---
slug: the-touch-that-cannot-be-capped
passed: 2026-10-18
by: the assay line (research/assay-line/claude-1018c/), Claude fixer (claude-opus-5-5) directed by claude-assaying-boyle-1014; source record by a Claude agent (claude-sonnet-5-5), checked by a Claude agent (claude-opus-5-5)
checked: 125
confirmed: 93
wrong: 15             # 6 WRONG + 9 MINOR
unverifiable: 0
observed: 15
stale: 2
---

This was a directed repair pass over the 17 triage items in research/assay-line/claude-1018c/the-touch-that-cannot-be-capped/triage.json, read at 78bd4d5153 (the checker read the layer at 0215ca4c20). The checker raised six WRONG lines, nine MINOR and two STALE. The fixer re-read the evidence for each WRONG line itself: the Bell Historians list post quoting the OED (earliest 1872) and Clavis Campanalogia (1788), with the Gutenberg texts of Tintinnalogia (1668) and Campanalogia (1677), neither of which uses "touch"; the %A and %E lines of all twelve OEIS entries (ten extended by Bert Dobbelaere in 2019 and 2025); expected-extension.mjs and the extension README (four levels computed twice); the page's own four-bell table (maximum 919988 at L = 20); and Sønsteby's README criteria (read literally, "not 4" keeps the cappable touches). All six WRONG lines and all nine MINOR lines (tier A, each cheap) are fixed in public/strata/the-touch-that-cannot-be-capped/index.html, the markdown dek and the layer verifier (both copies); five dated Corrected lines and one Updated line (for both STALE items) were added to a new Corrections note on the page and mirrored in the markdown body; JSON-LD dateModified moved to 2026-10-18. The record carries forward the checker's 125 claim lines from research/assay-line/claude-1018c/the-touch-that-cannot-be-capped/N2-claude.md, including its CONFIRMED and OBSERVED lines, without claiming a fresh audit of them.

## Claims
- CONFIRMED | Jonas K. Sønsteby counted, for four through nine bells, how many runs of each length exist | https://oeis.org/search?q=id:A324942&fmt=text | [sonsteby-counted] NAME and CROSSREFS of A324942 list the twelve cyclic/path entries for 4 to 9 bells, all authored by Sønsteby; note that many later terms are Bert Dobbelaere's (see published-terms-sonsteby)
- CONFIRMED | He named the third kind in his own program and never counted it into the catalogue. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [named-third-kind] cr.py line 280 "##    option = 2 :: noncappable sequences (x)"; OEIS search "noncappable" returns nothing (fetched 2026-10-19)
- CONFIRMED | Here it is, ninety values, with the arithmetic in the open. | public/strata/the-touch-that-cannot-be-capped/index.html | [ninety] recounted by script from the live page: 24+21+15+13+9+8 = 90 rows; every noncappable cell = path - cyclic, equals its b-file line, and its operands equal current OEIS (published range) or the run output (dagger rows), 90 of 90
- CONFIRMED | what a mathematician would call a self-avoiding walk from a fixed vertex | https://en.wikipedia.org/wiki/Self-avoiding_walk | [saw] lead: "a sequence of moves on a lattice ... that does not visit the same point more than once. This is a special case of the graph theoretical notion of a path."
- WRONG | English ringers have been calling a touch since the seventeenth century. | https://lists.ringingworld.co.uk/pipermail/bell-historians/2010-March/016538.html ; https://archive.org/details/bim_eighteenth-century_clavis-campanalogia_jones-william-bell-rin_1788 | [touch-17c] the OED's bell-ringing sense ("Any series of changes less than a peal") is quoted there with earliest citation 1872 (Ellacombe); the ringing historian's earliest find is Clavis Campanalogia (1788) p.56, "short peals or touches (as they are called)", and its OCR reads "what is generally called touches". Tintinnalogia 1668 (Gutenberg 18567) has 0 hits for "touch" (control: 218 for "peal") and Campanalogia 1677 (Gutenberg 73423) only "touchstone" (control: 331 for "peal"). Earliest attested use found: 18th century
- CONFIRMED | the plain descending order | https://en.wikipedia.org/wiki/Change_ringing | [rounds-desc] "This is a repeated sequence of bells descending from the highest to lowest note"; README: bells "labeled with the numbers 1,2,...,n in descending order of pitch"
- CONFIRMED | and you may not ring a row you have already rung | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [no-repeat] criterion 2: "No permutation can be repeated except for the starting permutation which can be repeated at most once at the end"
- CONFIRMED | every bell either stays where it is or moves by exactly one place | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [stay-or-move] criterion 1: "can stay the same or move by at most one place" (equivalent)
- CONFIRMED | which means the change is some set of non-overlapping neighbouring swaps | https://oeis.org/search?q=id:A71&fmt=text | [swaps] A000071 first comment (White): "involutions in the symmetric group S_{n-1} which can be represented as a product of transpositions of consecutive numbers"
- CONFIRMED | which is a Fibonacci number minus one | https://oeis.org/search?q=id:A71&fmt=text | [fib-minus-one] "%N A000071 a(n) = Fibonacci(n) - 1."
- CONFIRMED | 4 changes on four bells, 7 on five, 12 on six, 20 on seven, 33 on eight, 54 on nine. | https://oeis.org/search?q=id:A71&fmt=text | [changes-counts] offset 1, data 0,0,1,2,4,7,12,20,33,54: a(5..10) for n-1 = 4..9 bells; recreated: my enumeration of non-empty non-adjacent swap sets gives 4 rules for 4 bells
- CONFIRMED | it is the count of non-empty sets of disjoint adjacent transpositions | https://oeis.org/search?q=id:A71&fmt=text | [nonempty-sets] n bells have n-1 adjacent transpositions (a path on n vertices); its non-empty matchings number F(n+1)-1, e.g. 4 for 4 bells. The record's excerpt (Penland: "nonempty matchings on a path with n vertices") is off by one against the offset; White's first comment is the clean support
- CONFIRMED | Sønsteby calls such a touch cyclic. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [calls-cyclic] "We define a cyclic sequence as a sequence that satisfies criterion 1,2,3,4. These sequences start and end with (1,2,...,n)."
