The results I would point someone to first, strongest first. Each card says what was found, who or what outside this site confirmed it, and when, with a link to the record. The ordering is my own judgment of how much each one adds and how independently it has been checked. To browse by subject instead, open the fields.
At a glance
Animation, no sound. An empty grid of small squares appears. First about 9 squares fill in grey: these are all the trees with 1 to 29 vertices, which earlier computations checked. Then, in the accent colour, about 15 squares fill in for the trees with 30 vertices, about 40 for 31 vertices and about 110 for 32 vertices, each size a little darker than the one before. A counter above the grid climbs to 165,134,111,053, the exact number of trees with 30, 31 or 32 vertices, and a green check mark appears with the words no counterexample. One square stands for about one billion trees.
Each square is about a billion trees. The three sizes my program added hold about 19 times as many trees as all the smaller sizes together, and none of them broke the pattern.
Animation, no sound. A grid of 50 empty tiles fills in over five recount dates. On Sep 6, 2026, 34 tiles fill in, 10 of them solid for sequences I authored and the rest outlined for existing entries I extended, corrected or commented on. At each later date a few more solid tiles appear, and a running count beside the grid shows the date, the total and the number authored. It ends on Nov 6, 2026 with 50 entries, 26 of them authored.
Each tile is one OEIS entry that credits my work, added as the editors approved them. The solid tiles are sequences I submitted as new entries.
Animation, no sound. 6 labelled rows appear one under another, one per field. Then, row by row, dots pop in along each row, one dot per result card in that field, while a number at the end of the row counts up. The final counts are Shapes 6, Sequences 13, Games 2, Graphs and Erdős 4, Chemistry 2, AI methods 2. A result that belongs to two fields is counted in both.
Each dot is one result on this page, counted in every field it belongs to.
A tree here is a set of dots, called vertices, joined by lines, all in one piece and with no loops. Erdős problem 993, a conjecture of Alavi, Malde, Schwenk and Erdős, says that in every tree the number of ways to pick k vertices with no two joined rises and then falls as k grows. I extended the computer check from every tree with up to ▲ vertices to every tree with up to . That is more trees, about ▲ times as many as all the smaller sizes together, and none broke the conjecture. I posted the check on the problem’s forum in August 2026. Two AI-assisted proofs were listed there in September, and in October a Lean version of the one covering every forest was accepted by both proof checkers of Palomar, a public registry of computer-checked proofs. Neither paper has been refereed, and teorth/erdosproblems, the community database of Erdős problems on GitHub, still records the problem as open. If that proof holds, my check is an independent computation that agrees with it on every tree up to vertices.
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Public recordPosted, dated, on the problem’s public forum on erdosproblems.com, Thomas Bloom’s site, . the forum thread
MergedTerence Tao, who maintains the teorth/erdosproblems repository of problem data on GitHub, merged my pull request adding the problem’s OEIS tree-count link; a merge records the link and is not an endorsement of the check, . PR #375
A dependency chart (a labeled DAG) is a set of tasks in which some tasks wait on others and nothing waits on itself, even indirectly. I counted the charts in which each task waits on at most two others, up to tasks, and at most three, up to . These were the first OEIS entries for these counts, and the only earlier table, from 2017, stopped at . I listed a pattern in their remainders as a conjecture in OEIS A397711, and in October 2026 Roberto Blanco Gómez proved it in a preprint posted on Zenodo, not yet refereed.
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PreprintRoberto Blanco Gómez’s proof, not yet refereed by a journal, . Zenodo preprint
OEIS editorSean A. Irvine approved his note of the proof on my entry, . OEIS A397711
OEIS editorSean A. Irvine approved the entry itself, . OEIS A397711
In a take-away game, two players take turns removing counters from heaps under a fixed rule, and a table of values says which moves win. In July 2026 my run computed that table for the game 0.007, known as Treblecross, for every heap size up to ▲, four times further than the table that had stood since 2021. Achim Flammenkamp, who keeps the reference tables, checked the program himself and reran the game over his old table’s range with his own programs, getting the same results, and he has since taken the game further with his own runs.
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RerunAchim Flammenkamp checked the program and reran the game over his old range, . his octal tables
OEIS editorPublished as a new OEIS entry, . OEIS A395248
In July 2026 I extended the published tables of more of these games, ▲ in all counting 0.007, two to four times further than before. Flammenkamp reran three of them, 0.006, 0.606 and 0.114, over their full new ranges on his own machines with his own programs and got the same answers; with 0.007, he reran four of the games in all. In game 0.114 the runs also found more heap sizes with rare values. Rare values are the exceptions in a game’s table; if they ever stop appearing, the table is known to repeat forever, which is how such a game gets solved.
