${p}${p===dependency.upper.at(-1)?' (the result used)':' (hypothetical)'}, the bound is [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Each chip is an allowed edge count with its minimum-degree threshold. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [prose-35-0] Matching excerpt: "export function reach(upper,N,M,K,seed=10){ const levels={[N]:{[M]:K}}; for(let n=N-1;n>=seed;n--){const out={};for(const[mText,k]of Object.entries(levels[n+1])){ const mNext=Number(mText),maxD=Math.min(n,Math.floor(2*mNext/(n+1))); for(let [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Work backward through every possible minimum-degree deletion, keeping the weakest threshold if paths meet. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [prose-35-1] Matching excerpt: "export function reach(upper,N,M,K,seed=10){ const levels={[N]:{[M]:K}}; for(let n=N-1;n>=seed;n--){const out={};for(const[mText,k]of Object.entries(levels[n+1])){ const mNext=Number(mText),maxD=Math.min(n,Math.floor(2*mNext/(n+1))); for(let [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | For an ordinary unit-distance graph, a pair not listed as an edge may still be a unit distance. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-36-0] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | That is allowed. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-36-1] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Here the target already reaches the averaging upper bound, so its graph must list every unit pair. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-36-2] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Its ancestors are induced subgraphs: they inherit both edges and the absence of edges. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-36-3] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | If an ancestor forces a missing pair to have unit length, the final drawing would have an extra pair beyond the bound. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-36-4] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | That is the hereditary TU argument. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-37-0] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | It would be unsound to discard an arbitrary graph just because it has an unlisted unit pair. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-37-1] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Unknown verdicts were kept throughout the filter-only run. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-37-2] Matching excerpt: "- **Hereditarily free of TU gadgets and of the rhombus and triangle contradictions.** If an induced subgraph of G forces a unit distance on a non-edge (a TU gadget, L2; or the 4-cycle rows of Lemma R and the triangle rotations of Lemma T), then G has a 66th [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The browser checks the arithmetic of these records, not the graph generation that produced them. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [prose-40-0] Matching excerpt: "export function sumRun(run){ const levels=new Map(); for(const c of run.cells){ need(c.children===c.kept+c.pruned+c.reach_dropped,'Cell partition fails'); need(c.pruned===Object.values(c.pruned_by_kind).reduce((a,b)=>a+b,0),'Prune partition fails'); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Bars show kept graphs. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-41-0] Matching excerpt: "function updateBars(){const log=$('bar-scale').value==='log',max=Math.max(...run.rows.map(r=>r.kept));$('funnel-bars').replaceChildren(...run.rows.map(r=>{const row=document.createElement('div');row.className='bar-row';const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | A logarithmic scale makes the small tail visible; the linear option shows the change in absolute size. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-41-1] Matching excerpt: "function updateBars(){const log=$('bar-scale').value==='log',max=Math.max(...run.rows.map(r=>r.kept));$('funnel-bars').replaceChildren(...run.rows.map(r=>{const row=document.createElement('div');row.className='bar-row';const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Neither scale changes the counts. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-41-2] Matching excerpt: "function updateBars(){const log=$('bar-scale').value==='log',max=Math.max(...run.rows.map(r=>r.kept));$('funnel-bars').replaceChildren(...run.rows.map(r=>{const row=document.createElement('div');row.className='bar-row';const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Children here are canonical augmentations that already pass the edge window and forbidden-subgraph filters. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [prose-42-0] Matching excerpt: "export function sumRun(run){ const levels=new Map(); for(const c of run.cells){ need(c.children===c.kept+c.pruned+c.reach_dropped,'Cell partition fails'); need(c.pruned===Object.values(c.pruned_by_kind).reduce((a,b)=>a+b,0),'Prune partition fails'); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Pruned is the sum of the remaining TU and refutation columns; there are no other prune verdicts in this table. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [prose-42-1] Matching excerpt: "export function sumRun(run){ const levels=new Map(); for(const c of run.cells){ need(c.children===c.kept+c.pruned+c.reach_dropped,'Cell partition fails'); need(c.pruned===Object.values(c.pruned_by_kind).reduce((a,b)=>a+b,0),'Prune partition fails'); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | These are graph counts, not counts of embeddings. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [prose-42-2] Matching excerpt: "export function sumRun(run){ const levels=new Map(); for(const c of run.cells){ need(c.children===c.kept+c.pruned+c.reach_dropped,'Cell partition fails'); need(c.pruned===Object.values(c.pruned_by_kind).reduce((a,b)=>a+b,0),'Prune partition fails'); [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Gold, orange and blue mark edges chosen by the current instrument. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs | [prose-47-0] Matching excerpt: "export function graphView(svg,g,xy,highlights=[],vertices=[]){" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | A proof move's directions and order appear in its equations. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs | [prose-47-1] Matching excerpt: "export function graphView(svg,g,xy,highlights=[],vertices=[]){" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The search asks for an injective map preserving every pattern edge. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [prose-48-0] Matching excerpt: "export function checkMapping(pattern,host,map) { return Array.isArray(map)&&map.length===pattern.n&&new Set(map).size===map.length&&map.every(v=>Number.isInteger(v)&&v>=0&&vhost.adj[map[u]][map[v]]); }" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | It permits extra edges. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [prose-48-1] Matching excerpt: "export function checkMapping(pattern,host,map) { return Array.isArray(map)&&map.length===pattern.n&&new Set(map).size===map.length&&map.every(v=>Number.isInteger(v)&&v>=0&&vhost.adj[map[u]][map[v]]); }" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Each split covers both orientations. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [prose-51-0] Matching excerpt: "keys(m,['kind','edges','coefficients','d'],path+'.move');const p=pairs(m,3,path); need(Array.isArray(m.coefficients)&&m.coefficients.length===3,`${path}: invalid coefficients`);const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Every branch ends at an impossible edge length. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [prose-51-1] Matching excerpt: "keys(m,['kind','edges','coefficients','d'],path+'.move');const p=pairs(m,3,path); need(Array.isArray(m.coefficients)&&m.coefficients.length===3,`${path}: invalid coefficients`);const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | All three edges must be present, all three coefficients must be nonzero, and the starting relation must follow from the current row space. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [prose-53-0] Matching excerpt: "keys(m,['kind','edges','coefficients','d'],path+'.move');const p=pairs(m,3,path); need(Array.isArray(m.coefficients)&&m.coefficients.length===3,`${path}: invalid coefficients`);const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Each child must equal precisely the parent constraints plus its specified orientation row. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [prose-53-1] Matching excerpt: "keys(m,['kind','edges','coefficients','d'],path+'.move');const p=pairs(m,3,path); need(Array.isArray(m.coefficients)&&m.coefficients.length===3,`${path}: invalid coefficients`);const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The root is reconstructed from every graph rhombus. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-PROOFS.txt | [prose-57-0] Matching excerpt: "Every 3-cycle is an equilateral triangle. Its three sides have length one, so the cosine rule gives an angle of \(\pi/3\) at every vertex. Every 4-cycle is a rhombus, including the conclusion needed here that its diagonals have a common midpoint. Thus, for a [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - WRONG | For distinct points, a cycle of unit edges has coincident diagonal midpoints. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-PROOFS.txt ; public/strata/the-sixty-fifth-distance/app.mjs | [X2; prose-57-1] blind-PROOFS.txt:12-27 says every 4-cycle is a rhombus and derives p_a-p_b+p_c-p_d=0 for distinct vertices. A regular unit pentagon refutes the unrestricted cycle claim; a square is the positive control. The sentence now specifies a 4-cycle of unit edges (a rhombus). The actual checker already enumerated four-cycles, so this repairs prose and its coverage rather than its arithmetic. - CONFIRMED | A triangle supplies the equilateral alternatives used by the first splits. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-PROOFS.txt | [prose-57-2] Matching excerpt: "Every 3-cycle is an equilateral triangle. Its three sides have length one, so the cosine rule gives an angle of \(\pi/3\) at every vertex. Every 4-cycle is a rhombus, including the conclusion needed here that its diagonals have a common midpoint. Thus, for a [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Later splits use weighted edge relations; no guessed coordinates enter the refutation. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-PROOFS.txt | [prose-57-3] Matching excerpt: "Every 3-cycle is an equilateral triangle. Its three sides have length one, so the cosine rule gives an angle of \(\pi/3\) at every vertex. Every 4-cycle is a rhombus, including the conclusion needed here that its diagonals have a common midpoint. Thus, for a [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The browser checker supports only the split and nonunit-multiplier rules used here, and rejects other move kinds. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [prose-58-0] Matching excerpt: "const m=t.move;need(m&&['L3','L1b'].includes(m.kind),`${path}: unsupported rule`); need(Array.isArray(t.children)&&t.children.length===(m.kind==='L3'?2:0),`${path}: wrong child count`);" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | An acceptance is useful only if a nearby falsehood is rejected. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [prose-59-0] Matching excerpt: "}else if(kind==='tamper'){ const list=[...proofMutations(),['graph edge removed',()=>{}]];const cases=input.case==='all'?list:list.filter(([name])=>name===input.case); result=cases.map(([name,change])=>{ const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | These changes are made to fresh copies of the real certificate or graph. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [prose-59-1] Matching excerpt: "}else if(kind==='tamper'){ const list=[...proofMutations(),['graph edge removed',()=>{}]];const cases=input.case==='all'?list:list.filter(([name])=>name===input.case); result=cases.map(([name,change])=>{ const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | This is the project's computer-assisted result, not yet refereed outside the project. | git show 5a634e5551:research/the-sixty-fifth-distance/README.md | [prose-61-0] Matching excerpt: "This is the reproducibility packet for the standalone u(23) page. The browser checks the 23-point drawing in exact arithmetic, searches the frozen forbidden list when requested, and verifies the whole survivor certificate. Its enumeration funnel and large-run [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The independently implemented checks are still ours. | git show 5a634e5551:research/the-sixty-fifth-distance/README.md | [prose-61-1] Matching excerpt: "This is the reproducibility packet for the standalone u(23) page. The browser checks the 23-point drawing in exact arithmetic, searches the frozen forbidden list when requested, and verifies the whole survivor certificate. Its enumeration funnel and large-run [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The point count is live and changes when you move a point. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-63-0] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The proof check covers the whole supplied tree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-63-1] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The optional subgraph search really searches the frozen list. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-63-2] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | None repeats the archived exhaustive enumeration. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [prose-63-3] Matching excerpt: "async function start(){ [cfg,dependency,g6,certificate]=await Promise.all([json('configuration.json'),json('dependencies.json'),text('candidate.g6'),json('certificate.json')]); const [rawRun,recordedEvidence,...logs]=await [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The Python checker uses standard-library fractions and polynomial arithmetic. | git show 5a634e5551:research/the-sixty-fifth-distance/data/blind-REPORT.txt | [prose-71-0] Matching excerpt: "The only pre-existing project files consulted were `spec/FORMAT.md`, `spec/PROOFS.md`, `data/23-65.g6`, and `data/23-65.certs.jsonl`. No reference checker, prover, external project file, website, or third-party Python package was consulted. The verifier uses [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The browser's implementation was written for this page; it is not that archived blind program. | git show 5a634e5551:research/the-sixty-fifth-distance/README.md | [prose-71-1] Matching excerpt: "The verifier never regenerates or rewrites data. It recomputes all 253 squared distances by directly multiplying in the basis `[1, sqrt(3), sqrt(11), sqrt(33)]`, independently of the browser's expanded formula. It independently decodes graph6, enumerates [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The cell extract cannot prove that the graph generator omitted nothing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-73-0] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Exhaustiveness rests on the canonical augmentation argument, the enumeration and pruning implementations, and their archived checks. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-73-1] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The reproduction sample shares nauty with the production enumerator. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-73-2] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - OBSERVED | Its sampled parent indices were not retained. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-73-3] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | The large intermediate files and pruning certificates were replayed before deletion; they are not bundled into this page. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-74-0] Matching excerpt: "- **The six heavy slices.** Six slices (s50, s1082, s1535, s1651, s1721, s1814) outgrew the machines' 15 GB in that check, so a memory-bounded copy of the checker checked them. It is the reviewed checker with four marked streaming edits, which change how [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | They can be regenerated from the research procedure. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-74-1] Matching excerpt: "- **The six heavy slices.** Six slices (s50, s1082, s1535, s1651, s1721, s1814) outgrew the machines' 15 GB in that check, so a memory-bounded copy of the checker checked them. It is the reviewed checker with four marked streaming edits, which change how [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | The largest slices needed a streaming checker. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-74-2] Matching excerpt: "- **The six heavy slices.** Six slices (s50, s1082, s1535, s1651, s1721, s1814) outgrew the machines' 15 GB in that check, so a memory-bounded copy of the checker checked them. It is the reviewed checker with four marked streaming edits, which change how [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - OBSERVED | A partitioned diagnostic did not finish every dense piece with the unchanged in-memory checker; those slices are covered by the streaming whole-slice check, not by a claim that the diagnostic completed. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-74-3] Matching excerpt: "- **The six heavy slices.** Six slices (s50, s1082, s1535, s1651, s1721, s1814) outgrew the machines' 15 GB in that check, so a memory-bounded copy of the checker checked them. It is the reviewed checker with four marked streaming edits, which change how [...]" Recorded project event, retained as an observation; no new exhaustive fleet run was attempted. - CONFIRMED | Both exact certificate programs use the same written geometric implications. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-75-0] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | An error in a lemma could pass both. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-75-1] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The compiler, interpreters, machine arithmetic and source-to-output history remain part of the computation's trust chain. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-75-2] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The full re-run reduces reliance on the original worker artifacts; it does not formally verify the software. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [prose-75-3] Matching excerpt: "## 6. What is trusted - The platform: the compilers and interpreters, and nauty 2.8.8's canonical labelling and automorphism groups (both enumerators use it). - Our implementations of the enumerator (`udenum`), the driver (`run-dag2.py`) and the prune step. [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - MINOR | The free display choices are a deterministic graph layout, an optional logarithmic bar scale, and the rounded dragging grid. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs ; git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs ; git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [X3; prose-76-0] All three page clauses are true. graphLayout in draw.mjs:23-35 has deterministic initialization and fixed iterations; updateBars in app.mjs:53 switches between linear and logarithmic widths; snappedDelta in lattice.mjs:28-31 rounds the dragging grid. The source record now supplies all three excerpts and file locators. Counted as a confirmed MINOR source-record repair. - CONFIRMED | Graph-layout lengths and all decimals are illustrative. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs | [prose-76-1] Matching excerpt: "export function graphLayout(g){ const xy=Array.from({length:g.n},(_,i)=>[360+205*Math.cos(2*Math.PI*i/g.n),260+205*Math.sin(2*Math.PI*i/g.n)]); for(let t=0;t<280;t++){ const force=xy.map(()=>[0,0]); for(let i=0;iimport(pathToFileURL(path.join(pub,name)).href+'?verification='+Date.now());" Read against the full pinned source or fetched primary document; its scope supports the claim. - OBSERVED | Not yet put to that test. | git show 5a634e5551:scripts/check-placard.mjs:142 ; git show 5a634e5551:research/verifier-independence/verdicts.mjs ; git show 5a634e5551:research/verifier-independence/mutation-results.json | [prose-80-1] This is about the corpus sweep, not the slug's own mutation suite. The placard generator says "No dependence run yet" and returns "Not yet put to that test." A pinned scan of all 21 mutation/depends JSON files finds 0 rows for this slug; the identical slug search finds 4 for the preceding layer, the-sixty-first-distance. N1's baseline transcript "PASS 19 verification groups; 0 failures." does not establish that scope. The page's 255-case local mutation suite is a different test, so it is not evidence against this observation. - OBSERVED | Last verified 8 October 2026, when it was written. | git show 5a634e5551:research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt ; git log 5a634e5551 -- research/the-sixty-fifth-distance/the-sixty-fifth-distance-verifier-results.txt | [prose-81-0] The recorded run says "PASS 19 verification groups; 0 failures." Its pinned history and frontmatter are dated 2026-10-08. Recreated in scratch with the same 19 groups and 0 failures; a later replay does not contradict the stated earlier date. - CONFIRMED | Green lines are current unit pairs; faint dashed lines are lost pairs from the starting drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs | [drawing-caption-0] Matching excerpt: "export function pointView(svg,points,edges,original,selected,choose,drag,key){ const xy=points.map(p=>coordinates(p)); // Keep the camera fixed while dragging; a moving camera could hide the move. const scale=144,origin=[85,430]; const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Crossings do not create extra points. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs | [drawing-caption-1] Matching excerpt: "export function pointView(svg,points,edges,original,selected,choose,drag,key){ const xy=points.map(p=>coordinates(p)); // Keep the camera fixed while dragging; a moving camera could hide the move. const scale=144,origin=[85,430]; const [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Screen drawings are approximations. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [footer-0] Matching excerpt: "export function squared(v, D = denominator) { const [a,b,c,d] = v.map(BigInt); return { R: 6n*(a*a+a*b+b*b+c*c+c*d+d*d)+10n*a*c+5n*a*d+5n*b*c+10n*b*d, S: b*c-a*d, Q: 6n*D*D }; } export const difference = (a,b) => a.map((x,i) => x-b[i]); export const isUnit = [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Equality checks are exact. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [footer-1] Matching excerpt: "export function squared(v, D = denominator) { const [a,b,c,d] = v.map(BigInt); return { R: 6n*(a*a+a*b+b*b+c*c+c*d+d*d)+10n*a*c+5n*a*d+5n*b*c+10n*b*d, S: b*c-a*d, Q: 6n*D*D }; } export const difference = (a,b) => a.map((x,i) => x-b[i]); export const isUnit = [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | 13 23…30 17,770,330 14,227,296 3,543,034 2,649,736 877,724 15,574 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-13] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 14 26…33 149,368,305 111,094,819 38,273,486 26,673,717 11,240,806 358,963 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-14] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 15 29…37 842,594,946 492,690,622 349,904,324 214,552,374 127,976,366 7,375,584 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-15] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 16 33…41 1,058,712,809 580,930,642 477,782,167 251,563,636 211,707,116 14,511,415 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-16] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 17 37…43 430,213,696 213,648,700 216,564,996 106,789,432 101,641,378 8,134,186 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-17] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 18 41…46 148,671,082 69,977,653 78,693,429 40,355,890 35,233,396 3,104,143 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-18] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 19 45…50 11,975,593 4,368,436 7,607,157 3,456,001 3,738,733 412,423 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-19] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 20 50…53 154,347 75,745 78,602 38,816 35,515 4,271 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-20] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 21 55…56 2,026 1,320 706 360 308 38 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-21] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 22 60 30 29 1 0 0 1 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-22] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | 23 65 1 1 0 0 0 0 | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [funnel-row-23] All eight printed cells match the independently summed frozen cell rows; children = kept + pruned, and pruned = TU + triangle TU + triangle refuted. - CONFIRMED | The preceding value supplies the 60-edge bound after deleting a point. | git show 5a634e5551:src/content/strata/the-sixty-first-distance.md | [related-0-0] Matching excerpt: "dek: "Erdős asked in 1946 how many pairs among n points in the plane can be exactly one unit apart, and the exact answers are known only for tiny n. Alexeev, Mixon and Parshall took them to 21 points in 2024 and proved that 22 points allow at most 61 unit [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Its page lets you operate the same averaging step and the earlier enumeration. | git show 5a634e5551:src/content/strata/the-sixty-first-distance.md | [related-0-1] Matching excerpt: "dek: "Erdős asked in 1946 how many pairs among n points in the plane can be exactly one unit apart, and the exact answers are known only for tiny n. Alexeev, Mixon and Parshall took them to 21 points in 2024 and proved that 22 points allow at most 61 unit [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The 398 small obstructions prune this search. | git show 5a634e5551:src/content/strata/every-edge-but-one.md | [related-1-0] Matching excerpt: "dek: "Some graphs cannot be drawn with every edge exactly one unit long, and the smallest of them, the minimal forbidden graphs, sit inside every graph that cannot. Globus and Parshall found all 74 with at most nine vertices in 2019; here are the 324 on ten, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | That page gives them drawings with every edge at unit length except one; this survivor avoids the whole list and still fails. | git show 5a634e5551:src/content/strata/every-edge-but-one.md | [related-1-1] Matching excerpt: "dek: "Some graphs cannot be drawn with every edge exactly one unit long, and the smallest of them, the minimal forbidden graphs, sit inside every graph that cannot. Globus and Parshall found all 74 with at most nine vertices in 2019; here are the 324 on ten, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The Moser spindle turns unit distances into a colouring obstruction. | https://arxiv.org/html/1804.02385 | [related-2-0] Matching excerpt: "The lower bound was also noted by Nelson (see [Soi]) and arises because there exist 4-chromatic finite graphs that can be drawn in the plane with each edge being a straight line of unit length, the smallest of which is the 7-vertex Moser spindle [MM] (see [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Here the question is how many unit pairs a configuration can have, and which abstract graphs admit any such drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [related-2-1] Matching excerpt: "**Theorem.** No unit-distance graph on 23 vertices has 65 edges. Hence u(23) = 64." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The next deletion bound takes this result as its input. | git show 5a634e5551:src/content/strata/the-sixty-ninth-distance.md | [related-3-0] Matching excerpt: "dek: "Among 24 distinct points in the plane, the maximum number of unit pairs is 68. A known arrangement attains it; the Artificial Wasteland's exhaustive graph enumeration left one 69-edge survivor, excluded by a contained eleven-vertex graph and an exact [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | That page excludes its survivor by finding one certified smaller obstruction; here you can walk the whole survivor's proof tree. | git show 5a634e5551:src/content/strata/the-sixty-ninth-distance.md | [related-3-1] Matching excerpt: "dek: "Among 24 distinct points in the plane, the maximum number of unit pairs is 68. A known arrangement attains it; the Artificial Wasteland's exhaustive graph enumeration left one 69-edge survivor, excluded by a contained eleven-vertex graph and an exact [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The larger catalogue extends the forbidden filter to another order. | git show 5a634e5551:src/content/strata/every-edge-but-one-at-eleven.md | [related-4-0] Matching excerpt: "dek: "Some small graphs cannot be drawn with every edge exactly one unit long. Globus and Parshall classified the 74 minimal forbidden graphs on at most nine vertices; the Artificial Wasteland added 324 on ten and now 2,833 on eleven. Together these 3,231 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Its edge-deletion drawings expose why a small obstruction is minimal; here the older catalogue leaves a survivor requiring a separate geometric contradiction. | git show 5a634e5551:src/content/strata/every-edge-but-one-at-eleven.md | [related-4-1] Matching excerpt: "dek: "Some small graphs cannot be drawn with every edge exactly one unit long. Globus and Parshall classified the 74 minimal forbidden graphs on at most nine vertices; the Artificial Wasteland added 324 on ten and now 2,833 on eleven. Together these 3,231 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Alexeev, Mixon and Parshall | https://arxiv.org/abs/2412.11914v1 | [citation-external-1] Matching excerpt: "Authors: Boris Alexeev , Dustin G. Mixon , Hans Parshall" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The preceding value | git show 5a634e5551:src/content/strata/the-sixty-first-distance.md | [citation-related-2] Matching excerpt: "title: "The Sixty-First Distance"" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The next value | git show 5a634e5551:src/content/strata/the-sixty-ninth-distance.md | [citation-related-3] Matching excerpt: "title: "The Sixty-Ninth Distance"" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The disproof of Erdős's conjecture | https://arxiv.org/abs/2605.20695v1 | [citation-external-4] Matching excerpt: "Title: Remarks on the disproof of the unit distance conjecture" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Sawin's explicit lower bound | https://arxiv.org/abs/2605.20579v1 | [citation-external-5] Matching excerpt: "Title: An explicit lower bound for the unit distance problem" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The opening account at the preceding value | git show 5a634e5551:src/content/strata/the-sixty-first-distance.md | [citation-related-6] Matching excerpt: "title: "The Sixty-First Distance"" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Engel et al. | https://arxiv.org/abs/2406.15317v3 | [citation-external-7] Matching excerpt: "Authors: Peter Engel , Owen Hammond-Lee , Yiheng Su , Dániel Varga , Pál Zsámboki" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Frozen coordinates | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/configuration.json | [citation-local-8] Matching excerpt: "{ "n": 23, "claimedEdges": 64, "lattice": [ [ 0, 0, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 1, 0 ], [ 2, 0, 1, 0 ], [ 0, 1, 1, 0 ], [ 1, 1, 1, 0 ], [ 1, 0, 2, 0 ], [ 2, 0, 2, 0 ], [ 0, 1, 2, 0 ], [ 1, 1, 2, 0 ], [ 0, 0, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Engel et al., the Moser lattice section | https://arxiv.org/html/2406.15317v3 | [citation-external-9] Matching excerpt: "Theorem 2.5 . In the Moser lattice, there are 18 unit vectors in total." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Read the arithmetic | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [citation-local-10] Matching excerpt: "// Exact coordinates in Q(1, w1, w3, w1*w3). Pixels never decide an edge." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Alexeev, Mixon and Parshall, Schade's lemma | https://arxiv.org/html/2412.11914v2 | [citation-external-11] Matching excerpt: "Lemma 2 . A simple graph with n ≥ 1 n\geq 1 vertices and m m edges contains an induced subgraph with n − 1 n-1 vertices and at least ⌈ m ⋅ n − 2 n ⌉ \lceil m\cdot\frac{n-2}{n}\rceil edges." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Our preceding value | git show 5a634e5551:src/content/strata/the-sixty-first-distance.md | [citation-related-12] Matching excerpt: "title: "The Sixty-First Distance"" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Written lemmas and trust chain | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [citation-local-13] Matching excerpt: "# u(23) = 64: the argument, the evidence, and how to check it A reader's guide, written 2026-09-28 by the u(23) session (claude-answering-alexeev-u22) with codex (`gpt-6-astra`) as reviewer and collaborator. It is the entry point to everything else in this [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | AMP's linear-relation method | https://arxiv.org/html/2412.11914v2 | [citation-external-14] Matching excerpt: "Lemma 4 . Given a , b , c , x , y , z ∈ ℂ a,b,c,x,y,z\in\mathbb{C} such that a ​ x + b ​ y + c ​ z = 0 ax+by+cz=0 , | x | = 1 |x|=1 , | y | = 1 |y|=1 , and | z | = 1 |z|=1 , then ( x , y ) (x,y) necessarily satisfies ( | a | 2 + | b | 2 − | c | 2 + d ​ i ) ​ [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Cell and slice extract | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [citation-local-15] Matching excerpt: "{ "target": [ 23, 65 ], "sliceLevel": 12, "seed": 10, "rootK": 5, "reachLevels": { "10": [ 14, 15, 16, 17, 18, 19, 20 ], "11": [ 17, 18, 19, 20, 21, 22, 23 ], "12": [ 20, 21, 22, 23, 24, 25, 26, 27 ], "13": [ 23, 24, 25, 26, 27, 28, 29, 30 ], "14": [ 26, 27, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Original aggregate | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/aggregate.json | [citation-local-16] Matching excerpt: "{ "tool": "research/unit-distance-23/tools/aggregate_fleet.py", "tool_sha256": "4691dd2c0f4615e623dfbd8e85d2afe6942c352e901d414b74be38cdafde0865", "root": "/tmp/claude-1000/-home-liam/3f41b13a-dbc3-441e-923b-ef64a74a4856/scratchpad/fleet/results", [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Labelled graph | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/candidate.g6 | [citation-local-17] Matching excerpt: "V?