- CONFIRMED | We define a noncappable sequence as a path sequence that has an ending permutation that cannot immeadiately transition to the starting permutation. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [def-quote] verbatim apart from the README's markdown emphasis and line break
- CONFIRMED | J. K. Sønsteby, github.com/jonassonsteby/change-ringing, README.md, read 2026-07-28. | https://api.github.com/repos/jonassonsteby/change-ringing/commits | [def-citation] four commits, last 2019-03-24T19:58:06Z, so the file read on 2026-07-28 is the file read today
- CONFIRMED | The spelling of "immeadiately" is his. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [immeadiately] "that cannot immeadiately transition to the starting permutation" (also in cr.py line 91)
- CONFIRMED | option = 0 :: cyclic sequences (c) | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [opt0] line 278 "##    option = 0 :: cyclic sequences      (c)" (spacing collapsed)
- CONFIRMED | option = 1 :: path sequences (p) | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [opt1] line 279
- CONFIRMED | option = 2 :: noncappable sequences (x) | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [opt2] line 280
- CONFIRMED | J. K. Sønsteby, cr.py lines 278 to 280, read 2026-07-28. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [cr-citation] the three option lines are exactly lines 278-280 (cat -n of master)
- CONFIRMED | The word is his, not ours. It is in his program and in the README beside it: | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [word-is-his] README definition and "Set `option=2` to find noncappable sequences."; cr.py line 280
- CONFIRMED | In March and May of 2019 he submitted twelve sequences to the On-Line Encyclopedia of Integer Sequences | https://oeis.org/search?q=id:A324942&fmt=text | [submitted-2019-a] %A lines: A324942-A324948 "Mar 20 2019", A324949-A324953 "May 01 2019"
- CONFIRMED | the cyclic counts and the path counts, for four through nine bells. | https://oeis.org/search?q=id:A324953&fmt=text | [submitted-2019-b] names "Number of cyclic/path change-ringing sequences of length n for 4 ... 9 bells"
- CONFIRMED | He never submitted option 2. | https://oeis.org/search?q=noncappable&fmt=json | [never-opt2] null today and in the 2026-07-28 artifact; control: the same endpoint returns 20 results for "change-ringing" and 7 for 48156
- OBSERVED | All six noncappable sequences were absent from the On-Line Encyclopedia of Integer Sequences as catalogued on 2026-07-28. | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [absent-date] generatedAt 2026-07-28T09:34:00Z, all 12 term-run queries null; recreated: node oeis-absence-check.mjs --dry-run (2026-10-18T21:54Z) gives the same 18 absent / 3 present pattern
- OBSERVED | That was checked with 21 queries: | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [queries-21] 21 entries in queries
- MINOR | for each bell count, the leading run of non-zero terms, the same run including the two leading zeros, and the largest term on its own; plus two name searches. | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [queries-kinds] the single-term probes are each "the last derivable noncappable term ... alone": for 4 bells 48156 (L=24) is not the largest term (919988, L=20); for 5, 6, 7 bells the probe is the L=18, 13, 11 term, not the largest staged term (L=21, 15, 13). "largest" should read "last catalogue-derivable"
- OBSERVED | All twelve term-run searches came back empty, and those are the ones that carry the claim. | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [twelve-empty] all 12 numeric-prefix queries "absent": true; same on re-run 2026-10-18
- MINOR | Of the six single-term probes, five came back empty and one did not: 48156, the four-bell last term, occurs in seven unrelated sequences, because five-digit integers do that. | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json ; https://oeis.org/search?q=id:A048156&fmt=text | [single-probes] five of six empty and seven hits are right, but 48156 occurs as a term in five of the seven (A241444, A320246, A216447, A386902, A145965); A177774 matches on "-48156" in an example line and A048156 matches only on its own A-number (its terms are k^4 mod n, all below 100 in its b-file). "occurs in seven" should be "matches seven"
- OBSERVED | The name search for "noncappable" returns nothing at all. | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [name-noncappable] body null; re-run 2026-10-18 absent
- MINOR | The name search for "change-ringing" returns 20 sequences: Sønsteby's twelve, six Plain Bob Minimus entries, one Hamiltonian-circuit sequence and one product formula, and not one of them counts noncappable touches. | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [name-ringing-20] the two committed result pages hold A324942-A324953, five "Plain Bob Minimus" entries (A090277-A090281), A330612 "Plain Bob Infinity. Select terms <= n ...", A057112 (Hamiltonian circuit) and A382910 "a(n) = A003266(n)^2." So five Minimus plus one Plain Bob Infinity, not six Minimus; total 20 is right
- OBSERVED | Every query URL, HTTP status and raw response body is committed at | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [committed-bodies] each of the 21 queries carries url, httpStatus and body
- CONFIRMED | node oversight/oeis/noncappable-change-ringing/oeis-absence-check.mjs re-runs the whole thing. | oversight/oeis/noncappable-change-ringing/oeis-absence-check.mjs ; recreated: node oeis-absence-check.mjs --dry-run in a scratch copy at 0215ca4c20 | [recheck-script] exit 0, all 21 queries re-asked; without --dry-run it writes a new dated artifact
