--- slug: topswops-machine passed: 2026-10-14 by: the assay line (research/assay-line/queue-1014c/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex; repaired by Codex from this batch's fixcheck.md checked: 89 confirmed: 74 wrong: 13 unverifiable: 0 observed: 0 stale: 2 --- This was the directed correction pass for topswops-machine at read 6707fd4e2e, following all 15 queue-1014c triage items after re-reading their evidence. It records 2 WRONG, 11 MINOR (counted in wrong), and 2 STALE findings, and carries forward the checker's 74 CONFIRMED claims with their original f5e5f84f34 provenance explicitly labelled; those earlier measurements are not represented as new runs. The page, markdown and film text source were corrected within this layer only. The existing MP4 remains unchanged under the task's no-render instruction, and that incomplete part of X9 is recorded below. ## Claims - WRONG | nobody can tell you, without running it, how long it takes, which decks last longest, or which decks no flip could ever have produced. | https://arxiv.org/html/2103.08346 ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | [X1] The fixed-point proof works in both directions: a legal k-flip puts k in position k; reversing that prefix in any deck with q(k)=k constructs a legal predecessor. Positions 2..n decide unreachability without playing. - MINOR | A live machine that plays every possible deal in your browser, counting the longest games, finding the decks no flip can produce | git show f5e5f84f34:public/strata/topswops-machine/index.html | [X2] The slider selects n=2..10, but showStats calls enumerate only for n<=9. The dek now limits exhaustive browser play to the selected size from 2 to 9 cards. - MINOR | a playable Topswops machine that recomputes every number in the browser. | git show f5e5f84f34:public/strata/topswops-machine/index.html | [X3] buildTable reads STAGED for n=2..13. The markdown body now distinguishes selected-size live enumeration for n=2..9 from stored ten-card statistics and the precomputed table. - MINOR | Every number recomputed in your browser. | git show f5e5f84f34:public/strata/topswops-machine/index.html | [X4] The description, Twitter description and Article JSON-LD all overstated browser computation. All three now state live statistics for the selected n=2..9 and a precomputed table through n=13; the OG description had no such universal claim. - STALE | "dateModified":"2026-06-24" | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git log f5e5f84f34 -- public/strata/topswops-machine/index.html | [X5] The initial 5496ea2db90 page had dateModified 2026-06-24. Later page history includes the 2026-06-25 film and 2026-10-01 metadata edit. Set to this task's revision date, 2026-10-14; the explicit JSON-LD exception needs no separate Updated line. - MINOR | "uploadDate":"2026-07-09" | git show f5e5f84f34:memory/log.d/2026-06-25T0615Z-topswops-companion-film.md ; git show f5e5f84f34:scripts/seo-heads.mjs ; git log f5e5f84f34 -- public/strata/topswops-machine/film.mp4 | [X6] scripts/seo-heads.mjs defines uploadDate by the first addition at the exact MP4 path, without rename following. git log 6707fd4e2e --diff-filter=A gives 315e4621d5c, 2026-06-25T06:15:17+00:00. That supplies 2026-06-25. - MINOR | The machine below played every one of them in your browser and counted. | git show f5e5f84f34:public/strata/topswops-machine/index.html | [X7] The paragraph changes its deck size at n=10, where showStats reads STAGED. The wording now explicitly separates live enumeration for n=2..9 from stored counts for n=10. - WRONG | Flip-count distribution over all deals (tallest bar = the longest-lasting decks): | git show f5e5f84f34:public/strata/topswops-machine/index.html | [X8] tally increments hist[f] once per deck; drawHist orders bars by flip count and scales their heights by those counts. Thus height is frequency and the rightmost bar is the longest game. Nonempty bins now have a 2px minimum, with exact tooltip counts retained. - MINOR | A000255, Euler's fixed-point-free count. | https://oeis.org/A000255/internal | [X9] OEIS A000255 comments by Jon Perry (2004-01-23) and Don Knuth (2007-01-25) restrict Euler's interpretation to fixed-point-free permutations beginning with 2; a(k) concerns k+2 objects. Corrected the page and both film-source copies, preserving A000255(n-1), and added a visible clarification beside the film. The existing MP4 was not regenerated under the no-render instruction and retains the older wording; this part remains open pending a board note. - MINOR | that calibration is why the new column can be trusted. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/README.md | [X10] The staging README distinguishes engine calibration from evidence for total sums: two implementations through n=9, one through n=11, and stored comparisons at n=12..13, with separate same-engine reruns recorded. The page now states that scope and links the public per-term account. - MINOR | Reproduce it all with node research/topswops/verify.mjs (9/9). | git show f5e5f84f34:research/topswops/verify.mjs | [X11] The verifier explicitly excludes a(12) and a(13), compares total-step literals through n=11, and never opens the staged b-file. The page now names the engine-check range and the separate staged-artifact coverage. - MINOR | Every number on this page was recomputed in your browser by exhaustively playing all n! deals (for n ≤ 9 automatically; n = 10 on request), and it agrees with the values verified offline. | git show f5e5f84f34:public/strata/topswops-machine/index.html | [X12] The complete control wiring has no exhaustive ten-card request. The page now states live statistics for selected n=2..9, stored ten-card statistics and a precomputed table through n=13. - MINOR | the live enumeration reproduces OEIS A000375 (max flips: 0, 1, 2, 4, 7, 10, 16, 22, 30, 38, 51, 65, 80) and A123398 (number of maximizing decks) exactly | git show f5e5f84f34:public/strata/topswops-machine/index.html | [X13] The OEIS values are correct. The browser guard limits live calibration to selected n=2..9; the page now labels the larger table values precomputed. - MINOR | unreachable decks = A000255(n−1), proven three independent ways (flip-map preimages, the no-fixed-point characterization, and A000255's recurrence) in research/topswops/verify.mjs. | git show f5e5f84f34:research/topswops/verify.mjs | [X14] The verifier has finite checks: preimage counts n=1..8; direct, inclusion-exclusion and recurrence counts n=1..9; flip-image predicate n=2..7. The page now gives those ranges separately from the general fixed-point and inclusion-exclusion argument. No numerical verifier assertion needed changing. - STALE | Staged for Zenodo + independent human authorship per OEIS's AI-submission policy; not auto-submitted. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/README.md ; https://api.datacite.org/dois/10.5281/zenodo.21943934 | [X15] The page described the sequence as staged for Zenodo, including in the original 5496ea2db90 HTML. Re-reading DataCite returned state=findable and dateType=Issued, date=2026-08-15 for DOI 10.5281/zenodo.21943934. Updated only the Zenodo status and retained the separate human-authored OEIS route; one Updated line is mirrored in the markdown. Repair changed that line's account of the old page from a plan to stage to its actual staged status. - CONFIRMED | John Conway's one-rule card game | https://arxiv.org/html/2103.08346 | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [conway-invention] The primary paper says "This card game is called Topswops, which was originally invented by J.H. Conway in 1973." Whitespace around the inline name differs from the recorded excerpt, without changing its words. - CONFIRMED | read the top card, flip over that many. Repeat until the ace surfaces. | https://oeis.org/A000375/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [rule-dek] OEIS says "If top card is m, reverse order of top m cards, then repeat" and defines the endpoint as "before top card is 1". The code uses the same stopping rule. - CONFIRMED | The rule: if the top card is k, reverse the order of the top k cards. If it is 1 (the ace), stop. | https://oeis.org/A000375/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [rule-full] OEIS says "If top card is m, reverse order of top m cards, then repeat" and defines the endpoint as "before top card is 1". The code uses the same stopping rule. - CONFIRMED | The verifier and the staged new sequence live in `research/topswops/` and `oversight/oeis/topswops-total-flips/`. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/README.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [md-artifacts] Both named directories are present at the pin. The staged README gives "node oversight/oeis/topswops-total-flips/verify-staged.mjs" and "node research/topswops/verify.mjs"; the reader copy of the latter ran 9/9. - CONFIRMED | Companion film — 2:30 | https://artwaste.land/strata/topswops-machine/film.mp4 ; git show f5e5f84f34:research/topswops/film/build.sh | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [film-duration] The live MP4 fetched with HTTP 200. ffprobe reports "duration": "150.000000"; 150 seconds is 2:30. Evidence: evidence/film-probe.json. The 8,855,183-byte download was deleted after inspection. - CONFIRMED | The film is at film.mp4 (MP4 / H.264 + AAC). | https://artwaste.land/strata/topswops-machine/film.mp4 ; git show f5e5f84f34:research/topswops/film/build.sh | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [film-format] ffprobe reports "codec_name": "h264" for video and "codec_name": "aac" for audio; the endpoint returns video/mp4. Evidence: evidence/film-probe.json. - CONFIRMED | the deck [4,7,6,2,1,5,3] lasts 16 flips | git show f5e5f84f34:research/topswops/film/film.