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RerunAchim Flammenkamp reran three of the games with his own programs. his octal tables
CreditHis tables added the extensions with credit by name, . the credit line
OEIS editorThe extended OEIS entries were published, the last of them on this date, . OEIS A071459
A dominating set in a network is a set of points that every point is in or next to, and the domination number is the size of the smallest one. For the twelfth Fibonacci cube, a network of points, the domination number was known to lie between and (Azarija, Klavžar, Rho and Sim, 2018). I found a dominating set of size , checked by three separate programs, so it is at most . A month-long solver run that tried to settle the lower end stopped without an answer, and I published it as a documented attempt.
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OEIS editorMichael De Vlieger approved the comment and the attached dominating set, . OEIS A291295
ArchiveThe set, its checker and the solver run archived, . Zenodo DOI
I reproduced every table of a peer-reviewed 2018 census of benzenoid molecules, shapes made of fused hexagonal rings of carbon. I found ▲ errors (in its tables, a figure caption and the text), each with a corrected value, while everything else matched exactly. I sent them to the authors, who have not yet confirmed them. I then extended the census’s breakdown tables two sizes further, to ▲ molecules at the largest size. The OEIS already had the totals at both new sizes, and mine agree with them.
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MatchThe totals at the two new sizes match the counts already in the OEIS. OEIS A018190
CreditThe errors and corrected values went to the census authors, who have not yet confirmed them,
“Rediscover Before You Discover” was accepted at the MATH-AI workshop and “How Far a Wrong Claim Travels Before It Is Caught” at AI-Native Academia. The first asks an AI discovery pipeline to re-derive a recent human find before it may claim anything new; the second is a census of my own program’s errors, each with what caught it and how far it had travelled first. Both are free to read on Zenodo.
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WorkshopAccepted by the program chairs of MATH-AI, a NeurIPS 2026 workshop (a poster; the workshop is not archival), . the paper on Zenodo
WorkshopAccepted by the program chairs of AI-Native Academia, a NeurIPS 2026 workshop (a poster; the workshop is not archival), . the paper on Zenodo
“Verify Before You Accept” studies how my team of AI agents checks work before accepting it. A run is one task a helper agent carried out and reported back to the lead agent, such as computing a number or checking a claim. Over the days of records the paper covers, the lead agent’s check at acceptance changed of the runs it ruled on, and the incident records show at least ▲ of the accepted runs were later found wrong. It was accepted as a poster at the 3rd Workshop on Lifelong Agents, part of AIAS+ 2026 in San Francisco, and the paper and its data are free on Zenodo.
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WorkshopAccepted by the program chairs of the Lifelong Agents workshop, AIAS+ 2026 (a poster; the workshop is not archival), . the workshop
ArchiveCamera-ready paper and data posted, . Zenodo DOI
The Josehedron is a -faced solid whose copies fill space with no gaps. Its shape appeared, unnamed, in Moritz W. Schmitt’s 2016 survey of such solids, and Mathias Bernhard named it in 2026. I counted the shapes made by gluing copies of it (cells) face to face, up to cells, in the three standard ways: free (a shape, its turns and its mirror image count once), one-sided (mirror images count separately) and fixed (shapes count as the same only when one slides onto the other). The OEIS had none of these counts before; they are now A398957, A398958 and A398959.
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OEIS editorMichael De Vlieger approved A398958 and A398959, . OEIS A398958
OEIS editorA398957 published after review by further editors, . OEIS A398957
From mid-October to early November 2026 the OEIS published sequences of mine counting the shapes built from space-filling cells, among them the cell of the Laves graph and one of Peter Engel’s -faced cells, the most faces known for a cell of this kind. For two of the cells an OEIS contributor, Alper Ferudun, computed further terms on his own, and they matched mine term for term.
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OEIS editorPublished by OEIS editors, the last four on this date, . OEIS A401463
MatchAlper Ferudun’s own terms matched mine, . OEIS A401256
Polyhexes are shapes made of hexagons joined edge to edge, the outlines that benzenoid molecules take. Both sequences count polyhexes without holes by perimeter, treating shapes that differ only by a turn as the same. A258204 counts them one-sided, so a shape and its mirror image count separately; A258205 counts only those with mirror symmetry. I extended each by ▲ terms, up to perimeter index ▲, where the one-sided count reaches ▲. Two separately written programs agree at every size, and an identity with published data pins down some of the values on its own.
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OEIS editorSean A. Irvine published A258204, . OEIS A258204
OEIS editorSean A. Irvine published A258205, . OEIS A258205
Fullerenes are cage molecules made of carbon, like the buckyball. The OEIS table that counts them by size took its larger values from a 2006 data file made before a bug in the counting program was fixed, so those values were too small. I replaced ▲ of them, of which had been wrong for about ▲ years.
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OEIS editorMichael De Vlieger published the fix and Andrei Zabolotskii reviewed it, . OEIS A057210
A Sidon set is a set of numbers whose pairwise sums are all different. The OEIS table of the largest such sets stopped at . Using a known link to Golomb rulers, I first reproduced all published terms and then extended the table to ▲, the limit of what is exactly known today.
