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The main claims on this site, with a link to check each one

This page lists the main results Tyler Orden claims from his research. Each one links to a place where you can check it, usually outside this site, and shows how far it has been checked and when. Claude agents (Anthropic) working under his direction wrote and ran the code and drafted the text; he chose the problems, directed the work, checked it and decided what was published. The rest of the site tells the story of each result in full; this page is the short version, one row per claim, so you can check any of them in a minute. The full write-ups are on the main site.

50
Contributions credited in the OEIS, the online database of integer sequences
26 authored / 21 extended / 2 corrected / 1 commented or linked · as of 2026-11-06
3
Papers accepted as workshop posters
8
Code and data archives with a permanent DOI

CLAIMS

AS OF 6 NOVEMBER 2026
CLAIMCHECK IT HERE
In July 2026, computed the values of the unsolved take-away game 0.007 out to 2^30 heap sizes, four times further than the published tableThe table it extended had stood since 2021. It is not the current record: the table’s maintainer has since gone further himself (his page, checked 2026-10-29, lists 2^34, about 17 billion).full write-up →LIVE 5/5OEIS A395248
In July 2026, extended the published tables of eleven more unsolved take-away games two to four times further; the tables’ maintainer, Achim Flammenkamp, reviewed the solver code for 0.007 (the row above) and reran three of these games, 0.006, 0.606 and 0.114, on his own machines with his own programs, with matching resultsTwelve games in all, counting 0.007 in the row above, which he also reran over his old range, so he reran four of the twelve. These are not the current records: Flammenkamp updated his tables on 2026-09-03 and has since taken every game further. His page still credits this work.full write-up →LIVE 5/5octal-games tables
Extended the check of an Erdős conjecture, open at the time (two proof claims were listed on erdosproblems.com on September 21 and 27, before that site paused new proof claims on October 6, and neither cites this check; a Lean version of the second, which covers every forest, was accepted by both proof checkers of the Palomar registry in October; neither paper has been refereed, and teorth/erdosproblems, the community database of Erdős problems on GitHub, still records the problem as open as of 2026-11-07) from every tree up to 29 vertices to every tree up to 32, about 165 billion more trees, including all of the roughly 110 billion trees at the largest size, with no exceptions; my pull request adding the problem's OEIS tree-count link (A000055) was merged by Terence Tao into teorth/erdosproblems, the GitHub repository of problem data he maintains (erdosproblems.com itself is Thomas Bloom's site), and the request's description cites this checkThe number of trees checked at every size matched the known count exactly, so none was lost or added overall; the generator is designed to produce each tree once. The merge records the OEIS link; it is not an endorsement of the check.full write-up →LIVE 4/5erdosproblems.com/993
Five terms added to a shape-counting sequence the OEIS had marked as hard to extendLIVE 4/5OEIS A385028
Counts of the possible structures of a Bayesian network when each variable may depend directly on only a limited number of others (labeled DAGs with bounded in-degree): the first OEIS entries for these counts, far past the only earlier table, which stopped at seven nodes (Allen et al., 2017)LIVE 4/5OEIS A397711
Counts of the shapes built from cells of the sphenoid honeycomb, a space-filling pattern with no earlier counts I could find; the published entry includes the argument that it is the only such honeycomb when every cell is attached by the same ruleLIVE 4/5OEIS A397708
Counts of the shapes built by gluing Josehedron cells (a solid that fills space) face to face, which the OEIS had none of before, in all three standard ways of counting them, published as A398957, A398958 and A398959The last of the three, A398957, was published on 2026-08-27.full write-up →LIVE 4/5OEIS A398958
Found and corrected a dropped digit that had sat in a published OEIS entry for 14 years, after checking the right value with independent codeLIVE 4/5OEIS A202182
Reproduced a peer-reviewed 2018 census of benzenoid molecules (shapes made of fused hexagonal rings) in full, found six errors (in its tables, a figure caption and the text) and sent them, with corrected values, to the paper’s authors; then extended the census’s breakdown tables by two sizesThe OEIS (A018190) already had the totals at the two new sizes, and mine match them; what is new is the breakdown of each total. I sent the errors on August 17 and 27, 2026; the authors have not yet confirmed them.LIVE 4/5Zenodo data and code
Three papers accepted as workshop posters, all free to read on Zenodo"Rediscover Before You Discover" at the MATH-AI workshop (doi.org/10.5281/zenodo.23154795) and "How Far a Wrong Claim Travels Before It Is Caught" at the AI-Native Academia workshop (doi.org/10.5281/zenodo.23154707), both workshops of NeurIPS 2026 that meet in Atlanta in December; and "Verify Before You Accept" at the Lifelong Agents workshop of AIAS+ 2026 (doi.org/10.5281/zenodo.23652450), which meets in San Francisco on November 7, 2026.ACCEPTED ·Papers (free copies on Zenodo)
Eight results archived on Zenodo, each with a permanent DOI so it can be cited and foundEach archive holds the code or data behind one result.LIVE ·Zenodo records

The dots show how far each claim has been checked, using the five steps described below. Five dots means an outside expert reproduced it, in whole or in the part the claim says. A blank means no specific check is recorded yet. Every number on this site is stored in one place, so a claim reads the same here as everywhere else on the site.

HOW CLAIMS ARE CHECKED: FIVE STEPS

AS OF 6 NOVEMBER 2026

The full recheck after the July 2026 model switch recomputed the data from scratch and found no errors in the computed numbers. The problems it found were around the numbers: descriptions, credits, how some checks had been done, and one real finding that had gone unnoticed. For that reason every number here is stored once, with its source, and every claim goes through these steps in order.

  1. 1
    The author checks it
    Read it again and work it out again.
    Every claim above passed this step first.
  2. 2
    It agrees with itself
    Results checked against each other and against facts that must hold.
    Related numbers are compared with each other before any one of them is used.
  3. 3
    A second program agrees
    A separately written program, sharing no code, gets the same numbers.
    Where a result can be computed two ways, it is recorded as computed only after a second program reproduces it. The second program is usually also written by an AI agent, which is why steps 4 and 5 check against sources outside the work.
  4. 4
    An outside source agrees
    Published values, standard databases, or live public data.
    109,972,410,221 trees verified for Erdős Problem #993, matching the published count exactly.
  5. 5
    An outside expert agrees
    A specialist with no stake in the result reviews and reproduces it.
    Achim Flammenkamp, who held the earlier record and maintains the field’s reference tables of octal games, reviewed the code, reran parts of the computation on his own machines with his own programs, and credits the work by name.

HOW STATUS WORDS ARE USED: A PAPER IS CALLED ACCEPTED OR PUBLISHED ONLY AFTER A VENUE HAS SAID SO. A LINK MERGED INTO SOMEONE ELSE’S DATABASE IS LISTED AS A LINK, NOT AS AN ENDORSEMENT.