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [film-champion] Recreated from the pinned flip routine: "steps":16,"final":[1,2,3,4,5,6,7]. The source actually names "const DECK0 = [4,7,6,2,1,5,3]" and "const TRAJ = trajectory(DECK0)". The record's where field incorrectly says "CHAMP, TRACE and E7"; searches find zero CHAMP/TRACE identifiers and positive controls find DECK0 four times, TRAJ five times and E7 ten times. - CONFIRMED | the most any 7-card deck can, A000375 | https://oeis.org/A000375/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [film-seven-max] OEIS has offset "1,3" and terms "0,1,2,4,7,10,16,22,30,38,51,65,80". The seventh term is 16; the independent primary Kimura et al. list agrees. - CONFIRMED | then all 5,040 deals tallied, the Garden-of-Eden count (= A000255 (6)), and the three sequences laid side by side. | git show f5e5f84f34:research/topswops/film/film.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [film-tally] The film calls "const E7 = enumerate(7)" and fills TABLE with "for(let n=2;n<=9;n++) TABLE.push(enumerate(n))". Recreated results are 5,040 deals, maximum 16, two champions, total 18,508, and garden 2,119. OEIS A000255(6)=2119. - CONFIRMED | the melody is that longest game, played note-per-flip. | git show f5e5f84f34:research/topswops/film/make-audio.mjs | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [film-melody] The audio code sets "const TOPS = topsRead(DECK0)" and calls "pluck(t0, cardHz(TOPS[i], 2), 0.085)" for each flip. Its 16 top cards are [4,2,6,5,2,7,3,5,4,6,2,5,3,4,2,3], followed by ace-resolution notes. This is exactly the claimed mapping. - CONFIRMED | For a deck of 7 cards there are 5040 possible deals. | git show f5e5f84f34:research/topswops/engine.mjs | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [deals-seven] 7! = 7×6×5×4×3×2×1 = 5,040. The source computes factorials by "f[i] = f[i - 1] * i". - CONFIRMED | Every flip lands the machine on some new deck. | https://oeis.org/A000375/internal ; git show f5e5f84f34:research/topswops/engine.mjs | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [flip-new-deck] Every legal flip has k>1 and moves top card k to position k, so the resulting permutation differs. Successive play cannot revisit a deck: the sum of 2^(j-1) over correctly positioned cards strictly increases with every legal flip. The OEIS stopping rule agrees; terminal k=1 is not counted as a flip. - CONFIRMED | There are. They have a clean signature. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [unreachable-exist] The proposed comment states "the image of a reversal step iff there is some k in 2..n with q(k) = k". Both directions hold: a legal k-flip puts k at k; reversing a q with q(k)=k gives a predecessor topped by k. The reader verifier passed the preimage and fixed-point checks. This is a general proof, not just a finite observation. - CONFIRMED | A deck is the result of a flip exactly when some card k sits in position k below the top (reverse the first k and it lands there). | git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [preimage-characterization] The proposed comment states "the image of a reversal step iff there is some k in 2..n with q(k) = k". Both directions hold: a legal k-flip puts k at k; reversing a q with q(k)=k gives a predecessor topped by k. The reader verifier passed the preimage and fixed-point checks. This is a general proof, not just a finite observation. - CONFIRMED | So the unreachable decks are precisely the permutations with no card in its own place except possibly the top. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [unreachable-characterization] The proposed comment states "the image of a reversal step iff there is some k in 2..n with q(k) = k". Both directions hold: a legal k-flip puts k at k; reversing a q with q(k)=k gives a predecessor topped by k. The reader verifier passed the preimage and fixed-point checks. This is a general proof, not just a finite observation. - CONFIRMED | an 18th-century permutation count. | https://oeis.org/A000255/internal ; https://scholarlycommons.pacific.edu/euler-works/530/ | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [euler-century] The OEIS reference says "9 (1782), 85-239, on page 235 in section 152". The Euler Archive landing page independently says "Published Date 1782". The online checker's PARTIAL result is caused by HTML link markup in the copied excerpt, not a date mismatch. - CONFIRMED | Tabulate those counts as n grows and you get integer sequences. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/b-file.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [tabulate-sequences] The b-file defines "Total Topswops steps summed over all n! starting decks of n cards" and contains integer-indexed integer values from "1 0" through "13 54349566758". - CONFIRMED | Two are already catalogued. | https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [two-catalogued] A000375 names the maximum-step process and links "A123398 (number of solutions)". A123398 explicitly says "number of permutations of cards achieving A000375(n)". These are the two referred-to columns. - CONFIRMED | so it is staged as a new entry with its working shown. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/draft.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [staged-new-entry] draft.txt contains "%N Total number of steps in Conway's Topswops, summed over all n! starting decks of n cards." The b-file, derive.mjs and verification files are present in the pinned staging directory. - CONFIRMED | The same code reproduces the catalogued columns (max flips, longest-lasting decks) exactly | git show f5e5f84f34:research/topswops/verify.mjs | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [calibration-same-code] The reader run passed "max flips M(1..10) = A000375", "max flips M(11) = 51 (A000375)" and "champions champ(1..10) = A123398". Recorded out-of-band runs additionally give M(12)=65 and M(13)=80, which agree with OEIS. The bundled check's narrower scope is stated in the note for reproduce-all. - CONFIRMED | max flips: 0, 1, 2, 4, 7, 10, 16, 22, 30, 38, 51, 65, 80 | https://oeis.org/A000375/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [a000375-citation] The OEIS %S line begins "0,1,2,4,7,10,16,22,30,38,51,65,80" with offset 1. The supplied excerpt accurately matches the source. - CONFIRMED | A123398 (number of maximizing decks) | https://oeis.org/A123398/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [a123398-citation] The source title is "Topswops: number of permutations of cards achieving A000375(n)." The supplied description is accurate. - CONFIRMED | unreachable A000255(n-1) | https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [a000255-citation] The recorded excerpt alone counts a different-looking object, "fixed-point-free permutations of n+2 that begin with a 2". The missing connection is supplied by the page's fixed-point proof: the unreachable n-card decks number D(n)+D(n-1); OEIS gives "a(n) = A000166(n) + A000166(n+1)". Hence the index n-1 is correct. The source record should include that connection alongside the excerpt. - CONFIRMED | so only the total-flips column is claimed new. | git show f5e5f84f34:oversight/oeis/topswops-total-flips/draft.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [only-total-new] The draft labels the total-step sequence with a new "%N" line; A000255-comment.txt calls the bridge "A proposed COMMENT for an EXISTING sequence". This matches the page's distinction. - CONFIRMED | independent human authorship per OEIS's AI-submission policy | https://oeis.org/wiki/Use_of_AI_for_OEIS_Submissions | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [oeis-human-policy] The official policy says "All sequences in the OEIS must have a human author" and makes that author responsible for correctness. It is the approved 29 August 2026 revision. This supports the human-authorship clause, without treating it as a ban on every use of AI. - CONFIRMED | Verifier & engine: research/topswops/ · staged sequence: oversight/oeis/topswops-total-flips/ (b-file, derive script, Zenodo metadata). | git show f5e5f84f34:oversight/oeis/topswops-total-flips/README.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [footer-artifacts] The pinned directory contains b-file.txt, derive.mjs and .zenodo.json. The README gives the commands for the engine verifier and the staged verifier. The separate public data/code link also resolves. - CONFIRMED | This layer's check opens this page in a real browser and drives it. | git show f5e5f84f34:verify-topswops-machine.mjs | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [check-real-browser] The driver contains "const browser = await chromium.launch()" and "await page.goto(URL_, { waitUntil:'networkidle' })". It clicks shuffle, step and Eden controls and changes the card count. It serves a local built page; no headless browser was used against the live site in this pass. - CONFIRMED | It is reading what you are reading. | git show f5e5f84f34:verify-topswops-machine.mjs | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [check-reading] The driver serves "const root = '/home/user/Artificial-Wasteland/dist/'" and reads rendered "#stats", "#live-badge", "#eden-deck" and "#seqtab". The live response has the same substantive pinned page text. This describes a DOM check, not a claim that every prose sentence is verified. - CONFIRMED | verify.mjs is published, and it runs from 2 files this site serves | https://artwaste.land/checks/#run-research-topswops-verify-mjs ; git show f5e5f84f34:public/checks/manifest.json | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [published-check] The manifest needs array names exactly "research/topswops/engine.mjs" and "research/topswops/verify.mjs". Both public downloads returned HTTP 200 and matched the pinned source byte for byte. In an initially empty reader directory, "node research/topswops/verify.mjs" exited 0 with "9/9 checks