--- slug: pslq-constants passed: 2026-10-18 by: the assay line (research/assay-line/queue-1018/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex; reviewed and repaired by Codex checked: 67 confirmed: 54 wrong: 12 unverifiable: 0 observed: 0 stale: 1 --- This was the queue-1018 tier A decide-before-fix pass for pslq-constants at bc67d24748, using research/assay-line/queue-1018/pslq-constants/N1-sources.json and N2-codex.md. All ten triage decisions were completed and JSON-validated before layer edits; the fixer re-read their code or source evidence. The 53 CONFIRMED entries attributed to N2 retain that checker's source readings, and one additional catalogue-formula claim was re-read in this pass. An additional MINOR verifier-description finding, X11, was decided and JSON-validated before its edit after the full numerical run exposed it. The review recorded R1 and R2 before repairing their readouts. The twelve entries counted as wrong comprise six WRONG and six MINOR findings. No original triage decision or level was changed. ## Claims - WRONG | X1: "Before this page reports an audit number of its own, it must make a published relation return." | git show bc67d24748:public/strata/pslq-constants/index.html; research/pslq-constants/verify-audit-gate.mjs | [anchor-audit-lock] I re-read the authored page at bc67d24748, public/strata/pslq-constants/index.html:483-492: updateAudit writes "text('count-candidates',cell[0].toLocaleString())" without a gate, and startup calls "populate();buildTable();fitCanvas($('survival-plot'));runAnchor()". My current-page VM probe with anchor replaced by () => null reproduced "anchor failed, audit locked" with 17,160 candidates, 17,157 rejected, 3 alive, 4 confirmed, 35 table rows and enabled controls; the unmodified anchor returns the published vector. Implement the catalogue lock, clear stale results after failure, and replace the verifier's substring-only lock assertion with a failure-path UI check. This is one error shared by X1, X2, X6 and X8, with one Corrected line. - WRONG | X2: "The audit remains visually locked if this check fails." | git show bc67d24748:public/strata/pslq-constants/index.html; research/pslq-constants/verify-audit-gate.mjs | [anchor-audit-lock] I re-read the authored page at bc67d24748, public/strata/pslq-constants/index.html:483-492: updateAudit writes "text('count-candidates',cell[0].toLocaleString())" without a gate, and startup calls "populate();buildTable();fitCanvas($('survival-plot'));runAnchor()". My current-page VM probe with anchor replaced by () => null reproduced "anchor failed, audit locked" with 17,160 candidates, 17,157 rejected, 3 alive, 4 confirmed, 35 table rows and enabled controls; the unmodified anchor returns the published vector. Implement the catalogue lock, clear stale results after failure, and replace the verifier's substring-only lock assertion with a failure-path UI check. This is one error shared by X1, X2, X6 and X8, with one Corrected line. - MINOR | X3: "Sierpiński − 4 Masser-Gramain = 0" | https://members.loria.fr/PZimmermann/papers/mcom2635.pdf; https://oeis.org/A086057/internal; https://oeis.org/A086058/internal | [masser-gramain-catalogue-convention] I re-read Melquiond, Nowak and Zimmermann, mcom2635.pdf, p. 1235: "1.819776 < δ < 1.819833" concerns delta, not the catalogue MasserGramain row at 0.646245... . OEIS A086057, FORMULA, says "Equals Pi*(A086058 - 1)/4."; A086058, FORMULA, says "Equals 1 + A062089/Pi." Therefore the catalogue convention is one quarter of Sierpinski's constant. Keep the true equation; replace the unrelated source/excerpt with the OEIS formula evidence, using the source's exact words, and state the catalogue convention beside the identity. Cheap MINOR fix, no dated page line. - MINOR | X4: "compatible only if the full-source residual lies within half a last-place unit from each row, weighted by |a| and |b|" | public/strata/pslq-constants/index.html; research/pslq-constants/verify-pslq-constants.mjs | [holdout-rule-scope] I re-read verify-pslq-constants.mjs:398-407: sourceAlive