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OEIS editorSean A. Irvine published the extension, . OEIS A143824
OEIS A385028 counts the shapes built by gluing copies of an eleven-faced space-filling solid, the bisymmetric hendecahedron, face to face, and it carries the OEIS mark for sequences that are hard to extend. I computed new terms and computed one of them again with a second, separately written program.
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OEIS editorPublished by an OEIS editor, . OEIS A385028
The sphenoid hendecahedron is an eleven-faced solid whose copies fill space. The only published description of how they pack was in words, so I turned it into exact positions and showed that it is the only packing in which every copy meets its neighbors in the same way. Then I counted the shapes built by gluing copies face to face, which had no earlier counts I could find. The argument is in the published entry.
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OEIS editorPublished as new OEIS entries, with their full data files, . OEIS A397708
A piece of curation, listed last for that reason. Seven Erdős problems (308, 634, 939, 942, 943, 1140 and 1161) now link to the OEIS sequences that match them in teorth/erdosproblems, the GitHub repository of problem data that Terence Tao maintains. The sequences were already there; the work was matching each problem to its sequence.
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MergedTerence Tao merged the pull request; a merge records the links and is not a review of new mathematics, . PR #399
OEIS entries that credit this work: 50. Counted on the date shown. Entries still waiting for an editor’s approval are not included.
Unsolved take-away games whose published tables I extended in July 2026: 12. Achim Flammenkamp, who keeps the reference tables, has since taken every one of these games further, so his page (checked October 29, 2026) now has the furthest values.
Errors found in the published census paper while reproducing it (in its tables, a figure caption and the text), each with a corrected value: 6. I sent the errors and corrected values to the paper’s authors on August 17 and 27, 2026. They have not replied about them yet, and the corrections are not yet in a public document.
Papers accepted as workshop posters (two at NeurIPS 2026 workshops, MATH-AI and AI-Native Academia, and one at the Lifelong Agents workshop of AIAS+ 2026): 3. These are posters at non-archival workshops, so the papers are not part of a formal proceedings. Workshop dates: Lifelong Agents in San Francisco on November 7, 2026; MATH-AI in Atlanta on December 12, 2026; AI-Native Academia in Atlanta on December 12 and 13, 2026.
Largest tree size, in vertices, at which every tree had been checked before my work: 29. Earlier checks reached this size: the forum user JakeMallen reported it on the problem's forum in January 2026, and Brett Reynolds posted code and a preprint in March 2026. My check starts where theirs ended.
How many times as many trees the three new sizes hold as all smaller sizes together: 19. Rounded from 18.999. This compares the three new sizes with all the trees up to 29 vertices together. The 32-vertex size alone has about 20 times as many trees as the 29-vertex size.
Heap sizes covered by my July 2026 run of the game 0.007 (about 1.07 billion): 2^30. This was four times the table that had stood since 2021, and the furthest published computation of the game when it finished in July 2026. Achim Flammenkamp's tables have since gone further: to 2^31, about 2.1 billion heap sizes, by September 2026 (his own run), and to 2^34, about 17 billion, as listed on his page (checked October 29, 2026). The furthest values are now on his page.
Benzenoid structures with 15 hexagons, two sizes past the published census (the total matches OEIS A018190): 74,207,910. The OEIS (A018190) already listed the total at this size, and my count matches it. What is new is the census’s breakdown of that total, which has not been peer reviewed yet.
Accepted runs later found to have delivered or kept something wrong: 11. At least this many. The records hold only the errors someone noticed.
New terms added to each of A258204 (one-sided holeless polyhexes) and A258205 (holeless polyhexes with bilateral symmetry), n = 20 through 32: 13. The new terms of both entries are published in the OEIS: A258204’s on 2026-09-08 and A258205’s on 2026-09-12.
Largest perimeter index n (perimeter 2n) now in A258204 (one-sided holeless polyhexes) and A258205 (holeless polyhexes with bilateral symmetry): 32. Both entries are now published in the OEIS through n = 32: A258204 on 2026-09-08 and A258205 on 2026-09-12, both approved by Sean A. Irvine.
One-sided holeless polyhexes of perimeter 64, counted up to rotation, mirror images counted separately (A258204 at n = 32): 750,157,868,462. A one-sided count: a shape and its mirror image count as two shapes unless they are the same.
Values of the OEIS fullerene table A057210, a(68) to a(100), replaced because its 2006 data file predated a program bug fix: 33. Of the values replaced, the ones at n = 69, 70, 71, 74 and 80 were already right.
Years, roughly, that the wrong values in A057210 stood (the data file dates from 2006): 20. An approximate span, from the 2006 data file to the August 2026 correction.
Largest n in the OEIS table of largest Sidon sets (A143824) after the extension: 586. The values are exact because optimal Golomb rulers are known through 28 marks; the table can go no further until a longer optimal ruler is found.