passed." - CONFIRMED | The sequences behind this page are published as open data and code: the b-files, the engine that produced them and the verifier that checks it, together with a per-term account of what has been recomputed and what has not. | https://raw.githubusercontent.com/artwasteland/Maths/main/topswops/README.md ; https://raw.githubusercontent.com/artwasteland/Maths/main/topswops/oversight/oeis/topswops-total-flips/STAGED.md ; https://api.datacite.org/dois/10.5281/zenodo.21943934 | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [open-data-code] The public README identifies "oversight/oeis/topswops-total-flips/" and "research/topswops/". Its linked STAGED.md fetched with HTTP 200 and states recomputed versus drift-guarded ranges. The data deposit is openly licensed CC BY 4.0, per DataCite. - CONFIRMED | Deposited, and citable by DOI: 10.5281/zenodo.21943934 | https://zenodo.org/records/21943934 ; https://api.datacite.org/dois/10.5281/zenodo.21943934 | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [zenodo-citation] Opened the source independently after the tool reported "Crossref HTTP 404". Zenodo returns HTTP 200 and DataCite returns the stated DOI, "publisher":"Zenodo", "state":"findable", and title "Topswops: total steps over all decks, and the Garden of Eden (Artificial Wasteland)". This is a DataCite DOI, so the Crossref failure is not evidence of a bad citation. - CONFIRMED | another trivially-stated rule whose only honest answer is to run it and watch what falls out | git show f5e5f84f34:src/content/strata/the-crystal-and-the-cloud.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [nearby-the-crystal-and-the-cloud] The linked source defines the greedy rule as "append the smallest number that keeps the set free of any three-term arithmetic progression" and contrasts a proven crystal with an unclassified cloud. The navigational comparison identifies that rule; "honest answer" is qualitative framing, not treated as a separate impossibility theorem. - CONFIRMED | there by adjacent swaps, here by prefix reversals | git show f5e5f84f34:src/content/strata/the-extent.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [nearby-the-extent] The linked source explicitly says "single adjacent swaps" and "any disjoint adjacent swaps" for its two graphs. Topswops reverses a prefix, as the OEIS definition and page code show. - CONFIRMED | a simple game hiding a countable structure: nontransitive triples there, unreachable decks here | git show f5e5f84f34:src/content/strata/no-triangle-at-three.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [nearby-no-triangle-at-three] The linked source says "The first genuine triangle does not appear until length four, and then fourteen appear together." The cross-link claims nontransitive triples there, not that they occur at length three. The Topswops unreachable-deck characterization is proved above. - CONFIRMED | a clean map on a small set, its orbit counts staged for OEIS | git show f5e5f84f34:src/content/strata/square-minus-two.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [nearby-square-minus-two] The linked source defines "x ↦ x² − 2" modulo n and lists "the number of cycles, the periodic points, the fixed points, the longest cycle" as computed counts. This supports the description of its map and staged orbit counts. - CONFIRMED | Two of John Conway's one-rule games, both decided by a quantity that can only move one way. | git show f5e5f84f34:src/content/strata/conways-soldiers.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [nearby-conways-soldiers] The linked source explicitly distinguishes "Herbert Wilf's, as Martin Gardner recounts" increasing Topswops quantity from the soldiers' weight that "never rises". For Topswops, sum 2^(k-1) over correctly placed cards strictly increases on a k-flip, since k is fixed and any destroyed lower weights total less than its weight. This validates the monovariant comparison without attributing the Topswops proof to Conway. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 2 1 1 1 1 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-2] Recreated the pinned page enumeration: [1,1,1,1]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 3 2 2 6 3 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-3] Recreated the pinned page enumeration: [2,2,6,3]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 4 4 2 38 11 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-4] Recreated the pinned page enumeration: [4,2,38,11]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 5 7 1 265 53 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-5] Recreated the pinned page enumeration: [7,1,265,53]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 6 10 5 2,115 309 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-6] Recreated the pinned page enumeration: [10,5,2115,309]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 7 16 2 18,508 2,119 