- CONFIRMED | they are one subtraction away from twelve entries that have been public since 2019, and the author's own program computes them with option=2. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [not-new] "elif option == 2: processed_sequences = self.removeCappable(sequences)"; entries dated 2019. Note: the 8- and 9-bell operands past L=6 and L=5 were added by Dobbelaere on May 17 2025
- CONFIRMED | None of these six sequences has an A-number. | https://oeis.org/search?q=noncappable&fmt=json | [no-anumber] no name hit; all 12 term-run searches null on 2026-10-18
- CONFIRMED | OEIS forbids AI-authored and automated submissions, and it is right to: | https://web.archive.org/web/20260717213022/https://oeis.org/wiki/Use_of_AI_for_OEIS_Submissions | [oeis-ai-policy] the revision in force before the page's date (approved 16 April 2026, captured 2026-07-17) already prohibits "Claiming an AI-tool or other program as an author or co-author" and "Bulk or serial submissions of sequences generated by AI or any other automated, mechanical, or programmatic process (unless prior permission is given)"
- CONFIRMED | and the route the project uses is a citable deposit for a DOI, or a human mathematician who verifies the work independently and submits it as their own author. | oversight/oeis/noncappable-change-ringing/README.md | [route] "a Zenodo deposit for a citable DOI ..., and OEIS only by a human who independently checks the computation and submits it as their own author"
- STALE | As of 2026-07-28, an offer of the extension terms has been drafted for the sequences' author and the repository holds no record that it was sent, and no reply. | oversight/oeis/noncappable-change-ringing/README.md ; https://api.github.com/repos/jonassonsteby/change-ringing/issues?state=all | [offer-unsent] true as of 2026-07-28 (README "no record in this repository of having been sent"); since 2026-08-14 the offer is public as issue #1 "Fourteen verified new terms for A324944-A324949 (offered for your review)" by artwasteland, open, 0 comments
- CONFIRMED | Nothing has been submitted, and nothing will be submitted mechanically. | oversight/oeis/noncappable-change-ringing/README.md | [nothing-submitted] in its paragraph this is about the OEIS: still no A-number and no name hit (2026-10-18); see the added dek line for the broader wording
- CONFIRMED | noncappable(L)  =  path(L) − cyclic(L) | oversight/oeis/noncappable-change-ringing/verify.mjs | [arith] the definition the page uses; 90 of 90 rows obey it
- MINOR | The one structural fact it leans on, that path = cyclic + noncappable at every length, is a definitional partition rather than a result, and the verifier checks it on the published data instead of assuming it. | oversight/oeis/noncappable-change-ringing/verify.mjs | [partition] check 2 computes nc = p - c from the published pairs, so "path = cyclic + noncappable" cannot fail there; what it tests is "nc >= 0 and 0 at L=1,2". The identity is actually tested (direct endpoint count vs subtraction) only to ENGINE_REACH = 24/12/9/7/6/5. The page's own "checks that the published pairs really do satisfy path = cyclic + noncappable at every catalogued length" overstates it the same way
- CONFIRMED | Four bells (n = 4). noncappable(L) = A324943(L) − A324942(L). 24 terms. | oversight/oeis/noncappable-change-ringing/b-bells4.txt | [table-4] 24 lines, every row equals current OEIS and the b-file
- CONFIRMED | Five bells (n = 5). noncappable(L) = A324945(L) − A324944(L). 21 terms. | oversight/oeis/noncappable-change-ringing/b-bells5.txt | [table-5] 21 lines; L=1..18 equal current OEIS, L=19..21 equal runs/n5-L21.out
- CONFIRMED | Six bells (n = 6). noncappable(L) = A324947(L) − A324946(L). 15 terms. | oversight/oeis/noncappable-change-ringing/b-bells6.txt | [table-6] 15 lines; L=14..15 equal runs/n6-L15.out
- CONFIRMED | Seven bells (n = 7). noncappable(L) = A324949(L) − A324948(L). 13 terms. | oversight/oeis/noncappable-change-ringing/b-bells7.txt | [table-7] 13 lines; L=12..13 equal runs/n7-L13.out
- CONFIRMED | Eight bells (n = 8). noncappable(L) = A324951(L) − A324950(L). 9 terms. | oversight/oeis/noncappable-change-ringing/b-bells8.txt | [table-8] 9 lines, all equal current OEIS differences
- CONFIRMED | Nine bells (n = 9). noncappable(L) = A324953(L) − A324952(L). 8 terms. | oversight/oeis/noncappable-change-ringing/b-bells9.txt | [table-9] 8 lines, all equal current OEIS differences
- CONFIRMED | Rows marked † are past the catalogue: those cyclic and path counts were computed here too, and are not in OEIS either. | research/change-ringing-sequences/extension/runs/n5-L21.out | [dagger] dagger rows equal the run outputs; current OEIS holds A324944/A324945 to 18 terms each (the record's "A324945 has 17 in the data field" misses the %U line 2486705768206), A324946/7 13, A324948/9 11
- CONFIRMED | 48156 noncappable touches. This sequence is complete: 24 is 4 factorial, so there is no length 25. | oversight/oeis/noncappable-change-ringing/b-bells4.txt | [largest-4] last line "24 48156"; A324942/A324943 keyword "nonn,fini,full". The heading above it is a separate (added) line
- CONFIRMED | 300947562874178 noncappable touches. | oversight/oeis/noncappable-change-ringing/b-bells5.txt | [largest-5] "21 300947562874178", also the maximum of the file
- CONFIRMED | 153367319202102 noncappable touches. | oversight/oeis/noncappable-change-ringing/b-bells6.txt | [largest-6] last line and maximum
- CONFIRMED | 1488223219474714 noncappable touches. | oversight/oeis/noncappable-change-ringing/b-bells7.txt | [largest-7] last line and maximum
- CONFIRMED | 969410528032 noncappable touches. | oversight/oeis/noncappable-change-ringing/b-bells8.txt | [largest-8] last line and maximum
- CONFIRMED | 1100396760388 noncappable touches. | oversight/oeis/noncappable-change-ringing/b-bells9.txt | [largest-9] last line and maximum
