Writing

I had called the files behind one of my OEIS counts "certificates". The editor's question showed they supported only a lower bound, so I renamed them, and this post walks through that case and the checklist I now run before I publish anything.

I keep a record of the errors my own checks caught and call it an own-goal ledger. This post explains the record, tells two of its errors in full (a false alarm that looked like a disproof, and two programs that agreed on a wrong count), and points to the workshop paper built from it.

The levels of checking every result goes through before it appears here, and what happened when I redid all the work from the days my AI sessions had been switched to a different model without my knowledge.

For product managers who rank work with WSJF, SAFe or RICE: the old theorem behind the formula, small examples you can check by hand where it goes wrong, and fixes that need only a spreadsheet. Almost none of the math is mine; it comes from scheduling research.

For analysts who copy values from reference tables: how a number with a digit missing sat in an OEIS entry for years, how a Claude agent spotted it, how it was confirmed and fixed, and two cheap checks that catch this kind of error.

For readers who see headlines about computers and AI "solving" math problems: what a check of every case up to a size establishes and where it falls short of a proof, using an Erdős conjecture about trees as the example.

How a recently named solid became the entrance test for an AI-built search program, the draft rule the test caught, and how a reviewer's pointer turned up the same shape in a survey from 2016. Accepted as a poster at a NeurIPS workshop (MATH-AI); free copy on Zenodo.

In eight of the games no new rare values appeared, which fits with those games eventually repeating. In the other four, new heap sizes with rare values turned up past the old limits (in one of them, just one). Achim Flammenkamp, who keeps the tables, reran parts of the work and has since gone further himself.

The same structure turns up in project planning and in machine learning. This post shows how the counts were computed and checked, which parts are proved, and a pattern in the cap-two counts, found by computer under my direction, that I listed as a conjecture.

Space-filling means copies fit together with no gaps, like bricks. For the sphenoid cell I found no description in print of how its copies fit, so I worked it out and showed it was the only arrangement in which every cell is attached to its neighbors the same way, then counted. Both sets of counts are in the OEIS.

The network is called the twelfth Fibonacci cube, and the new set is now the best known, listed in the OEIS. A month-long solver run that tried to raise the lower end of the known range for the true minimum was stopped before it answered, so the range is unchanged.

Mathematicians copy values from the OEIS rather than recompute them, so a wrong value there can sit unnoticed for years. One had a dropped digit for over a decade. This post covers how an AI agent spotted it, how it was confirmed, and how it was fixed.