Every claim on this site is one click from its proof.
The audit-trail reading of a public research notebook for AI-assisted mathematics by Tyler Orden. Not a blog. Each number carries a receipt: a source, a verification method, and a date. The notebook holds the full entries; this page holds the claims.
34
Credited OEIS contributions
10 authored / 21 extended / 2 corrected / 1 commented-or-linked · as of 2026-09-06
5
Submissions awaiting a decision
1
In invited major revision
7
DOI-archived artifacts
CLAIMS REGISTRY
AS OF 4 SEPTEMBER 2026
| CLAIM | PROOF | ||
|---|---|---|---|
| In July 2026, Sprague-Grundy values of the unsolved octal game .007 computed through 2^30 heap positions, four times the prior record boundA fourfold extension of the bound standing since 2021, not the current frontier: the previous record holder has since reached a higher bound (his page as fetched on 2026-09-04 lists 2^31). | LIVE | 5/5 | OEIS A395248 |
| In July 2026, eleven unsolved octal games extended 2x to 4x past bounds standing since 2021; solver source reviewed and computation reproduced by Achim FlammenkampWith the .007 game on its own row above, the campaign extended twelve games in all; the registry keeps the two counts apart. Dated on purpose: on 2026-09-03 Flammenkamp updated his tables and has since pushed all twelve games further, so the July bounds are a dated record, not the current frontier; his credit line to the author remains on the page. | LIVE | 5/5 | octal-games tables |
| OEIS cross-reference for Erdős Problem #993 merged by Terence Tao; roughly 110 billion trees verified, matching the reference count exactlyA merged pull request is a merged pull request, not an endorsement. | LIVE | 4/5 | erdosproblems.com/993 |
| Hard-designated sequence extended five terms | LIVE | 4/5 | OEIS A385028 |
| First enumeration of labeled DAGs with bounded in-degree, the Bayesian network structure search space | LIVE | 4/5 | OEIS A397711 |
| First polyform counts on a honeycomb, with a published uniqueness proof | LIVE | 4/5 | OEIS A397708 |
| Polyforms of the Josehedron honeycomb enumerated for the first time, in three symmetry classes, published as A398957, A398958 and A398959The fixed class, A398957, published on 2026-08-27 after an editor round, completing the family.notebook entry → | LIVE | 4/5 | OEIS A398958 |
| A 14-year-old published error found, proven wrong four independent ways, corrected with credit | LIVE | 4/5 | OEIS A202182 |
| Paper in invited major revision at the Journal of Integer Sequences; the referee compiled and ran the codeThe revised manuscript went back to the journal on 2026-08-25 and awaits the referee, with no response recorded as of 2026-09-04; in revision is not accepted. | IN REVISION | 5/5 | no public link yet |
| Mathematical chemistry census extension: the published census reproduced in full, six errors in its tables documented with corrections, and the census extended two full sizes; manuscript in preparation for resubmissionSubmitted 2026-08-22; rejected after review on 2026-09-01, the second rejection after a desk rejection on 2026-08-21. Reframed around how the three indices behave as size grows, with the referee’s tie confound tested directly, and in preparation for resubmission with no venue named. In preparation is not submitted. Every extension total anchors to the published A018190 values, and the original authors have the manuscript and the errata. The data and code deposit is one of the DOI-archived artifacts below. | IN PREPARATION | · | no public link yet |
| SaaS-metrics paper, submitted August 2026Submitted 2026-08-23 after the author’s full rewrite; assigned a manuscript number and with the editor since 2026-08-28; no decision as of 2026-09-04. Submitted is not published. | SUBMITTED | · | no public link yet |
| Verification-methods proposal built from the program’s own audit archive, submitted 2026-08-29 to a data-science journalA proposal, not a full article; the response window runs to roughly mid-October and a rejection at this venue is final. The submitted text carries the program’s OEIS tally as it stood in its records; the live database count is smaller by one, a difference recorded in the program’s own error ledger for correction at the first editorial touchpoint. Submitted is not published. The venue is not named here because its preprint policy is not in the site’s venue registry. | SUBMITTED | · | no public link yet |
| Three workshop papers submitted 2026-09-06 to double-blind venuesReviews are due from the author 2026-09-20; notifications are expected 2026-09-29. Per this site’s publishing policy, a double-blind paper carries no title, venue, or PDF anywhere on this site until notification. Submitted is not published. | SUBMITTED | · | no public link yet |
| Seven research artifacts archived on Zenodo with DOIsORCID-linked is stated only for the records this site’s own sources verified the ORCID on (the two minted in September 2026); the original five are unchanged but not individually re-checked since 2026-08-29. | LIVE | · | Zenodo records |
Tier is the highest rung of the five-rung verification ladder documented in the public record for that claim. A tier of · means no specific rung is documented yet. Figures inside these claims are owned by the fact registry (data/facts.ts) and change only with it.
METHODS: THE VERIFICATION LADDER
AS OF 4 SEPTEMBER 2026
The founding observation, from 240+ archived audit runs of the program behind this site: numbers survive, prose fails. Computed values held up under every re-check; the errors that slipped through lived in narrative, attribution, and the checks themselves. So the site is built around registered facts, not paragraphs. Every claim climbs this ladder in order.
- 1Self-reviewThe author re-reads and re-derives.Every entry in the registry above passed this rung before climbing any other.
- 2Internal consistencyResults checked against each other and known invariants.Invariant checks run across results before any single number is trusted on its own.
- 3Fresh-code re-derivationAn independent implementation, sharing no code, reproduces the numbers.An independent re-implementation must reproduce a result before it is registered as computed.
- 4External ground truthPublished reference values, canonical databases, live APIs.109,972,410,221 trees verified for Erdős Problem #993, matching the published reference count exactly.
- 5Hostile expertA skeptical outside authority reviews and reproduces the work.Achim Flammenkamp, previous record holder and keeper of the field’s canonical octal-games tables, reviewed the solver source, reproduced the computation independently, and credits the work by name.
STATUS DISCIPLINE: submitted is not published, merged is not endorsed, in revision is not accepted. A merged pull request is a merged pull request, not an endorsement.
ARTICLE PIPELINE
8 IN QUEUE / 0 PUBLISHED
| # | TITLE | SUMMARY | STATUS |
|---|---|---|---|
| 01 | Records with a witness | How the previous record holder reviewed the solver, reproduced the computation, and put the results on the field’s canonical table. | DRAFT |
| 02 | Two implementations agreed, and both were wrong | Two independent enumerators matched each other exactly and still failed the external anchor; agreement is not correctness. | DRAFT |
| 03 | The bottleneck was in their bibliography | A 2018 five-author census stopped at its computational limit; the fix was a 1961 theorem cited in their own reference list. | PLANNED |
| 04 | Reproduce first, then extend | Reproducing all of a published census before adding to it, and how six errata in the source paper surfaced as a byproduct. | PLANNED |
| 05 | The 110 billion trees behind one merged line | What a merged pull request into a mathematician’s database is, and what it is not. | DRAFT |
| 06 | A 14-year-old dropped digit | Canonical databases carry old errors; this one was proven wrong four independent ways before the correction shipped. | PLANNED |
| 07 | The world’s poset tables now end at these values | Extending partial-order counting sequences to the new published frontier. | PLANNED |
| 08 | What a laptop does now | What a 15-minute reproduction of a once-hard census says about compute, and what it says nothing about. | PLANNED |
Titles and summaries only. No article ships until its claims are registered above. The same queue, written for readers, is the explainer hub.