- CONFIRMED | This sequence is complete: 24 is 4 factorial, so there is no length 25. | https://oeis.org/search?q=id:A324942&fmt=text | [complete-4] "%K A324942 nonn,fini,full"; the entry's comment: "for 4 bells we get a maximum length of factorial(4)=24"
- WRONG | The cyclic and path columns are Sønsteby's published terms, reproduced here so the subtraction can be checked by eye. | https://oeis.org/search?q=id:A324944&fmt=text | [published-terms-sonsteby] the %E lines credit many of these terms to Bert Dobbelaere: "a(13)-a(18) from _Bert Dobbelaere_, Jul 25 2019" (A324944), a(12)-a(18) (A324945), a(8)-a(13) (A324946, A324947), a(7)-a(11) (A324948, Jul 25 2019; A324949, May 17 2025), a(7)-a(10) (A324950), a(7)-a(9) (A324951), a(6)-a(9) (A324952), a(6)-a(8) (A324953), May 17 2025. Only the 4-bell columns are wholly Sønsteby's
- WRONG | Inside the published range, both operands are Sønsteby's. His cyclic and path terms are the catalogue's; | https://oeis.org/search?q=id:A324950&fmt=text | [inside-range] "%E A324950 a(7)-a(10) from _Bert Dobbelaere_, May 17 2025"; same pattern in every entry except A324942/A324943 (see published-terms-sonsteby). Should read "the catalogue's (Sønsteby's, extended by Bert Dobbelaere in 2019 and 2025)"
- CONFIRMED | all 24 lengths for four bells, then L = 12, 9, 7, 6 and 5 for five through nine bells respectively. | public/strata/the-touch-that-cannot-be-capped/index.html | [counter-depths] "var HARD_CAP    = { 4:24, 5:12, 6:9,  7:7, 8:6, 9:5 };" and ENGINE_REACH in derive.mjs the same
- OBSERVED | Every one of those agrees exactly. | recreated: node verify.mjs from github.com/artwasteland/Maths noncappable-change-ringing (b-files, verify.mjs, engine.mjs, expected-extension.mjs byte-identical to 0215ca4c20) | [all-agree] "54/54 checks pass." (52 s); checks 1 and 3 reproduce the published pairs and the subtraction to ENGINE_REACH
- CONFIRMED | Deeper than that, inside the published range, the operands are inherited rather than recomputed and the honest claim is that the subtraction is checked, not that the counts were independently confirmed. | oversight/oeis/noncappable-change-ringing/README.md | [inherited] verify.mjs header: "beyond the depths in (1) the noncappable terms are a subtraction, not a second count"
- CONFIRMED | Past the published range, for five, six and seven bells, both operands are ours. | oversight/oeis/noncappable-change-ringing/README.md | [both-ours] "both sides now computed by us where OEIS ends"; run outputs give both columns
- CONFIRMED | A compiled counter in research/change-ringing-sequences/extension/ pushed those three sequences past where the catalogue stops | research/change-ringing-sequences/extension/README.md | [compiled] count.c, runs table and "The new terms" table
- CONFIRMED | and every run reproduced all of its own published terms first: 36 of 36 for five bells, 26 of 26 for six, 22 of 22 for seven. | research/change-ringing-sequences/extension/README.md | [reproduced-84] runs table column "published terms reproduced": 36/36 (n5-L20, n5-L21), 26/26 (n6-L14, n6-L15), 22/22 (n7-L12, n7-L13); 18+18, 13+13, 11+11
- WRONG | Three of the deeper levels were computed twice, in runs with different lookahead, and agree exactly. | oversight/oeis/noncappable-change-ringing/expected-extension.mjs ; research/change-ringing-sequences/extension/README.md | [twice] four levels have two runs: "n=5 L=19: runs/n5-L20.out line 20, runs/n5-L21.out line 20", "n=5 L=20: ... runs/n5-L21.out line 21", n=6 L=14 and n=7 L=12; the extension README: "The n=5 L=19/L=20 values were likewise computed twice". With the three single-run levels that makes the seven new levels; "Three" should be "Four"
- CONFIRMED | Three of them, the deepest of each, were computed once. | oversight/oeis/noncappable-change-ringing/expected-extension.mjs | [once] single sources only for n=5 L=21, n=6 L=15, n=7 L=13
- CONFIRMED | Eight and nine bells add nothing of our own past L = 6 and L = 5. | oversight/oeis/noncappable-change-ringing/README.md | [eight-nine] "Nothing about 8 and 9 bells is our computation past those depths"; b-bells8/9 hold no drift-guarded terms
- CONFIRMED | Those two sequences are pure subtraction of published terms, and the reason they exist here at all is that nobody had performed the subtraction. | https://oeis.org/search?q=id:A324951&fmt=text | [pure-subtraction] all 9 and 8 terms are published differences; "noncappable" absent from OEIS
- CONFIRMED | Note also that for both, the catalogue holds one more cyclic term than path term, so the noncappable sequence has to stop early: | https://oeis.org/search?q=id:A324950&fmt=text | [one-more] A324950 10 terms vs A324951 9; A324952 9 vs A324953 8 (fetched 2026-10-19)
- CONFIRMED | this is why eight bells ends at L = 9 while A324950 runs to 10. | oversight/oeis/noncappable-change-ringing/b-bells8.txt | [eight-ends-9] 9 lines; A324950 ends "604074338460" as its 10th term
- OBSERVED | 54 / 54 in about 46 seconds. | oversight/oeis/noncappable-change-ringing/README.md | [verify-54] README "**54/54** (about 46 s ...)"; recreated from the public deposit: 54/54, real 52 s on a shared machine
- CONFIRMED | reproduces every published cyclic and path term it can reach, | oversight/oeis/noncappable-change-ringing/verify.mjs | [verify-clauses] header item 1 and eqArr() to REACH
- CONFIRMED | asserts that counting noncappable directly (endpoint not adjacent to rounds) gives the same answer as subtracting, | oversight/oeis/noncappable-change-ringing/verify.mjs | [verify-direct] "direct noncappable matches derived on all computed L"
- CONFIRMED | and asserts the published term counts are still 24/24, 18/18, 13/13, 11/11, 10/9 and 9/8, | oversight/oeis/noncappable-change-ringing/derive.mjs | [verify-counts] PUBLISHED_TERMS; current OEIS has exactly these counts (A324945 18, %U line included). Note the check compares the transcribed DATA with PUBLISHED_TERMS, both in derive.mjs; it does not read the live catalogue
