A table of quantum dimensions that summed wrong

The first entry in the corrections series is also the most embarrassing to explain, because the error was in a table the framework had been printing since its second paper, and the error was visible to anyone who added up the columns. This post is about the quantum dimension table, why nobody added it up for a year, and what the programme built from the wreckage.

The table

The framework’s central calculation, the 2592, is a product of three contributions: 2 from SU(2), 36 from SU(3), and 36 from the cyclic factor, timesing to 2592, the boundary category’s total quantum dimension. The SU(2) and cyclic columns were correct from the start. The SU(3) column was wrong: it summed to 36 through a count that included six phantom anyons, sectors that the fusion rules do not actually admit, listed in the table and counted in the total.

How it hid for a year

The table looked right, which is the whole problem. It had rows, columns, checkmarks, the visual grammar of verified data. Every individual row was defensible if you did not check it against the fusion rules. And nobody checked, for a year and several papers, for the least glamorous reason in science: the total, 2592, was load-bearing downstream, and everybody in the programme knew the downstream results were fine, so the table felt confirmed by its consequences. The technical term for that feeling is circular validation, and it is the standard way wrong tables survive in otherwise careful work.

The exposure came from outside the framework’s momentum: the anyon-Standard-Model functor paper needed the SU(3) content in detail, and building the functor required re-deriving the sectors from the fusion rules rather than from the table. The functor paper, ironically, died its own death shortly after, but its re-derivation survived: the SU(3) content is 30, the six phantoms are not there, and the correct product is 2 times 30 times 36 times the grading factor, still landing on 2592 through the corrected path.

What was rebuilt

The repair touched three things, in increasing order of importance. The table: recomputed from the fusion rules, with the phantom sectors removed and each row’s admissibility checked. The downstream results: every number that consumed 2592 re-audited, and the surprising, load-bearing finding that the total survives the correction, because the category’s dimension is fixed by the fusion algebra and the wrong table had been compensating errors, not a wrong total. And the paper that found it: archived for its own reasons, but credited in the ledger as the audit that caught the longest-lived error in the programme.

The rule

The rule this corpse bought is the cheapest in the whole method series: sums get added. Every table with a total gets its columns summed, by the reader, before the total is cited. The check is seconds long, it requires no physics, and it would have caught this error on day one. The reason it is a rule rather than a habit is that the failure it prevents does not feel possible from the inside: nobody who has just built a table doubts their own sum, and the point of the rule is that the feeling is exactly what the rule is for. The archive’s shortest correction entry is its most reproducible failure: any team, any field, any year, tables get built, sums get trusted, and nobody adds them up.

The next entry is the failure that forced the question, of every number in every table, whether its inputs were chosen before or after the answer: the Yukawa ratios.