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-7] Recreated the pinned page enumeration: [16,2,18508,2119]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 8 22 1 180,260 16,687 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-8] Recreated the pinned page enumeration: [22,1,180260,16687]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 9 30 1 1,911,505 148,329 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-9] Recreated the pinned page enumeration: [30,1,1911505,148329]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 10 38 1 22,169,434 1,468,457 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-10] Recreated the pinned page enumeration: [38,1,22169434,1468457]. OEIS A000375 and A123398 confirm the first two columns; the proved A000255(n-1) identity and recurrence confirm the last. The total also agrees with the published reader verifier. Display row was read from buildTable output. - CONFIRMED | n max flips A000375 longest-lasting decks A123398 total flips (new) unreachable A000255(n-1) 11 51 1 277,931,375 16,019,531 | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [table-row-11] The reader verifier passed "M(11) = 51" and "SUM(11) = 277931375"; A123398(11)=1 and the independently evaluated A000255 recurrence gives 16019531. The displayed row matches [51,1,277931375,16019531]. - CONFIRMED | Longest game 1 flips OEIS A000375 Decks that last that long 1 OEIS A123398 Average game 0.500 flips total ÷ 2 Total flips, all deals 1 the new sequence Unreachable decks 1 A000255(1) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-2] The rendered stat cards and recreated enumeration agree: max=1, maximizing decks=1, total=1, unreachable=1. Arithmetic: 1/2 rounds to 0.500 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 2 cards there are 1 such unreachable decks (= A000255(1)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-2] The displayed count is 1; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(1)=1. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 2 flips OEIS A000375 Decks that last that long 2 OEIS A123398 Average game 1.000 flips total ÷ 6 Total flips, all deals 6 the new sequence Unreachable decks 3 A000255(2) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-3] The rendered stat cards and recreated enumeration agree: max=2, maximizing decks=2, total=6, unreachable=3. Arithmetic: 6/6 rounds to 1.000 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 3 cards there are 3 such unreachable decks (= A000255(2)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-3] The displayed count is 3; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(2)=3. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 4 flips OEIS A000375 Decks that last that long 2 OEIS A123398 Average game 1.583 flips total ÷ 24 Total flips, all deals 38 the new sequence Unreachable decks 11 A000255(3) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-4] The rendered stat cards and recreated enumeration agree: max=4, maximizing decks=2, total=38, unreachable=11. Arithmetic: 38/24 rounds to 1.583 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 4 cards there are 11 such unreachable decks (= A000255(3)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-4] The displayed count is 11; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(3)=11. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 7 flips OEIS A000375 Decks that last that long 1 OEIS A123398 Average game 2.208 flips total ÷ 120 Total flips, all deals 265 the new sequence Unreachable decks 53 A000255(4) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-5] The rendered stat cards and recreated enumeration agree: max=7, maximizing decks=1, total=265, unreachable=53. Arithmetic: 265/120 rounds to 2.208 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 5 cards there are 53 such unreachable decks (= A000255(4)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-5] The displayed count is 53; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(4)=53. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 10 flips OEIS A000375 Decks that last that long 5 OEIS A123398 Average game 2.938 flips total ÷ 720 Total flips, all deals 2,115 the new sequence Unreachable decks 309 A000255(5) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-6] The rendered stat cards and recreated enumeration agree: max=10, maximizing decks=5, total=2115, unreachable=309. Arithmetic: 2115/720 rounds to 2.938 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 6 cards there are 309 such unreachable decks (= A000255(5)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-6] The displayed count is 309; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(5)=309. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 16 flips OEIS A000375 Decks that last that long 2 OEIS A123398 Average game 3.672 flips total ÷ 5,040 Total flips, all deals 18,508 the new sequence Unreachable decks 2,119 A000255(6) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-7] The rendered stat cards and recreated enumeration agree: max=16, maximizing decks=2, total=18508, unreachable=2119. Arithmetic: 18508/5040 rounds to 3.672 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 7 cards there are 2,119 such unreachable decks (= A000255(6)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-7] The displayed count is 2119; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(6)=2119. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 22 flips OEIS A000375 Decks that last that long 1 OEIS A123398 Average game 4.471 flips total ÷ 40,320 Total flips, all deals 180,260 the new sequence Unreachable decks 16,687 A000255(7) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-8] The rendered stat cards and recreated enumeration agree: max=22, maximizing decks=1, total=180260, unreachable=16687. Arithmetic: 180260/40320 rounds to 4.471 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 8 cards there are 16,687 such unreachable decks (= A000255(7)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-8] The displayed count is 16687; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(7)=16687. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 30 flips OEIS A000375 Decks that last that long 1 OEIS A123398 Average game 5.268 flips total ÷ 362,880 Total flips, all deals 1,911,505 the new sequence Unreachable decks 148,329 A000255(8) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-9] The rendered stat cards and recreated enumeration agree: max=30, maximizing decks=1, total=1911505, unreachable=148329. Arithmetic: 1911505/362880 rounds to 5.268 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 9 cards there are 148,329 such unreachable decks (= A000255(8)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-9] The displayed count is 148329; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(8)=148329. The preimage proof supplies the link to unreachable decks. - CONFIRMED | Longest game 38 flips OEIS A000375 Decks that last that long 1 OEIS A123398 Average game 6.109 flips total ÷ 3,628,800 Total flips, all deals 22,169,434 the new sequence Unreachable decks 1,468,457 A000255(9) | git show f5e5f84f34:public/strata/topswops-machine/index.html ; git show f5e5f84f34:research/topswops/verify.mjs ; https://oeis.org/A000375/internal ; https://oeis.org/A123398/internal ; https://oeis.org/A000255/internal | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [stats-10] The rendered stat cards and recreated enumeration agree: max=38, maximizing decks=1, total=22169434, unreachable=1468457. Arithmetic: 22169434/3628800 rounds to 6.109 flips. Definitions and catalogued columns agree with OEIS. The n=10 values are accurate even though the ordinary UI reads them from STAGED. - CONFIRMED | For 10 cards there are 1,468,457 such unreachable decks (= A000255(9)). | git show f5e5f84f34:public/strata/topswops-machine/index.html ; https://oeis.org/A000255/internal ; git show f5e5f84f34:oversight/oeis/topswops-total-flips/A000255-comment.txt | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-count-10] The displayed count is 1468457; independently evaluating "a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1" gives A000255(9)=1468457. The preimage proof supplies the link to unreachable decks. - CONFIRMED | No card sits in its own place except possibly the top | git show f5e5f84f34:public/strata/topswops-machine/index.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-generated-signature] The sampler rejects any deck satisfying "a[j] === j + 1" for j>=1. Generated examples in the page probe and the preimage proof support the displayed signature. - CONFIRMED | no flip can produce this deck | git show f5e5f84f34:public/strata/topswops-machine/index.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [eden-generated-unreachable] The sampler's no-fixed-point condition exactly excludes flip preimages. A k-flip must end with q(k)=k; the shown deck has no such k>1. The page probe exercised the control for each n=2..10. - CONFIRMED | recomputed live in your browser — matches | git show f5e5f84f34:public/strata/topswops-machine/index.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [badge-match] The match guard compares "live.max === st[0]", "live.champ === st[1]", "live.total === st[2]" and "live.garden === st[3]". Re-created n=2..9 results agree in all four fields and emit the quoted badge. - CONFIRMED | histogram shown for n ≤ 9 | git show f5e5f84f34:public/strata/topswops-machine/index.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [histogram-limit] "if (!hist)" displays the quoted message, and only n<=9 supplies hist through the ordinary UI. The n=10 probe has the offline badge and no live histogram. - CONFIRMED | The ace surfaced. Done in | git show f5e5f84f34:public/strata/topswops-machine/index.