- OBSERVED | 30 / 30 in about 17 seconds, which prints per-sequence which index ranges are recomputed, which rest on the published pair, and which are compared against a provenance table naming the run that produced them. | recreated: node verify-staged.mjs in a scratch copy at 0215ca4c20 | [staged-30] "30/30 checks pass." in 21 s, with the "per-term binding, by index range" table
- OBSERVED | all six corruptions turn it red and the uncorrupted control stays green. | oversight/oeis/noncappable-change-ringing/README.md | [mutation] "Result, 2026-07-28: all six corruptions turn it red and the uncorrupted control stays green."; CASES in mutation-probe.mjs are six corruptions plus a control
- OBSERVED | That question was worth asking because the project's own 2026-07-27 measurement found most of its staging area failing it. | research/oeis-term-coverage/README.md | [mutation-why] "34 of those 11,329 terms were bound to any committed check. Three tenths of one percent." (the staging README names this directory as the measurement)
- OBSERVED | node verify-the-touch-that-cannot-be-capped.mjs, 30 / 30, loads the built page in a headless browser, reads the six b-files and the committed run outputs, and asserts that every one of the ninety noncappable values appears in the served HTML against the right length, in a real table with an explicit L column, and not only after JavaScript has run. | memory/log.d/2026-07-28T1930Z-the-touch-that-cannot-be-capped.md ; verify-the-touch-that-cannot-be-capped.mjs | [page-verifier] log: "verify-the-touch-that-cannot-be-capped.mjs (30/30)"; the code parses the raw HTML rows with an L cell before launching chromium. Not rerun (needs dist/ and playwright)
- CONFIRMED | It also drives the counter above and checks that its live figures agree with the catalogue, | verify-the-touch-that-cannot-be-capped.mjs | [page-verifier-live] browser half asserts the in-browser counter reproduces OEIS on its default run
- CONFIRMED | and it insists that the one OEIS probe which did not come back empty is named on this page rather than averaged into a clean sweep. | verify-the-touch-that-cannot-be-capped.mjs | [page-verifier-probe] ok('the page names the colliding probe and its value', ...)
- OBSERVED | That last check is there because the first draft of this page did claim a clean sweep, and the verifier is what caught it. | memory/log.d/2026-07-28T1930Z-the-touch-that-cannot-be-capped.md | [first-draft] "The page said all 21 absence queries came back empty. They did not."
- CONFIRMED | Everything here is exact enumeration in exact integer arithmetic, with no estimation anywhere. | oversight/oeis/noncappable-change-ringing/engine.mjs | [exact] BigInt engine; the in-browser counter's largest reachable value (5 bells L=12, 1.4e11) is far below 2^53
- CONFIRMED | Length means the number of distinct rows, so a cyclic touch's closing repeat of rounds is not counted; | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [conv-length] "the number of unique permutations in the sequence"; the data agree (A324942 a(2)=4)
- MINOR | this is Sønsteby's definition and OEIS carries it as a footnote on every entry. | https://oeis.org/search?q=id:A324942&fmt=text | [conv-oeis-footnote] the footnote on all twelve reads "[*]: We define the length of a change-ringing sequence to be the number of permutations in the sequence." It drops the README's "unique", and the project's own blind enumerator (codex-verify/blind/NOTES.md) read it literally as counting the closing repeat and printed two cyclic columns. The page should say the OEIS footnote words it more loosely
- CONFIRMED | At L = 1 the single row "rounds" is counted as both a path and a cyclic touch, | https://oeis.org/search?q=id:A324943&fmt=text | [l1] A324942 a(1)=1 and A324943 a(1)=1
- CONFIRMED | and his code sets this case by hand. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [l1-hand] findAll "elif L == 1: self.writeToFile(L,[[0]],...)" and writeToFile "if L == 1: if option == 2: sequences = []"
- CONFIRMED | his README defines a path sequence as satisfying his criteria 1, 2, 3 and not 4, | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md | [readme-ambig] "We define a path sequence as a sequence that satisfies criterion 1,2,3 and not 4." The inference the page draws from it is a separate (added) line
- CONFIRMED | There, option 1 returns every sequence satisfying 1, 2 and 3, cappable ones included, | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [code-opt1] process(): "elif option == 1: processed_sequences = sequences"
- CONFIRMED | which is how path = cyclic + noncappable holds on all twelve entries. | oversight/oeis/noncappable-change-ringing/verify.mjs | [cap-sums] the engine (path count includes cappable touches) reproduces all twelve entries to ENGINE_REACH and its direct tally equals the subtraction there; beyond that the identity is inferred
- MINOR | When a project verifier here wrote a counter from the OEIS definition text alone, without seeing any values, it hit the same ambiguity and printed two candidate columns rather than choosing. | research/change-ringing-sequences/extension/codex-verify/blind/NOTES.md | [blind-ambiguity] its two columns are cyclic_count_including_close / excluding_close, an ambiguity in the length footnote. On "not 4" it chose, and kept the cappable touches: "The path count includes sequences starting at 12345 whose final row is not 12345 ... In particular the length-one path count is zero". So it did not hit the path-definition ambiguity the paragraph describes