_QPIGD@AGOoHKE_o?Q??HK?WqH@PO_m@CWCaHN_?F_" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Complete certificate | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [citation-local-18] Matching excerpt: "{ "g6": "V?_QPIGD@AGOoHKE_o?Q??HK?WqH@PO_m@CWCaHN_?F_", "verdict": "refuted", "witness": { "field": { "interval": [ "13436/4735", "62183/21914" ], "minpoly": [ 256, 0, -684, 0, 81 ] }, "tree": { "A": [ [ [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Proof checker | git show 5a634e5551:public/strata/the-sixty-fifth-distance/proof.mjs | [citation-local-19] Matching excerpt: "// A finite checker, not an embedding search. Supports only this tree's L3/L1b rules." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Exact field arithmetic | git show 5a634e5551:public/strata/the-sixty-fifth-distance/field.mjs | [citation-local-20] Matching excerpt: "// BigInt fractions, polynomial arithmetic, Sturm isolation and exact row spaces." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | AMP's Heron rule | https://arxiv.org/html/2412.11914v2 | [citation-external-21] Matching excerpt: "Lemma 4 . Given a , b , c , x , y , z ∈ ℂ a,b,c,x,y,z\in\mathbb{C} such that a ​ x + b ​ y + c ​ z = 0 ax+by+cz=0 , | x | = 1 |x|=1 , | y | = 1 |y|=1 , and | z | = 1 |z|=1 , then ( x , y ) (x,y) necessarily satisfies ( | a | 2 + | b | 2 − | c | 2 + d ​ i ) ​ [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | VERIFY-ALL row log | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/verify-all.txt | [citation-local-22] Matching excerpt: "s955 a01 all: whole, CHAIN OK, certificates replayed in 69 pruned cells; result files identical to the fleet's copy (f92-kd4uz5); files checked = copy's (digest) s344 a01 all: from level 13, CHAIN PARTIAL (levels below 13 not inspected (--from-n 13)), [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Empty-tree control | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/control22-check.txt | [citation-local-23] Matching excerpt: "parameters: target (22,61), root minimum degree 5, u-bar override refused, top level empty, known none; checker target_check.py sha256 1716d48763cc2e908fb99f0402432800702182ee3dbc4ddc3e80cedeb3505e2d; audit verify-chain.py sha256 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Calibration | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/calib2157-check.txt | [citation-local-24] Matching excerpt: "parameters: target (21,57), root minimum degree 3, u-bar override the fleet 22=60 only, top level holding the known graphs, known engel-21-57.g6 sha256 06f0d779a598292e6be4e2758097d7e0a1c2364fc348cda7d197751ed2a98aff (5 graphs); checker target_check.py sha256 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Ancestor control | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/level22-control.txt | [citation-local-25] Matching excerpt: "self-test: with Engel graph 1's form removed from the union, missing = [1] self-test: Engel graph 0 with the pair (0,1) flipped is not found self-test: Engel graph 1 also placed in a second slice is reported Engel file: [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Per-slice replay records | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/aggregate.json | [citation-local-26] Matching excerpt: "{ "tool": "research/unit-distance-23/tools/aggregate_fleet.py", "tool_sha256": "4691dd2c0f4615e623dfbd8e85d2afe6942c352e901d414b74be38cdafde0865", "root": "/tmp/claude-1000/-home-liam/3f41b13a-dbc3-441e-923b-ef64a74a4856/scratchpad/fleet/results", [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Replay scope | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/g4-scope.txt | [citation-local-27] Matching excerpt: "G4-SCOPE COPIES (23,65): 1955 copies, sha256 15fdb9599e746e6751af9da2bd4df01390ff44fbe83c6977ee377ddea665a946 G4-SCOPE OK: 101 of 101 full-mode replays and 1854 of 1854 slice-mode replays in their mode's scope; 0 problem(s)" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Acceptance and rejection log | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/blind-check.txt | [citation-local-28] Matching excerpt: "verifier: research/unit-distance-23/blind-verifier/verify_tree.py sha256 1bafc054ee736f4c7275a7ccb0a747bd2839ce7fefc3b5e04858265d1b015f67 s50of1920/23-65.g6 graph 0 V?_QPIGD@AGOoHKE_o?Q??HK?WqH@PO_m@CWCaHN_?F_ certs [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Earlier acceptance lines | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/top-level-check.txt | [citation-local-29] Matching excerpt: "s50: 1 kept graph(s) in 1 copy; udcheck.py: ACCEPT certificates records=1 forbidden=0 tu=0 embedded=0 refuted=1 unknown=0 proof_nodes=15 s50: 1 kept graph(s) in 1 copy; udcheck398.py: ACCEPT certificates records=1 forbidden=0 tu=0 embedded=0 refuted=1 [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Final review and response | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/G5-round26.txt | [citation-local-30] Matching excerpt: "# G5 round 26: read by gpt-6-astra (codex exec, a fresh session, reasoning max, read-only), 2026-09-29 ## Prompt G5 round 26 (u(23), repository checkout /tmp/claude-1000/-home-liam/3f41b13a-dbc3-441e-923b-ef64a74a4856/scratchpad/g5r26-tree (a detached [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The research account of these limits | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [citation-local-31] Matching excerpt: "# u(23) = 64: the argument, the evidence, and how to check it A reader's guide, written 2026-09-28 by the u(23) session (claude-answering-alexeev-u22) with codex (`gpt-6-astra`) as reviewer and collaborator. It is the entry point to everything else in this [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Sources and terms | git show 5a634e5551:public/strata/the-sixty-fifth-distance/NOTICE.txt | [citation-local-32] Matching excerpt: "The Sixty-Fifth Distance Artificial Wasteland, 2026-10-08 Coordinate data Peter Engel, Owen Hammond-Lee, Yiheng Su, Dániel Varga and Pál Zsámboki, "Diverse beam search to find densest-known planar unit distance graphs", arXiv:2406.15317v3, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The May disproof | https://arxiv.org/abs/2605.20695v1 | [citation-external-33] Matching excerpt: "Title: Remarks on the disproof of the unit distance conjecture" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Sawin's construction | https://arxiv.org/abs/2605.20579v1 | [citation-external-34] Matching excerpt: "Title: An explicit lower bound for the unit distance problem" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The historical upper bound | https://arxiv.org/html/2412.11914v2 | [citation-external-35] Matching excerpt: "A unit-distance graph is a simple graph G G for which there exists an injection f : V ⁡ ( G ) → ℝ 2 f\colon V(G)\to\mathbb{R}^{2} such that { u , v } ∈ E ⁡ ( G ) \{u,v\}\in E(G) implies ‖ f ⁡ ( u ) − f ⁡ ( v ) ‖ = 1 \|f(u)-f(v)\|=1 . Let U ⁡ ( n ) U(n) denote [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Coordinates | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/configuration.json | [citation-local-36] Matching excerpt: "{ "n": 23, "claimedEdges": 64, "lattice": [ [ 0, 0, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 0, 1, 0 ], [ 2, 0, 1, 0 ], [ 0, 1, 1, 0 ], [ 1, 1, 1, 0 ], [ 1, 0, 2, 0 ], [ 2, 0, 2, 0 ], [ 0, 1, 2, 0 ], [ 1, 1, 2, 0 ], [ 0, 0, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Certificate | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [citation-local-37] Matching excerpt: "{ "g6": "V?