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [step-finished] The terminal branch is guarded by "if (after[0] === 1)". Driving the champion deck yields exactly "The ace surfaced. Done in 16 flips." after 16 legal reversals. - CONFIRMED | The ace is already on top — 0 flips | git show f5e5f84f34:public/strata/topswops-machine/index.html | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [initial-zero] newDeal resets "stepsTaken = 0" and displays this only under "if (current[0] === 1)". The stated rule halts immediately in that case. The terminal-deck probe also reports zero flips. - CONFIRMED | And every game length, from zero flips up to the longest, is reached by some deck | git show f5e5f84f34:research/topswops/verify.mjs | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [film-all-lengths] The verifier passed "distinct flip-counts = M+1, n=1..10". There is also a general argument: follow a longest terminating game with M steps; its successive states require M,M-1,...,0 remaining flips. Every intermediate length is therefore attained for any n. - CONFIRMED | When a check finds something false, the page says what changed and when. | git show f5e5f84f34:assay/README.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [site-corrections] The documented rule is "add a dated Corrected YYYY-MM-DD: ... line on the page for what was false when written". The pinned neighboring the-extent source supplies a concrete positive control, "Corrected 2026-09-28", followed by six changes. Read as the published correction process, not a guarantee that no undiscovered errors remain. - CONFIRMED | (added) | https://artwaste.land/og/topswops-machine.png | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [added-og-size] The fetched PNG IHDR is exactly 1200 by 630 pixels. Kept byte count, SHA-256 and dimensions in evidence/og-probe.json. Add this omitted metadata claim to the source record; the image itself was removed after inspection. - CONFIRMED | (added) Nothing here may lie about anything real; that rule never bends. | git show f5e5f84f34:WAKE.md | Checker re-read at f5e5f84f34, retained from research/assay-line/queue-1014c/topswops-machine/N2-codex.md: [added-site-rule] public/media/plain-button.js:45 displays this policy. WAKE.md:17 calls its two rules "these never bend", and :20 says "It must never lie about anything real." This is a stated rule, not an assertion that every existing sentence is already error-free. Add the omitted policy statement to the source record. ## Findings - [fixed] X1: Replaced the absolute need-to-run claim with what the machine computes and the fixed-point test; added and mirrored the dated Corrected line. - [fixed] X2: Qualified the frontmatter dek to exhaustive browser enumeration for the selected size from 2 to 9 cards; record only. - [fixed] X3: Qualified the markdown body to selected-size browser enumeration and identified the stored ten-card statistics and precomputed table; record only. - [fixed] X4: Qualified all three universal metadata promises to live n=2..9 statistics and a precomputed table; record only. - [dated] X5: Refreshed Article dateModified from 2026-06-24 to 2026-10-14. Metadata-only exception: the Corrected lines date this revision, so no extra Updated line was added. - [fixed] X6: Changed VideoObject uploadDate from 2026-07-09 to 2026-06-25 using the exact-path first-addition commit; record only. - [fixed] X7: Replaced the unconditional completed-browser-play sentence with explicit live 2..9 and stored 10-card modes; record only. - [fixed] X8: Corrected the histogram legend from tallest to rightmost for the longest games, stated that height means frequency, and gave nonempty bins a 2px minimum. Added and mirrored the dated Corrected line. - [open note:417217] X9: Added beginning with 2 to the Euler interpretation in the page and the film source, including its source comment, and added a visible clarification beside the film. The existing public/strata/topswops-machine/film.mp4 still has the old caption because rendering or re-encoding media is forbidden for this task. The media finding remains open pending a board-issued note; no note id has been invented. - [fixed] X10: Replaced the calibration assurance with its scope and the separate per-term total-sum coverage link; record only. - [fixed] X11: Replaced reproduce it all with engine checks including totals n=1..11 and separate staged checks; record only. - [fixed] X12: Removed the every-number claim and nonexistent ten-card enumeration request, stating the actual live and stored ranges; record only. - [fixed] X13: Limited live OEIS calibration to the selected n=2..9 and identified the larger values as precomputed; record only. - [fixed] X14: Replaced three general proofs with three finite cross-checks and their exact ranges, keeping the general proof separate; record only. - [dated] X15: Changed the superseded Zenodo staging status to the issued deposit, retaining the distinct OEIS route. Added one Updated 2026-10-14 line and mirrored it in markdown.