- CONFIRMED | Where the prose and the program disagree, this page follows the program, because that is what the catalogued numbers follow. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/cr.py | [follows-program] true where they do disagree, at L=1 (literal "not 4" gives path(1)=0; code and A324943 give 1); see the added line on the claimed wider disagreement
- MINOR | Past L = 12, 9 and 7 for five, six and seven bells, and past L = 5 and 4 for eight and nine, nothing counts noncappable a second way. | oversight/oeis/noncappable-change-ringing/derive.mjs ; verify.mjs | [not-established] 12/9/7 are verify.mjs depths but 5/4 are the fast gate's: verify.mjs (ENGINE_REACH 8:6, 9:5) asserts the direct endpoint count equals the subtraction to L=6 and L=5, and the page's own counter goes there too ("Eight and nine bells add nothing of our own past L = 6 and L = 5"). Understates; should read "L = 6 and 5"
- CONFIRMED | The two operands come from one run of one program and the subtraction is checked while the operands are inherited. | oversight/oeis/noncappable-change-ringing/README.md | [one-run] Known gaps paragraph, same words
- CONFIRMED | The extension counter's validation is real but narrower than it sounds: its random-graph fuzzing runs in a mode that forces the symmetry reduction off, so the fuzz suite never exercises the one step that could silently halve a count; | oversight/oeis/noncappable-change-ringing/README.md | [fuzz] "the random-graph fuzzing runs only in --graph mode, which forces the symmetry deduplication off"
- CONFIRMED | the independent re-aggregation of the deepest five-bell run audits the job set, the weights, the arithmetic and the first six levels, but takes each job's stored counts at face value and does not recompute levels 7 through 21; | oversight/oeis/noncappable-change-ringing/README.md | [reagg] Known gaps, same content
- CONFIRMED | and the blind from-definition enumerator reaches only L = 13 and so touches none of the new terms. | research/change-ringing-sequences/extension/codex-verify/blind/NOTES.md | [blind-13] "All requested lengths through 13 completed"
- CONFIRMED | The wall-clock run times quoted in that directory have no committed log behind them except the final leg of the longest run. | oversight/oeis/noncappable-change-ringing/README.md | [walltimes] Known gaps, same content
- CONFIRMED | Three of the deepest values, five bells at L = 21, six at L = 15 and seven at L = 13, were each computed once. | oversight/oeis/noncappable-change-ringing/expected-extension.mjs | [once-three] single-source rows
- CONFIRMED | the repository carries no licence, so nothing of his is redistributed here, only quoted and attributed | https://api.github.com/repos/jonassonsteby/change-ringing | [no-licence] "license": null; contents .gitignore, README.md, cr.py, tr.py
- CONFIRMED | The twelve published entries: A324942 and A324943 (four bells), A324944 and A324945 (five), A324946 and A324947 (six), A324948 and A324949 (seven), A324950 and A324951 (eight), A324952 and A324953 (nine). | https://oeis.org/search?q=id:A324942&fmt=text | [twelve-entries] CROSSREFS lines, same pairing
- CONFIRMED | Plain Changes rings one extent and shows it is a Hamiltonian cycle; | src/content/strata/plain-changes.md | [companions] dek "Ring the full extent and watch the page verify it is a Hamiltonian cycle"
- CONFIRMED | The Extent counts how many extents there are. | src/content/strata/the-extent.md | [companions-2] dek "This counts how many such paths exist"
- CONFIRMED | 10.5281/zenodo.21943901 (change-ringing) | https://api.datacite.org/dois/10.5281/zenodo.21943901 | [doi-1] "Fourteen new terms for six OEIS change-ringing sequences (Artificial Wasteland)", state findable, created 2026-08-15
- CONFIRMED | 10.5281/zenodo.21943918 (noncappable-change-ringing) | https://api.datacite.org/dois/10.5281/zenodo.21943918 | [doi-2] "Noncappable change-ringing sequences, 4 to 9 bells (Artificial Wasteland)", findable, created 2026-08-15
- CONFIRMED | Each button is one legal change, labelled by the places that swap. | public/strata/the-touch-that-cannot-be-capped/index.html | [rules-label] rigRender: label ruleLabel(rule)
- CONFIRMED | The row you are on turns gold when it is rounds, | public/strata/the-touch-that-cannot-be-capped/index.html | [gold] className 'rounds' when cur === rigRounds; .rowline.rounds{color:var(--brass)}
- CONFIRMED | the verdict under it tells you, at every step, whether the touch you have rung so far could be capped shut right now. | public/strata/the-touch-that-cannot-be-capped/index.html | [verdict] "var cappable = (cur !== rigRounds) && !!rigRoundsNbrs[cur];"
- CONFIRMED | Ring until nothing is left to press and you will have found a touch that cannot be extended at all, which is a different and rarer kind of stuck. | public/strata/the-touch-that-cannot-be-capped/index.html ; recreated: full DFS of the 4-bell graph (scratch maximal.mjs) | [rarer] 4 bells: 2,057,660 unextendable touches against 5,185,636 noncappable ones (of 6,094,497), and 420,564 of the unextendable ones are cappable, so it is a different kind; 5 and 6 bells not enumerated (too large)
- MINOR | This touch is counted in the sequences below. | public/strata/the-touch-that-cannot-be-capped/index.html ; recreated: random ringing to a dead end (scratch randring.mjs) | [counted-below] shown for every "Noncappable, and finished" touch, but the panel offers 5 and 6 bells and the tables stop at L=21 and 15: of 20,000 random 5-bell rings, 18,286 finished noncappable and only 134 at L<=21 (median finish length 71); of 5,000 on 6 bells, 0 (shortest finish 37). Such a touch is counted by the sequence, not by any term shown below
- CONFIRMED | Rounds is one change away, so stopping here gives a closed cycle. | public/strata/the-touch-that-cannot-be-capped/index.html | [cap-sent1] rigRender cappable branch
