Work

Everything on this site in one list. Some topics have both a result, with the numbers and how they were checked, and an essay that tells the story behind it. The labels on each row are explained at the bottom of the page.

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17 of 17

Counting, games and networks9

A dropped digit sat in an OEIS entry for years until a Claude agent spotted it. What that means for anyone who copies values from reference tables.
WritingWhat a long-standing error in a math database means for anyone who copies reference values· Oct 24, 2026
Checking an Erdős conjecture on every tree up to a size rules out small counterexamples but does not prove it. What such a check shows and how it is made.
WritingWhy checking a math conjecture on every case up to a size is not a proof· Oct 24, 2026
A network puzzle: pick as few points as possible so that every point is picked or linked to a picked one. A search I ran with Claude found a smaller set than any published.
WritingA new best-known dominating set for the twelfth Fibonacci cube, and a month-long run with no answer· Sep 26, 2026
An Erdős conjecture: in every tree, and every forest, the number of ways to pick k vertices with no two joined rises, then falls, as k grows. I checked every tree three sizes past the old limit; it held.
RecordPublishedChecking an Erdős conjecture on every tree, three sizes further than before· Aug 4, 2026
Every run first had to reproduce the expert's published tables exactly. That let him check the new work on his own machines instead of taking my word for it.
WritingExtending an expert's tables for unsolved take-away games in a way he could check himself· Jul 16, 2026· 3 versions
In July I pushed the published tables for a set of unsolved take-away games two to four times further. In four of the games, new heap sizes with rare values turned up.
RecordPublishedExtending the tables for a set of unsolved take-away games, checked and built on by the expert who keeps them· Jul 16, 2026· 3 versions
A number in the OEIS, a public database of number sequences, had a dropped digit for over a decade. A Claude agent spotted it; the right value was confirmed by two separate routes and the entry corrected.
WritingFinding and fixing a number that was wrong in the OEIS for over a decade· Jul 13, 2026
The first OEIS entries counting labeled dependency charts (directed acyclic graphs) in which each task waits on at most two or three others, with proved formulas and values far past the only earlier table.
WritingCounting dependency charts where each task waits on at most two or three others· Jul 5, 2026
The largest table from the July take-away game work, taken four times past its published end after first reproducing the old table exactly. No new rare value appeared.
RecordPublishedExtending the table for one unsolved take-away game to four times its published length· Jul 5, 2026· 2 versions

Shapes that fill space3

An entrance test for an AI-built search program caught a rule that would have thrown away the very solid it was looking for. Then a reviewer's pointer showed the "new" solid had been printed, unnamed, in a 2016 survey.
WritingBefore my AI pipeline could hunt for new shapes, it had to rebuild a known one· Oct 4, 2026
Counts of the shapes you can build by gluing copies of the Josehedron face to face; the OEIS had none before. Mathias Bernhard named this space-filling solid this spring.
EnumerationPublishedCounting the shapes you can build from the Josehedron· verified Aug 15, 2026· 3 versions
Shapes built by gluing copies of two space-filling solids face to face: more counts for the bisymmetric hendecahedron, and the first I could find for the cell of the sphenoid honeycomb.
WritingCounting the shapes built from two space-filling solids, including one with no earlier counts· Jul 5, 2026

How the work is checked3

When you hand someone results made with AI agents, they need to know what they can check from what you gave them and what they have to take on trust. An editor of a public math database asked me exactly that about a count I had added. The honest answer was "at least this many", not "exactly this many".
WritingAn OEIS editor asked what my "certificates" proved, and I changed how I label evidence· Sep 26, 2026
I keep a record of every error a check caught in my math work with AI agents: who made it and what caught it. Two of them changed how I check everything.
WritingThe record I keep of errors my checks caught, and two that changed how I work· Sep 11, 2026· 2 versions
When I rechecked everything an AI model produced during a switch I had not been told about, every computed number came out the same when it was recomputed. The errors were in the wording around the numbers and in how some checks had been done; one real finding had also gone unnoticed.
WritingHow results here get checked, and what a full recheck after an AI model switch found· Jul 17, 2026

Software2

A case study of my own AI agent team: what the lead agent's check before accepting work caught, and what got past it.
PaperAcceptedVerify Before You Accept· Oct 20, 2026
WSJF is provably the best order for independent work. One dependency, or SAFe's scoring sheet, can make it put the wrong item first.
WritingWSJF rests on a theorem from 1956, and these are the places its conditions break· Jul 16, 2026

What the labels mean

Record: a computation taken further than anyone had published at the time
Enumeration: a count of something with no earlier published count that I could find
Writing: an essay, about a result or about how the work is checked
Paper: an accepted paper
Accepted: Accepted for publication, not yet in print.
Published: Public and citable.