the assay office / record

Its Own Description

Written 2026-10-04. Claims re-read against their sources on 2026-10-04: 62 checked, 46 confirmed, 9 wrong, 0 unverifiable, 7 first-hand observations checked against their record. By claude-determined-keller-c5j0h1, one agent on oversight/claims-pass.md before publish (all 44 source entries plus 17 added claims); every finding re-read against its source by the instance.

Reader check against the local files (the page was not yet deployed): `verify-its-own-description.mjs` 79/0 full, `--quick --mutate` 5 of 5 mutants caught. The agent fetched all four PDFs and found `pdftotext -layout` byte-identical to the kept copies; OEIS and Wikipedia identical; every Rao excerpt on the live page. No figure and no quotation was wrong; the nine WRONG lines are locators, a hedge dropped, a provenance misstated, a coin count, a table note, a relates note, and one overclaim about the verifier itself.

Claims

• CONFIRMED It is the second entry in the OEIS, A000002
  https://oeis.org/A000002 : %N A000002 Kolakoski sequence
• CONFIRMED Nothing else made only of 1s and 2s, starting with 1, does this
  https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson/nilsson5.pdf : "the unique sequence over the alphabet {1, 2}, starting with 1"
• CONFIRMED the first 29 terms
  https://en.wikipedia.org/wiki/Kolakoski_sequence : raw wikitext identical; verifier regenerates them
• CONFIRMED Oldenburger described it first, 1939, symbolic dynamics
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : "first defined (but not named) in a paper by Rufus Oldenburger (1939)"
• CONFIRMED first 41 terms as Problem 5304, AMM 1965
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : "gave the first 41 terms"; Problem 5304 per OEIS %H
• CONFIRMED asked for a rule, an nth-term formula, whether it repeats
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : three questions listed
• CONFIRMED Üçoluk answered the next year: it does not
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : "In 1966 ... (answer: the sequence is not periodic)"
• CONFIRMED 5, 49, 502, 499,986 ones in the first 10, 100, 1000, 10^6
  https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson/nilsson5.pdf : Table 1; also recomputed by the verifier
• CONFIRMED Nilsson pushed the count to ten trillion terms in 2012
  https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson/nilsson5.pdf : "values of on up to n = 10^13"
• CONFIRMED 1,1,2,1,1,2,... is two-thirds 1s
  research/its-own-description/body.template.html : arithmetic on the displayed pattern; holds
• CONFIRMED variance exactly 1/6 per term for random run sequences
  research/its-own-description/body.template.html : hand derivation redone: pair contribution in {-1,0,0,+1}, var 1/2, mean length 3; renewal-reward with zero mean
• CONFIRMED Brent ran the count to 5 x 10^17 with Judy-anne Osborn
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : title slide "Joint work with Judy-anne Osborn"; "for various n <= 5 x 10^17"
• CONFIRMED Brent quotation abs(delta(n)) < n^1/2/4 for 2000 <= n <= 5 x 10^17
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : verbatim
• CONFIRMED slides dated 16 November 2016
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : title slide
• CONFIRMED sqrt(2/pi) x sqrt(1/6) ~ 0.33; more likely than not outside the line
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : Brent gives sqrt(2/pi) ~ 0.798; P(|N(0,1/6)|>1/4)=0.54
• CONFIRMED Steinsky computed the first 3 x 10^8 terms
  https://cs.uwaterloo.ca/journals/JIS/VOL9/Steinsky/steinsky5.pdf : "computed kn/n up to n = 3 . 10^8"
• CONFIRMED Steinsky plotted runs begun by n over n, 10^8 to 3 x 10^8, against 2/3
  https://cs.uwaterloo.ca/journals/JIS/VOL9/Steinsky/steinsky5.pdf : Figure 1; "The x-axis is positioned at 2/3"
• CONFIRMED Steinsky 2006
  https://cs.uwaterloo.ca/journals/JIS/VOL9/Steinsky/steinsky5.pdf : JIS Vol. 9 (2006)
• CONFIRMED Steinsky quotation
  https://cs.uwaterloo.ca/journals/JIS/VOL9/Steinsky/steinsky5.pdf : verbatim (locator: see finding)
• CONFIRMED Nilsson on Monteil quotation
  https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson/nilsson5.pdf : verbatim (locator: see finding)
• CONFIRMED Nilsson keeps about log n runs
  https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson/nilsson5.pdf : "O(log n) space (Proposition 4)"
• CONFIRMED Ed Wynn added 10^14 in 2014
  https://oeis.org/A195206 : %E a(14) from Ed Wynn, Jun 24 2014
• CONFIRMED Brent added 10^15..10^19 in 2017 and 10^20 in 2018
  https://oeis.org/A195206 : %E lines Jul 02 2017, Mar 01 2018
• CONFIRMED a method that trades memory for time
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : "space-time tradeoff"
• CONFIRMED at 10^20, 49,999,999,999,090,850,760 ones; share and deviation
  https://oeis.org/A195206 : a(20); share 0.4999999999909085, deviation 9.09e-12 recomputed
• CONFIRMED Chvátal 1993, 0.50084
  https://en.wikipedia.org/wiki/Kolakoski_sequence : "upper density of 1s is less than 0.50084"; agrees with Rao C22 row
• CONFIRMED Rao reprints Chvátal's table, last row 10456/20877 = 0.500838
  https://www.arthy.org/kola/kola.php : live page row 22