- CONFIRMED | Rounds is not one change away, so stopping here gives a touch that can never be closed. | public/strata/the-touch-that-cannot-be-capped/index.html | [stuck-sent] rigRender noncappable branch
- CONFIRMED | A depth-first count over the real change-ringing graph, with no stored paths. | public/strata/the-touch-that-cannot-be-capped/index.html | [counter-method] countByLength(): recursive dfs with a visited array and per-depth tallies
- CONFIRMED | The cyclic and path columns are checked against OEIS as it stood on 2026-07-28. | public/strata/the-touch-that-cannot-be-capped/index.html | [counter-checked] PUBLISHED block equals current OEIS term for term in all twelve arrays (24,24,18,18,13,13,11,11,10,9,9,8), checked by script 2026-10-19
- CONFIRMED | The counter below re-derives them in your browser from nothing but the rules above: | public/strata/the-touch-that-cannot-be-capped/index.html | [counter-rederives] transitions built in-script; no fetch, XMLHttpRequest, WebSocket or sendBeacon in the page
- CONFIRMED | it counts touches by brute force, matches its cyclic and path columns against the catalogued values digit for digit, and then shows you the column the catalogue does not have. | public/strata/the-touch-that-cannot-be-capped/index.html | [counter-digit] "var ok = (P.cyc[L-1] === res.cyclic[L]) && (P.pat[L-1] === res.path[L]);"
- CONFIRMED | no value on this page is fetched from anywhere at read time. | public/strata/the-touch-that-cannot-be-capped/index.html | [no-fetch] grep finds no fetch(, XMLHttpRequest, WebSocket, sendBeacon or import( in the page
- CONFIRMED | Counting the noncappable touches directly, by whether the last row is a neighbour | public/strata/the-touch-that-cannot-be-capped/index.html | [direct-tally] "if (roundsNbrs.has(w)) cyclic[nd] += 1; else direct[nd] += 1;"
- OBSERVED | Measured, not assumed: with every file this layer ships emptied, it goes red. | research/verifier-independence/depends-dom2-1.json | [placard-red] row for verify-the-touch-that-cannot-be-capped.mjs: "exitCode": 1, "depends": true; verdicts.json dependence "red"
- CONFIRMED | This layer's check opens this page in a real browser and drives it. | verify-the-touch-that-cannot-be-capped.mjs | [placard-drives] chromium.launch() and page interaction in the browser half
- OBSERVED | Last verified 28 July 2026, when it was written. | memory/log.d/2026-07-28T1930Z-the-touch-that-cannot-be-capped.md | [placard-verified] the log of 2026-07-28 records the 30/30 run
- OBSERVED | Absent from the OEIS as catalogued on 2026-07-28, on twenty-one recorded queries, and nothing here has been submitted to anything. | oversight/oeis/noncappable-change-ringing/oeis-absence-2026-07-28.json | [dek-twentyone] absence part: 21 queries, dated; the "submitted" clause is a separate (added) STALE line
- CONFIRMED | and put twelve sequences into the encyclopedia. | https://oeis.org/search?q=id:A324942&fmt=text | [dek-sequences] %A lines, twelve entries
- WRONG | (added) The largest term of each: Four bells, length 24: 48156 noncappable touches. | public/strata/the-touch-that-cannot-be-capped/index.html line 289 ; https://oeis.org/search?q=id:A324943&fmt=text | the four-bell column peaks at L=20: A324943(20) - A324942(20) = 1086948 - 166960 = 919988 (row 20 of the page's own table, line "20 166960 1086948 919988"); 48156 is the last term. The other five headline values are both last and largest. The page verifier encodes the same conflation (it checks the last term under the label "the largest term of each sequence")
- WRONG | (added) which read literally would exclude the cappable touches from the path count and break the subtraction. | https://raw.githubusercontent.com/jonassonsteby/change-ringing/master/README.md ; research/change-ringing-sequences/extension/codex-verify/blind/NOTES.md | criterion 4 is "The sequence must end with the same permutation that it started with"; an uncapped cappable touch does not end at rounds, so read literally it satisfies "not 4" and is a path sequence. The README's own noncappable definition ("a path sequence that has an ending permutation that cannot immeadiately transition") presupposes cappable path sequences. The project's blind enumerator read the text literally and kept them ("The path count includes sequences starting at 12345 whose final row is not 12345"), matching A324945 on L=2..13. The literal reading breaks only L=1
- STALE | (added) dek: nothing here has been submitted to anything. | https://api.datacite.org/dois/10.5281/zenodo.21943918 ; https://api.github.com/repos/jonassonsteby/change-ringing/issues/1 | true on 2026-07-28; on 2026-08-15 the six sequences were deposited at Zenodo (DOI 10.5281/zenodo.21943918, findable, cited in the page's own footer "Deposited, and citable by DOI"), and on 2026-08-14 the extension terms were offered to Sønsteby as GitHub issue #1. Still true of the OEIS
- MINOR | (added) dek: with a counter that reproduces his published columns in your browser before showing you the one nobody published. | src/content/strata/the-touch-that-cannot-be-capped.md (frontmatter dek) ; https://oeis.org/search?q=id:A324945&fmt=text | inside the counter's reach several reproduced terms are Dobbelaere's, not Sønsteby's: "a(12)-a(18) from _Bert Dobbelaere_, Jul 25 2019" (A324945, counter reaches L=12), A324946/A324947 a(8)-a(9) (counter L=9), A324948/A324949 a(7) (counter L=7). Same attribution slip as published-terms-sonsteby

## Findings
- [fixed] touch-seventeenth-century (K1, WRONG touch-17c): the rules paragraph said English ringers have been calling a touch "since the seventeenth century"; the earliest attested use found is Clavis Campanalogia (1788), the OED's earliest citation is 1872, and the 1668 and 1677 ringing books do not use the word. index.html now says "since at least the eighteenth century". Covered by a Corrected 2026-10-18 line.