uses "2n * absBig(residual) <= absBig(q[1]) * ulpX + absBig(q[2]) * ulpY". The page runPair at index.html:490 instead uses "Math.abs(r.holdout)>1e-12" on binary64 values. The exact half-last-place rule is correct for the offline grid. Label it as the offline rule and disclose the separate live threshold, including its inclusive boundary. Cheap MINOR scope clarification, no dated page line. - MINOR | X5: "Run the independent checker with node research/pslq-constants/verify-pslq-constants.mjs." | research/pslq-constants/verify-pslq-constants.mjs; research/assay-line/queue-1018/pslq-constants/N2-codex.md | [checker-checkout-required] I re-read verify-pslq-constants.mjs:24-28 and main:568-572: it reads the repository-relative DATA, PROVENANCE, HTML and MARKDOWN files, beginning with "fs.readFileSync(DATA)". N2's isolated-download run fails with "ENOENT" for data/b000.txt; the page placard says "Running it needs the repository around it." Put the repository-checkout requirement beside the command. Cheap MINOR clarification, no dated page line. - WRONG | X6: "The catalogue audit stays locked unless that vector returns in its normalized form." | git show bc67d24748:src/content/strata/pslq-constants.md; research/pslq-constants/verify-audit-gate.mjs | [anchor-audit-lock] I re-read src/content/strata/pslq-constants.md:20, "The catalogue audit stays locked unless that vector returns in its normalized form." I re-read the authored page at bc67d24748, public/strata/pslq-constants/index.html:483-492: updateAudit writes "text('count-candidates',cell[0].toLocaleString())" without a gate, and startup calls "populate();buildTable();fitCanvas($('survival-plot'));runAnchor()". My current-page VM probe with anchor replaced by () => null reproduced "anchor failed, audit locked" with 17,160 candidates, 17,157 rejected, 3 alive, 4 confirmed, 35 table rows and enabled controls; the unmodified anchor returns the published vector. Implement the catalogue lock, clear stale results after failure, and replace the verifier's substring-only lock assertion with a failure-path UI check. This is one error shared by X1, X2, X6 and X8, with one Corrected line. - WRONG | X7: "Rows that encode known identities, aliases, padded endings, and definitions that were not independently recomputed remain visibly classified rather than being promoted into new mathematics." | git show bc67d24748:src/content/strata/pslq-constants.md; public/strata/pslq-constants/index.html | [row-classifications-visible] I re-read src/content/strata/pslq-constants.md:26 and the page at bc67d24748. index.html:489 populates selectors with "ox.textContent=row.label;oy.textContent=row.label". The four cards at :142-145 classify only those identities; :168 gives the general warning "sometimes with conspicuous zero endings". There are no per-row alias, padding or independently-unrecomputed categories. Replace the summary promise with the four cards and general zero-ending warning actually shown, and add a separate Corrected line. Keep WRONG: the promised visible classification does not exist. - WRONG | X8: "anchor failed, audit locked" | git show bc67d24748:public/strata/pslq-constants/index.html; research/pslq-constants/verify-audit-gate.mjs | [anchor-audit-lock] I re-read the authored page at bc67d24748, public/strata/pslq-constants/index.html:483-492: updateAudit writes "text('count-candidates',cell[0].toLocaleString())" without a gate, and startup calls "populate();buildTable();fitCanvas($('survival-plot'));runAnchor()". My current-page VM probe with anchor replaced by () => null reproduced "anchor failed, audit locked" with 17,160 candidates, 17,157 rejected, 3 alive, 4 confirmed, 35 table rows and enabled controls; the unmodified anchor returns the published vector. Implement the catalogue lock, clear stale results after failure, and replace the verifier's substring-only lock assertion with a failure-path UI check. This is one error shared by X1, X2, X6 and X8, with one Corrected line. - MINOR | X9: "pi and e at five places" | public/strata/pslq-constants/index.html; research/pslq-constants/README.md | [five-significant-digits-label] I re-read index.html:131, :469 and :491: the button says "pi and e at five places" but calls "preset('Pi','exp(1.0)',5)" and admitted takes the first p significant digits. My current-page probe uses approximately 3.1415 and 2.7182, whereas quick(5) uses 3.14159 and 2.71828. Change the button to "pi and e at five significant digits" and correct the README's dismissal of that ambiguity. Keep the checker's MINOR precision classification; no dated page line. - STALE | X10: ""dateModified":"2026-08-01"" | git show bc67d24748:public/strata/pslq-constants/index.html; research/pslq-constants/verify-pslq-constants.mjs | [stale-date-modified] I re-read index.html:27, "dateModified":"2026-08-01", and verify-pslq-constants.mjs:604, "jsonLd.dateModified === frontmatterDate". Read-only git log confirms later page edits on 2026-09-27 and 2026-10-01. This is the JSON-LD exception: decision fix, retaining STALE, with no Updated line. Set dateModified to the requested pass date 2026-10-18 and check it against the most recent dated correction/update in Markdown, while retaining the publication-date assertion. This is the layer's only STALE item, so there are no remaining stale items to combine into an Updated line. - CONFIRMED | "A short integer vector can be a theorem, a transcription error, or the shadow cast by rounded inputs." | https://arxiv.org/abs/1707.05037; https://www.davidhbailey.com/dhbpapers/cpslq.pdf; recreated: node probe-page.mjs | N2 re-read: [6: integer-vector-interpretation] The cited abstract concerns approximate inputs and finite computer precision. The paper, the published BBP theorem, and the reproduced five-place counterexample jointly support the contrast. The excerpt alone does not illustrate a transcription error. - CONFIRMED | "It is the coefficient vector printed in Ferguson, Bailey, and Arno's published PSLQ analysis, for the Bailey-Borwein-Plouffe formula." | https://www.davidhbailey.com/dhbpapers/cpslq.pdf | N2 re-read: [11: published-vector] Opened the PDF with curl and pdftotext after UNREADABLE. Printed p. 3 gives the coefficient vector (4, 0, 0, -2, -1, -1, 0, 0, -1) for X1 through X8 followed by pi. The title page names Ferguson, Bailey and Arno; the 1999 publication is independently identified by Crossref. - CONFIRMED | "Xj = Σk≥0 16−k/(8k+j)" | https://www.davidhbailey.com/dhbpapers/cpslq.pdf | N2 re-read: [12: bbp-series-definition] Opened and read PDF p. 3. Its Xj definition is the sum of 1/(16^k(8k+j)); multiplying numerator and denominator gives the displayed 16^(-k)/(8k+j). The source-record control character is a text-extraction artifact, not a different formula. - CONFIRMED | "This claim is only about the fixed snapshot, grammar, precision grid, coefficient grid, holdout rule, and null comparison below." | git show 1fde322cb4:research/pslq-constants/spec.json | N2 re-read: [24: novelty-scope] The spec new_number.what specifies the fixed 188-row snapshot, 17,578 pairs, precision and coefficient grids, and holdout counts. Its hazards expressly exclude broader novelty. The page narrows its claim to those conventions. - CONFIRMED | "Automated searches for relations among constants are already published, most broadly in The Ramanujan Library." | https://arxiv.org/abs/2412.12361v2; https://arxiv.org/html/2412.12361v2 | N2 re-read: [25: published-automated-searches] The abstract describes automated library enrichment using PSLQ and reports 75 connections; its full text uses a hypergraph of integer polynomial relations. This supports the broader published search precedent. - CONFIRMED | "every finite input is rational" | https://openstax.org/books/contemporary-mathematics/pages/3-4-rational-numbers | N2 re-read: [26: finite-input-rational] OpenStax states: "All numbers that can be expressed as a terminating decimal are rational." Here finite input means a finite decimal representation, not every real number with finite magnitude. - CONFIRMED | "PSLQ output is not