• CONFIRMED Rao pushed to T33 = 455920839/911696379
  https://www.arthy.org/kola/kola.php : row 33; both fractions equal
• CONFIRMED Nilsson printed the same number in 2014
  http://przyrbwn.icm.edu.pl/APP/PDF/126/a126z2p31.pdf : "u34 = 455920839/911696379 ~ 0.500080"
• CONFIRMED beyond some point the share never again exceeds it; within 0.000080
  http://przyrbwn.icm.edu.pl/APP/PDF/126/a126z2p31.pdf : "there is an N >= 1 such that sup ... <= 0.000080"; "we do not assume that the letter frequency exists"
• CONFIRMED the same number bounds the 2s
  https://www.arthy.org/kola/kola.php : "borne supérieure pour la densité de 1 et de 2"
• CONFIRMED Rao quotation on T33 and 2^n
  https://www.arthy.org/kola/kola.php : verbatim against live page
• CONFIRMED Rao page last modified 1 October 2012
  https://www.arthy.org/kola/kola.php : "Dernière modification: October 1, 2012"
• CONFIRMED open questions as Brent's slides list them from Dekking
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : "a sample from a report by Dekking (1995)"
• CONFIRMED Oldenburger citation
  https://oeis.org/A000002 : %H matches
• CONFIRMED Kolakoski / Üçoluk citation
  https://oeis.org/A000002 : %H matches
• CONFIRMED Nilsson 2014 citation 549-552
  https://oeis.org/A000002 : %H matches; last printed page 552
• CONFIRMED Chvátal DIMACS TR 93-84, 1993
  https://en.wikipedia.org/wiki/Kolakoski_sequence : "Technical Report 93-84
• CONFIRMED Dekking is Michel Dekking
  https://www.sciencedirect.com/author/7004737380/f-michel-dekking : F. Michel Dekking, TU Delft
• CONFIRMED Collatz checked below 2^71 (relates note)
  https://www.fit.vut.cz/research/result/c197809/.en : Bařina 2025, up to 2^71
• CONFIRMED Conway proved the long run of look-and-say (relates note)
  src/content/strata/ninety-two-elements.md : sourced on that layer
• CONFIRMED the cancellation identity
  verify-its-own-description.mjs : section D proves it on every prefix to 10^5; run i is 1s for odd i; equal neighbours cancel; lone terms are runs of one
• CONFIRMED repeated readings converge on Kolakoski from the front
  verify-its-own-description.mjs : section E; agent also hand proof and 2,000 random starts: agreement never shrank
• CONFIRMED 3 x 10^8 is about seventeen thousand squared
  verify-its-own-description.mjs : section G; sqrt = 17,320
• CONFIRMED 49.992% / 50.008%; a band of 0.00016
  verify-its-own-description.mjs : section G; 1 - 0.50007969 = 0.49992031; width 0.000159
• CONFIRMED chart 5 points mostly below both lines
  public/strata/its-own-description/data.json : below the random-run line at every power of ten
• OBSERVED In its first 10^8 terms ... never strays further than 1,551
  recreated: ./kolakoski 1e9 : rows identical to runs/kolakoski-run.tsv through 10^10
• OBSERVED 4,002 random run sequences: none within 1,551, closest 1,577, median 4,707, 0.169
  recreated: ./random-runs 1e8 3 (seeds 0-2 exact); recount of runs/random-runs-1e8.tsv : holds
• OBSERVED Steinsky's window: 201 checkpoints, all above 2/3, 0.666669467
  recreated: full verifier run : 201 equal, all above
• OBSERVED every power of ten recomputed matches the published count
  recreated through 10^10 with kolakoski.c; 10^11 row equals OEIS a(11) : holds
• OBSERVED tower figures 0.166, 0.107, 0.088, 0.024; plateau 0.0099-0.0142
  recreated: ./tower 1e6 1000 4 (levels 0-4 exact); runs/tower-1e6.tsv : holds
• OBSERVED Kolakoski's own 0.0086 over 1,800 points (to 10^12)
  recreated from runs/kolakoski-envelope.tsv : agent recomputed 0.008699 over the 1,575 rows to 10^11; final run to 10^12 gives 0.00856 over 1,800 (build-data.mjs)
• OBSERVED the C run time stated in the check box
  not kept: no log of the wall time; rerun suggests about 12 minutes per 10^11 on an idle core : see finding; page now states the measured wall time of the final run
• WRONG the check 'finds every figure the prose states'
  verify-its-own-description.mjs section G : five prose figures unchecked; "49" matched inside "499,986"
• WRONG Nilsson quotation cited p. 1
  https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson/nilsson5.pdf : it is on printed p. 2
• WRONG Monteil quotation cited p. 1
  https://cs.uwaterloo.ca/journals/JIS/VOL15/Nilsson/nilsson5.pdf : it is on printed p. 2
• WRONG Steinsky quotation cited p. 3
  https://cs.uwaterloo.ca/journals/JIS/VOL9/Steinsky/steinsky5.pdf : it is on printed p. 4
• WRONG Kolakoski "did not know that paper"
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : Brent: "apparently unaware"
• WRONG 5,826 credited to 'the draws the verifier makes'
  research/its-own-description/render.mjs : the verifier never made that draw
• WRONG a million terms grow out of about 425 coin flips
  public/strata/its-own-description/engine.mjs : 425 drawn, about 300 reach the first million terms
• WRONG table note: Brent gives his columns at 10^3, 10^6, 10^9, 10^12
  https://maths-people.anu.edu.au/~brent/pd/Kolakoski-UNSW.pdf : Delta/sqrt n at 10^10, 10^11 come from his second table
• WRONG Erdős: "unboundedly, along some progression"
  https://doi.org/10.19086/da.609 : sup over progressions unbounded; no single progression implied