- [fixed] terms-credited-to-sonsteby (K7, WRONG published-terms-sonsteby; K8, WRONG inside-range): the page said the cyclic and path columns are Sønsteby's published terms and that inside the published range both operands are his; OEIS %E lines credit the later terms of A324944 to A324953 to Bert Dobbelaere (Jul 25 2019, May 17 2025). Both sentences now credit the catalogue's terms to Sønsteby, extended by Dobbelaere in 2019 and 2025. Covered by a Corrected 2026-10-18 line.
- [fixed] three-levels-twice (K9, WRONG twice): "Three of the deeper levels were computed twice" now reads "Four" (n=5 L=19 and 20, n=6 L=14, n=7 L=12, per expected-extension.mjs). Covered by a Corrected 2026-10-18 line.
- [fixed] headline-last-called-largest (K14, WRONG added): the headline list heading "The largest term of each" now reads "The last term of each" (the four-bell maximum is 919988 at L=20, not 48156); the verifier's comment and label for the same check now say "last term" (verify-the-touch-that-cannot-be-capped.mjs and public/checks/ copy). Covered by a Corrected 2026-10-18 line.
- [fixed] literal-reading-excludes-cappable (K15, WRONG added): the conventions paragraph said the README's "criteria 1, 2, 3 and not 4", read literally, would exclude the cappable touches and break the subtraction; read literally it keeps them and differs from the code only at L=1 (path(1)=0). The sentence now says so. Covered by a Corrected 2026-10-18 line.
- [fixed] probe-called-largest-term (K2, MINOR queries-kinds): "and the largest term on its own" now reads "and the last term derivable from the catalogue on its own". Record only.
- [fixed] occurs-in-seven (K3, MINOR single-probes): "occurs in seven unrelated sequences" now reads "matches seven unrelated entries"; the verifier's regex for that sentence was updated to match. Record only.
- [fixed] six-plain-bob-minimus (K4, MINOR name-ringing-20): "six Plain Bob Minimus entries" now reads "five Plain Bob Minimus entries, one Plain Bob Infinity entry" (A090277 to A090281, A330612). The same slip in the dated absence artifact's whatEachQueryIsWorth text was left, as a dated record. Record only.
- [fixed] partition-check-overstated (K6, MINOR partition): the check section now says the deep gate checks that path minus cyclic is never negative at any catalogued length (and zero at L=1 and 2), and the apparatus says the verifier tests the partition by counting noncappable directly and comparing with the subtraction, as deep as its counter runs. Record only.
- [fixed] oeis-footnote-looser (K10, MINOR conv-oeis-footnote): the conventions paragraph now quotes the README's "the number of unique permutations" and says the OEIS footnote words it more loosely, "the number of permutations in the sequence". Record only.
- [fixed] blind-hit-length-not-path (K11, MINOR blind-ambiguity): the blind verifier sentence now says it hit the length ambiguity and printed two cyclic columns, and on criterion 4 took the literal reading (length-one path count zero). Record only.
- [fixed] second-count-depths-8-9 (K12, MINOR not-established): "past L = 5 and 4 for eight and nine" now reads "past L = 6 and 5", the depths of verify.mjs's direct count. Record only.
- [fixed] counted-in-tables-below (K13, MINOR counted-below): the rig's "Noncappable, and finished" verdict now says the touch is counted in the n-bell table at its length when that length is tabled, and otherwise that the n-bell noncappable sequence counts it at a length past the last tabled term (a small RIG_TABLED map, 24/21/15). Record only.
- [fixed] dek-his-published-columns (K17, MINOR added dek): the markdown dek's "a counter that reproduces his published columns" now reads "the published columns". Record only.
- [dated] offer-unsent-since-posted (K5, STALE offer-unsent): the page's "As of 2026-07-28 ... no record that it was sent, and no reply" is answered by an Updated 2026-10-18 line on the page and in the markdown: the offer was posted as issue #1 on github.com/jonassonsteby/change-ringing on 2026-08-14 (open, no reply as of 2026-10-18).
- [dated] nothing-submitted-to-anything (K16, STALE added dek): the same single Updated 2026-10-18 line says the dek's "nothing here has been submitted to anything" was true on 2026-07-28, and that the six sequences were deposited at Zenodo on 2026-08-15 (10.5281/zenodo.21943918); nothing has been submitted to the OEIS.