_QPIGD@AGOoHKE_o?Q??HK?WqH@PO_m@CWCaHN_?F_", "verdict": "refuted", "witness": { "field": { "interval": [ "13436/4735", "62183/21914" ], "minpoly": [ 256, 0, -684, 0, 81 ] }, "tree": { "A": [ [ [ 1 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [ 0 ], [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Run extract | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/run.json | [citation-local-38] Matching excerpt: "{ "target": [ 23, 65 ], "sliceLevel": 12, "seed": 10, "rootK": 5, "reachLevels": { "10": [ 14, 15, 16, 17, 18, 19, 20 ], "11": [ 17, 18, 19, 20, 21, 22, 23 ], "12": [ 20, 21, 22, 23, 24, 25, 26, 27 ], "13": [ 23, 24, 25, 26, 27, 28, 29, 30 ], "14": [ 26, 27, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Credits and terms | git show 5a634e5551:public/strata/the-sixty-fifth-distance/NOTICE.txt | [citation-local-39] Matching excerpt: "The Sixty-Fifth Distance Artificial Wasteland, 2026-10-08 Coordinate data Peter Engel, Owen Hammond-Lee, Yiheng Su, Dániel Varga and Pál Zsámboki, "Diverse beam search to find densest-known planar unit distance graphs", arXiv:2406.15317v3, [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | research/the-sixty-fifth-distance/verify-the-sixty-fifth-distance.mjs | git show 5a634e5551:research/the-sixty-fifth-distance/verify-the-sixty-fifth-distance.mjs | [check-program-reference] Matching excerpt: "// Read-only verification. --quick omits repeated full-list/negative controls only." Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | "datePublished":"2026-10-08" | git show 5a634e5551:src/content/strata/the-sixty-fifth-distance.md | [metadata-datePublished] Matching excerpt: "date: 2026-10-08" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | "dateModified":"2026-10-08" | git show 5a634e5551:src/content/strata/the-sixty-fifth-distance.md | [metadata-dateModified] Matching excerpt: "date: 2026-10-08" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Live drawing: 23 points, 253 pairs tested, 64 unit pairs, 0 collisions. Whole certificate: 15 nodes accepted, 8 leaves refuted. Record arithmetic: 11 levels and 1,920 slice rows checked. Forbidden search: Not yet requested. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [runtime-live-check] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | 253 pairs checked; all points distinct. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [runtime-point-status] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | in the lattice basis. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [runtime-point-coordinates] All 23 displayed coordinate vectors match configuration.json and the actual app, including "Point 0: (0, 0, 0, 0) in the lattice basis." - CONFIRMED | Exactly unit. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [runtime-pair-distances] All 506 recorded ordered-pair readouts match the app and exact squaring, including "|p1 − p0|² = 1 + 0√33. Exactly unit." Both unit and nonunit outputs are exercised. - CONFIRMED | 18 integer unit landings tested. Best with distinct points: 64 unit pairs. This is only this anchor with the other points fixed. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs | [runtime-landings] The complete status and all 18 recorded direction/count/button rows match the actual app for moving 0, anchor 1. The positive baseline attains 64; collision landings have disabled buttons. - CONFIRMED | With u(22) = 60 (the result used), the bound is floor(23 × 60 / 21) = 65. Above the starting drawing, 65 would remain before refutation. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-dependency-60] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | With u(22) = 61 (hypothetical), the bound is floor(23 × 61 / 21) = 66. Above the starting drawing, 65 through 66 would remain before refutation. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-dependency-61] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | With u(22) = 62 (hypothetical), the bound is floor(23 × 62 / 21) = 67. Above the starting drawing, 65 through 67 would remain before refutation. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-dependency-62] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 10: 7 allowed edge counts, all at most u(10) = 20. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-10] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 11: 7 allowed edge counts, all at most u(11) = 23. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-11] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 12: 8 allowed edge counts, all at most u(12) = 27. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-12] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 13: 8 allowed edge counts, all at most u(13) = 30. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-13] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 14: 8 allowed edge counts, all at most u(14) = 33. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-14] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 15: 9 allowed edge counts, all at most u(15) = 37. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-15] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 16: 9 allowed edge counts, all at most u(16) = 41. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-16] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 17: 7 allowed edge counts, all at most u(17) = 43. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-17] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 18: 6 allowed edge counts, all at most u(18) = 46. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-18] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 19: 6 allowed edge counts, all at most u(19) = 50. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-19] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 20: 4 allowed edge counts, all at most u(20) = 54. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-20] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 21: 2 allowed edge counts, all at most u(21) = 57. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-21] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Order 22: 1 allowed edge counts, all at most u(22) = 60. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/records.mjs | [runtime-ancestor-22] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - MINOR | Order 23: 1 allowed edge counts, all at most u(23) = undefined. Each label gives edges / minimum degree. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs ; public/strata/the-sixty-fifth-distance/app.mjs ; public/strata/the-sixty-fifth-distance/data/dependencies.json ; research/the-sixty-fifth-distance/tools/dom-harness.mjs | [X5; runtime-ancestor-23] The pinned updateAncestor indexed upper[23], but dependencies.json has indices 0 through 22 and upper[22]=60. The decoded candidate is the hypothetical (23,65) target, with minimum degree 5. The readout now labels that target without asserting a maximum; all lower orders retain their text. The main verifier now runs the actual app and checks the status and independently derived chips for all 14 selectable orders. Counted as wrong for this MINOR runtime repair. - CONFIRMED | Original survivor | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/candidate.g6 | [runtime-candidate-facts] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | p(α) has ascending coefficients (256, 0, -684, 0, 81); α lies in (13436/4735, 62183/21914). The polynomial is irreducible and this interval contains exactly 1 real root. Display α ≈ 2.837592. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-field] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root Both orientations remain. Current constraint rank: 18. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p8 − p0 z = p8 − p4 (1 + i·(0))·x + (-1 + i·(0))·y + (1 + i·(0))·z = 0 Δ = 3 d = 23/8·α − 9/32·α^3 The weighted relation is in the row space. The checker verifies d² = Δ and checks both child spaces, with +id and −id. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / +d Both orientations remain. Current constraint rank: 19. Every supplied matrix has been checked against the constraints required here. x = p20 − p0 y = p22 − p0 z = p22 − p20 (1 + i·(0))·x + (-1 + i·(0))·y + (1 + i·(0))·z = 0 Δ = 3 d = 23/8·α − 9/32·α^3 The weighted relation is in the row space. The checker verifies d² = Δ and checks both child spaces, with +id and −id. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / +d / +d Both orientations remain. Current constraint rank: 20. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p20 − p0 z = p6 − p4 (1 + i·(0))·x + (-1/2 + i·(-23/16·α + 9/64·α^3))·y + (1/2 + i·(23/48·α − 3/64·α^3))·z = 0 Δ = 11/9 d = -15/8·α + 9/32·α^3 The weighted relation is in the row space. The checker verifies d² = Δ and checks both child spaces, with +id and −id. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.0.0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / +d / +d / +d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p7 − p5 x = ωy ω = (-23/72 + 1/32·α^2) + i·(23/48·α − 3/64·α^3) |ω|² = 35/192 − 3/256·α^2 ≠ 1 Display approximation: 0.087933 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.0.0.0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / +d / +d / −d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p7 − p5 x = ωy ω = (-1/18 − 1/32·α^2) + i·(23/48·α − 3/64·α^3) |ω|² = 1/12 + 3/256·α^2 ≠ 1 Display approximation: 0.177692 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.0.0.1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / +d / −d Both orientations remain. Current constraint rank: 20. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p20 − p0 z = p6 − p4 (1 + i·(0))·x + (-1 + i·(0))·y + (1/2 + i·(23/48·α − 3/64·α^3))·z = 0 Δ = 11/9 d = -15/8·α + 9/32·α^3 The weighted relation is in the row space. The checker verifies d² = Δ and checks both child spaces, with +id and −id. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.0.1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / +d / −d / +d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p13 − p12 x = ωy ω = (7/132 + 3/176·α^2) + i·(149/352·α − 63/1408·α^3) |ω|² = 3/44 ≠ 1 Display approximation: 0.068182 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.0.1.0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / +d / −d / −d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p13 − p12 x = ωy ω = (13/66 − 3/176·α^2) + i·(13/44·α − 9/352·α^3) |ω|² = 3/44 ≠ 1 Display approximation: 0.068182 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.0.1.1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / −d Both orientations remain. Current constraint rank: 19. Every supplied matrix has been checked against the constraints required here. x = p20 − p0 y = p22 − p0 z = p22 − p20 (1 + i·(0))·x + (-1 + i·(0))·y + (1 + i·(0))·z = 0 Δ = 3 d = 23/8·α − 9/32·α^3 The weighted relation is in the row space. The checker verifies d² = Δ and checks both child spaces, with +id and −id. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / −d / +d Both orientations remain. Current constraint rank: 20. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p20 − p0 z = p6 − p4 (1 + i·(0))·x + (-1 + i·(0))·y + (1/2 + i·(-23/48·α + 3/64·α^3))·z = 0 Δ = 11/9 d = -15/8·α + 9/32·α^3 The weighted relation is in the row space. The checker verifies d² = Δ and checks both child spaces, with +id and −id. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.1.0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / −d / +d / +d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p13 − p12 x = ωy ω = (13/66 − 3/176·α^2) + i·(-13/44·α + 9/352·α^3) |ω|² = 3/44 ≠ 1 Display approximation: 0.068182 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.1.0.0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / −d / +d / −d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p13 − p12 x = ωy ω = (7/132 + 3/176·α^2) + i·(-149/352·α + 63/1408·α^3) |ω|² = 3/44 ≠ 1 Display approximation: 0.068182 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.1.0.1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / −d / −d Both orientations remain. Current constraint rank: 20. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p20 − p0 z = p6 − p4 (1 + i·(0))·x + (-1/2 + i·(23/16·α − 9/64·α^3))·y + (1/2 + i·(-23/48·α + 3/64·α^3))·z = 0 Δ = 11/9 d = -15/8·α + 9/32·α^3 The weighted relation is in the row space. The checker verifies d² = Δ and checks both child spaces, with +id and −id. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.1.1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / −d / −d / +d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p7 − p5 x = ωy ω = (-1/18 − 1/32·α^2) + i·(-23/48·α + 3/64·α^3) |ω|² = 1/12 + 3/256·α^2 ≠ 1 Display approximation: 0.177692 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.1.1.0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root / −d / −d / −d An edge has the wrong length. Current constraint rank: 21. Every supplied matrix has been checked against the constraints required here. x = p4 − p0 y = p7 − p5 x = ωy ω = (-23/72 + 1/32·α^2) + i·(-23/48·α + 3/64·α^3) |ω|² = 35/192 − 3/256·α^2 ≠ 1 Display approximation: 0.087933 This branch is impossible. Both displacements are graph edges. They cannot both have unit length with this exact multiplier. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-proof-root.1.1.1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 1/57: p0 + p1 = p12 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-0] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 2/57: p0 + p11 = p12 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-1] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 3/57: p0 + p15 = p4 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-2] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 4/57: p0 + p16 = p8 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-3] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 5/57: p0 + p18 = p8 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-4] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 6/57: p0 + p19 = p4 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-5] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 7/57: p0 + p21 = p20 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-6] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 8/57: p0 + p8 = p4 + p12. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-7] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 9/57: p1 + p11 = p6 + p12. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-8] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 10/57: p1 + p14 = p6 + p18. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-9] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 11/57: p1 + p16 = p11 + p18. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-10] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 12/57: p1 + p19 = p18 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-11] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 13/57: p1 + p20 = p11 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-12] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 14/57: p1 + p21 = p6 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-13] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 15/57: p1 + p8 = p12 + p18. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-14] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 16/57: p10 + p14 = p17 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-15] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 17/57: p11 + p15 = p16 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-16] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 18/57: p14 + p15 = p16 + p17. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-17] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 19/57: p14 + p19 = p17 + p18. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-18] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 20/57: p14 + p20 = p16 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-19] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 21/57: p14 + p22 = p18 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-20] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 22/57: p15 + p18 = p16 + p19. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-21] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 23/57: p15 + p21 = p17 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-22] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 24/57: p15 + p22 = p19 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-23] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 25/57: p16 + p22 = p18 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-24] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 26/57: p17 + p22 = p19 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-25] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 27/57: p2 + p10 = p7 + p13. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-26] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 28/57: p2 + p15 = p7 + p19. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-27] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 29/57: p2 + p17 = p10 + p19. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-28] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 30/57: p2 + p18 = p19 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-29] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 31/57: p2 + p20 = p7 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-30] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 32/57: p2 + p21 = p10 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-31] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 33/57: p2 + p3 = p13 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-32] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 34/57: p2 + p9 = p13 + p19. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-33] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 35/57: p3 + p10 = p13 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-34] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 36/57: p3 + p14 = p5 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-35] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 37/57: p3 + p17 = p9 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-36] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 38/57: p3 + p18 = p5 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-37] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 39/57: p3 + p19 = p9 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-38] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 40/57: p3 + p20 = p21 + p22. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-39] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 41/57: p3 + p9 = p5 + p13. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-40] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 42/57: p4 + p16 = p8 + p15. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-41] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 43/57: p4 + p17 = p15 + p19. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-42] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 44/57: p4 + p18 = p8 + p19. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-43] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 45/57: p5 + p16 = p14 + p18. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-44] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 46/57: p5 + p17 = p9 + p14. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-45] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 47/57: p5 + p19 = p9 + p18. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-46] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 48/57: p6 + p16 = p11 + p14. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-47] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 49/57: p6 + p17 = p14 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-48] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 50/57: p6 + p20 = p11 + p21. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-49] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 51/57: p7 + p16 = p15 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-50] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 52/57: p7 + p17 = p10 + p15. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-51] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 53/57: p7 + p21 = p10 + p20. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-52] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 54/57: p8 + p11 = p12 + p16. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-53] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 55/57: p8 + p14 = p16 + p18. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-54] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 56/57: p9 + p10 = p13 + p17. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-55] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Rhombus 57/57: p9 + p15 = p17 + p19. The diagonals share a midpoint in any injective unit drawing. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-rhombus-56] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | All 398 patterns searched: no copy in the survivor. Absence of these small obstructions does not prove drawability. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-filter-original] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Planted control graph, decoded live: 23 vertices, 71 edges; minimum degree 5; 38 triangles. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-graph-planted] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Planted control caught. Pattern C~, map 0→0, 1→1, 2→2, 3→3. Every mapped edge verified. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/graph.mjs | [runtime-filter-planted] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root: incorrect constraint row space | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-tamper-root matrix] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root: wrong child count | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-tamper-missing orientation] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root: weighted edge relation is not forced | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-tamper-false coefficient] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Interval does not isolate one real root | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-tamper-root interval] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root.1.1: d squared differs from Heron discriminant | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-tamper-false discriminant] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | root.0.0.0: x = omega*y is not forced | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-tamper-false leaf multiplier] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Certificate names the wrong graph | git show 5a634e5551:public/strata/the-sixty-fifth-distance/worker.mjs | [runtime-tamper-graph edge removed] Recreated by the actual pinned app and worker in n2-runtime-audit.mjs; exact recorded text and any displayed_values match. This tests calculations and DOM events, with no claim about rendered CSS or a live browser. - CONFIRMED | Current node's exact constraint matrix | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/certificate.json | [runtime-all-matrices] All 304 displayed matrix rows at all 15 nodes match the source record and certificate.json byte for byte; independent Python replay and the JavaScript checker accept the supplied row spaces. - CONFIRMED | The last deletion has no slack. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [condition-label-0] Matching excerpt: "A (23,65) unit-distance graph G would have to satisfy all of the following (`CONTRACT.md` Sections 0 to 3 and amendments 1 to 4; `research/unit-distance-22/enum/PRUNING.md`; `RHOMBUS-SPEC.md`; `research/unit-distance-22/check/PROOFS.md`): - **Minimum degree [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | Small impossibilities stay impossible. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [condition-label-1] Matching excerpt: "A (23,65) unit-distance graph G would have to satisfy all of the following (`CONTRACT.md` Sections 0 to 3 and amendments 1 to 4; `research/unit-distance-22/enum/PRUNING.md`; `RHOMBUS-SPEC.md`; `research/unit-distance-22/check/PROOFS.md`): - **Minimum degree [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | A missing edge cannot be compulsory. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [condition-label-2] Matching excerpt: "A (23,65) unit-distance graph G would have to satisfy all of the following (`CONTRACT.md` Sections 0 to 3 and amendments 1 to 4; `research/unit-distance-22/enum/PRUNING.md`; `RHOMBUS-SPEC.md`; `research/unit-distance-22/check/PROOFS.md`): - **Minimum degree [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - CONFIRMED | The ancestry has to fit. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/data/archive/PROOF-AND-CHECKS.txt | [condition-label-3] Matching excerpt: "A (23,65) unit-distance graph G would have to satisfy all of the following (`CONTRACT.md` Sections 0 to 3 and amendments 1 to 4; `research/unit-distance-22/enum/PRUNING.md`; `RHOMBUS-SPEC.md`; `research/unit-distance-22/check/PROOFS.md`): - **Minimum degree [...]" Read against the full pinned source or fetched primary document; its scope supports the claim. - MINOR | Exact unit-distance configuration. Select a point with Tab or the labelled point selector; arrow keys move it. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/lattice.mjs ; git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs ; git show 5a634e5551:public/strata/the-sixty-fifth-distance/app.mjs | [X6; svg-exact-description] The page claim is true. measure tests exact norms; pointView in draw.mjs:15-18 adds tabindex=0 and the keydown listener; app.mjs:26,31-33,111 connects point callbacks, arrow moves and the labelled selector. The source record now quotes and cites those controls alongside the exact arithmetic. Counted as a confirmed MINOR source-record repair. - CONFIRMED | Labelled graph layout with highlights from the selected instrument; these lengths do not represent unit distances. | git show 5a634e5551:public/strata/the-sixty-fifth-distance/draw.mjs | [svg-graph-description] Matching excerpt: "export function graphLayout(g){ const xy=Array.from({length:g.n},(_,i)=>[360+205*Math.cos(2*Math.PI*i/g.n),260+205*Math.sin(2*Math.PI*i/g.n)]); for(let t=0;t<280;t++){ const force=xy.map(()=>[0,0]); for(let i=0;i