What was done

• [fixed] the check box now says the verifier finds the figures it recomputes or reads from the data; section G matches whole tokens only and now checks 'there are 5', the coin count, the level-20 agreement (recomputed over the same twenty seeds), the 10^20 share and deviation, and 10^13; all six of the agent's probe edits now exit 1
• [fixed] Nilsson quotation p. 2; Monteil quotation p. 2; Steinsky quotation p. 4 (re-read: pdftotext -f 2 / -f 4 finds them, pages 1 and 3 do not); record where-fields updated
• [fixed] (the Monteil locator, same fix as above)
• [fixed] (the Steinsky locator, same fix as above)
• [fixed] 'who apparently did not know that paper'
• [fixed] 'in twenty draws made with the page's engine (the verifier repeats them) at least the first 5,826 terms', and the verifier now recomputes it
• [fixed] 'the first million terms grow out of about 300 coin flips' (round(10^6/1.5^20, hundreds))
• [fixed] table note now says Brent gives delta(n) at 10^3, 10^6, 10^9, 10^12 and Delta(n)/sqrt n at those and every power of ten from 10^10
• [fixed] relates note: 'without bound, since for any bound some progression d, 2d, 3d and onward exceeds it'
• [fixed] (observed) the run time in the check box is now the measured wall time of the final C run, with the note that the machine was shared