proof." | https://arxiv.org/html/2412.12361v2; https://www.davidhbailey.com/dhbpapers/cpslq.pdf | N2 re-read: [28: pslq-not-proof] The Ramanujan Library conclusion calls numerical results "conjectures awaiting proofs". The PSLQ analysis also distinguishes an alleged finite-precision relation from a proof about the real numbers. - CONFIRMED | "1 − 2φ + √5 = 0Definition-confirmed and source-alive." | https://oeis.org/A001622/internal; git show 1fde322cb4:research/pslq-constants/data/b000.txt | N2 re-read: [32: identity-1] OEIS defines phi by (1+sqrt(5))/2, so the displayed identity follows by rearrangement. The companion source-record entry and exact source arithmetic establish source-alive: residual 1 at scale 10^-63, within weighted allowance 1.5*10^-63. - CONFIRMED | "φ − 2 cos(π/5) = 0" | https://oeis.org/A001622/internal | N2 re-read: [34: identity-2] OEIS A001622 explicitly gives "Equals 2*cos(Pi/5)". Rearranging yields the identity. - CONFIRMED | "1 + √5 − 4 cos(π/5) = 0" | https://oeis.org/A001622/internal | N2 re-read: [36: identity-3] Combining the two formulas in OEIS A001622, 2*phi=1+sqrt(5) and phi=2*cos(pi/5), gives 1+sqrt(5)-4*cos(pi/5)=0. - CONFIRMED | "Definition-confirmed from their published formulas and source-alive." | https://www.plouffe.fr/simon/constants/sierpinski.txt; https://oeis.org/A086057/internal; https://oeis.org/A086058/internal; git show 1fde322cb4:research/pslq-constants/data/b000.txt | N2 re-read: [40: identity-4-sierpinski-definition] Plouffe supplies "-Pi*ln(Pi)+2*Pi*gamma+4*Pi*log(GAMMA(3/4));" and the K expansion. That excerpt defines only Sierpinski, not both sides or source survival. Combining it with OEIS A086057/A086058 and exact b000 arithmetic confirms the full claim; the record should cite all three pieces. - CONFIRMED | "A source-level rejection is not a proof of mathematical falsehood." | https://arxiv.org/abs/1707.05037 | N2 re-read: [42: source-rejection-limits] The empirical-input paper analyzes approximate rather than exact inputs and the resulting error control. Independently, this page provides a constructive example: its true phi/cos identity fails the printed-digit interval. Extra arithmetic precision cannot recover digits missing from the input. - CONFIRMED | "c + ax + by = 0; primitive integers; a and b both nonzero" | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [44: check-convention-21] gridColumn calls pslq([one,admitted[i],admitted[j]],...), primitive divides by the gcd and normalizes sign, and q[1]===0n or q[2]===0n is excluded before counting. The source-record locator normaliseRelation is inaccurate: the function is named primitive. - CONFIRMED | "first p significant decimal digits, truncated; p ∈ {8,12,16,24,32,40,48}" | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [45: check-convention-22] admittedInt uses row.digits.slice(0,p).padEnd(p,'0'). PRECISIONS is [8,12,16,24,32,40,48]. These are significant digits, not decimal places. - CONFIRMED | "γ = √(4/3); tolerance 10−(p−1); 500 steps; working precision max(60,p+30)" | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [46: check-convention-23] The verifier defines gamma=sqrt(4/3), tolerance=dec(1n,-(p-1)), MAX_STEPS=500 and workingPrecision(p)=Math.max(60,p+30). It also uses a maximum-coefficient early exit. These are the offline census conventions. - CONFIRMED | "H = max(|c|,|a|,|b|) after gcd division and first-nonzero-positive sign" | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [47: check-convention-24] primitive divides coefficients by their common gcd and flips a negative first nonzero coefficient. gridColumn then reduces over absBig(q[i]) to obtain the maximum absolute coefficient. The source-record locator normaliseRelation is inaccurate; searching for function primitive finds the implementation. - CONFIRMED | "xorshift32 seeded by FNV-1a of mode, row index, and label; shuffle preserves leading digit, exponent, and length; random preserves exponent and length" | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [49: check-convention-26] nullCatalogue seeds fnv1a from mode:index:label, advances