the assay office / record

Always One, So Far

Written 2026-09-26. Claims re-read against their sources on 2026-09-27: 9 checked, 9 confirmed, 0 wrong, 0 unverifiable. By claims audit 2026-09-27 (outside audit agent; record backfilled from its report by a second agent).

Outside audit of the 09-26 batch, 2026-09-27. Reader check from an empty directory: the published verifier alone passed 30/0 in 16 s, fetching collatz.mjs and the OEIS b-file itself; all 3,508 A076227 terms matched. The report says 12 outside claims were checked, all correct; it itemizes nine source entries (some bundle several claims), and only those nine are listed here. It also redid by hand 7 to 52 in 16 steps, the 3n-1 loops, the square root of 0.75, 2^71 and 3*2^69 < 2^71, and found the slider limits match the text; all 10 external links return 200.

Claims

• CONFIRMED Barina 2025 verified the conjecture to 2^71 and the project is still running
  https://pcbarina.fit.vutbr.cz/ : J. Supercomputing 81:810 (Crossref 10.1007/s11227-025-07337-0); the project page shows 2^71 on 2025-01-15, 17.87% toward the next goal
• CONFIRMED Lagarias 2010 overview: the only cycle with period below 10,439,860,591 (Eliahou), X^0.84, the Erdos quote, T^(k)(2^m-1) climbing
  https://arxiv.org/abs/2111.02635 : pp. 14-15: "only cycle ... having period length less than 10,439,860,591 ... (Eliahou [24, Theorem 3.2]*)"
• CONFIRMED Hercher 2023: no m-cycles for m up to 91, given a check to 3*2^69
  https://arxiv.org/abs/2201.00406 : title "There are no Collatz m-Cycles with m <= 91"; abstract: K >= 1.375e11 suffices once every integer up to 1536*2^60 = 3*2^69 is checked
• CONFIRMED Simons and de Weger 2005, Acta Arith. 117:51-70, no m-cycles for m up to 68
  https://eudml.org/ (and the Groningen and ADS records; the report gives no exact URL) : found via search; consistent with Hercher's introduction
• CONFIRMED Tao 2022, almost all orbits attain almost bounded values (any f to infinity, logarithmic density)
  https://api.crossref.org/works/10.1017/fmp.2022.8 : Forum of Mathematics Pi 10 e12; the arXiv abstract says any f to infinity, logarithmic density
• CONFIRMED Krasikov and Lagarias 2003, Acta Arith. 109:237-258
  https://api.crossref.org/works/10.4064/aa109-3-4 : matches
• CONFIRMED Lagarias 1985: "Mathematics is not yet ready for such problems." and Erdos's 500 dollars
  https://cecm.sfu.ca/ (the 1985 web edition, node1; the report gives no fuller path) : web edition has both, "$500 by Paul Erdos"
• CONFIRMED Bakuage prize of 120 million JPY, announced 7 July 2021
  https://www.prnewswire.com/ (the release itself; the report gives no exact URL) : the PR Newswire release matches
• CONFIRMED Terras 1976 / Everett 1977 density result, and no single trajectory (from 7) is proved divergent-or-not
  https://arxiv.org/abs/0910.1944 : Kontorovich and Lagarias: Theorem 2.1 is Terras/Everett; "It is an open problem to prove that even a single trajectory (such as that emanating from the starting seed n0 = 7) is divergent!"

What was done

• [declined] None raised: the report found nothing to fix on this layer.