xorshift32, shuffles only row.digits.slice(1), and retains row exponent and length. Random mode generates a nonzero leading digit and the remaining decimal digits. - CONFIRMED | "four algebraic or named-definition identities; no numerical persistence is promoted to proof" | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs; https://oeis.org/A001622/internal; https://oeis.org/A086057/internal; https://oeis.org/A086058/internal | N2 re-read: [50: check-convention-27] The three golden-ratio identities follow algebraically from OEIS A001622. The fourth is K=4c for the catalogue convention, confirmed by A086057 and A086058. None is new. Section F and the exact holdout arithmetic classify three as source-alive. - CONFIRMED | "32 terms per Xj, IEEE 754 binary64 PSLQ; offline check uses 160 decimal places with guard digits" | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [51: check-convention-28] bbpX sums exactly 32 terms using JavaScript Number. The verifier defines CLAIM=160 and FXS=210, giving fifty fixed-point guard digits; its independent anchor search uses 170 working digits. - CONFIRMED | "The source URL states no explicit licence." | https://www.plouffe.fr/simon/b000.txt | N2 re-read: [52: standalone-licence] The fetched file is 188 numeric rows only. Case-insensitive licen[cs]e/copyright/permission search finds zero occurrences here and 46 in Gutenberg 634, a positive control; the same file search finds Zeta(9). This is a statement about the fetched text, not a legal conclusion about reuse. - CONFIRMED | "Project Gutenberg's permission statement for a larger Plouffe collection does not clearly settle reuse terms for this standalone file." | https://www.gutenberg.org/cache/epub/634/pg634.txt | N2 re-read: [53: gutenberg-permission] The introduction thanks Plouffe "for his kind permission to distribute this collection of constants." It refers to that ebook collection; it does not identify the separate b000 URL. The page correctly records uncertainty rather than asserting a licence. - CONFIRMED | "The uncertainty is recorded rather than inferred away." | git show 1fde322cb4:research/pslq-constants/data/PROVENANCE.md | N2 re-read: [54: licence-uncertainty-recorded] PROVENANCE.md has a Licence section saying the standalone URL states no explicit terms and the ebook statement does not unambiguously license the current standalone file. - CONFIRMED | "Working precision does not create trusted source precision." | https://arxiv.org/abs/1707.05037 | N2 re-read: [56: working-vs-source-precision] The empirical-input paper analyzes approximate rather than exact inputs and the resulting error control. Independently, this page provides a constructive example: its true phi/cos identity fails the printed-digit interval. Extra arithmetic precision cannot recover digits missing from the input. - CONFIRMED | "The four confirmed relations are catalogue calibration, not new identities." | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs; https://oeis.org/A001622/internal; https://oeis.org/A086057/internal; https://oeis.org/A086058/internal | N2 re-read: [57: prose-31-1] The three golden-ratio identities follow algebraically from OEIS A001622. The fourth is K=4c for the catalogue convention, confirmed by A086057 and A086058. None is new. Section F and the exact holdout arithmetic classify three as source-alive. - CONFIRMED | "Otherwise a one-row rational approximation would be counted once for every unrelated partner, a reader-reachable vacuity." | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [60: prose-32-2] With b=0, c+a*x is independent of y, so the identical one-row approximation is eligible for every partner. The exclusion removes these from the pair census. The statement describes the degeneracy, not an assertion that every PSLQ run must choose the same vector. - CONFIRMED | "This page does not test products, powers, logarithms, or larger tuples." | git show 1fde322cb4:research/pslq-constants/verify-pslq-constants.mjs | N2 re-read: [63: limits-1] gridColumn searches only [1,x,y] over i