Why I publish my own corrections

Fourteen entries in the corrections series, counting the retracted papers, the back-solved coefficients, the post-hoc phase, the broken instanton, the unbounded probability, and the copied sum. A research programme publishing its own failures at this rate is unusual enough that the behaviour needs a defence, and this post is it.

The arithmetic of trust

A correction that stays private costs the programme nothing today and everything later. The reason is base rates: any framework this size produces errors at a roughly constant rate, and a reader who sees fourteen corrections attached to a corpus can estimate that rate and discount accordingly. A reader who sees a clean corpus cannot estimate anything, and the rational response to the unmeasurable is to assume the worst, because clean is exactly what a corpus with unmeasured errors looks like. Publishing corrections converts an unbounded liability, hidden errors of unknown number, into a bounded one, errors of known number and documented species. That conversion is the entire argument, and it is arithmetic, not virtue.

The second arithmetic: corrections compound. Each one documents a failure mode, and the species are few. A back-solved coefficient, a post-hoc selection, a dimensional cancellation, an unbounded formula, a copied sum, a dependency on an archived result. Six species cover the fourteen. Any future result in this programme gets checked against six known diseases before it is believed, which is why the correction rate should fall even as the corpus grows, and the falling rate is itself verifiable from the archive’s dates.

What the corrections bought

Three things, in ascending order of importance. First, the specific repairs: the corrected eta invariant, the bounded permeability, the derived capacity replacing the numerology, the honest a zero, all now load-bearing and clean. Second, the method machinery: the status labels, the provenance checklist, the dependency ledger, the preregistration rules, each of which exists because one of the fourteen made it necessary. Third, and least replaceable: the corpus’s credibility is now measured. A reader knows the error rate, the species, and the repair latency, and can price the claims accordingly. No amount of confident prose purchases that, and it is the one asset in this programme that strictly appreciates.

The part that is not noble

The post should end honestly about motive. Several of these corrections were forced: the audits that found them were run because the programme’s own numbers were about to be used in work that mattered, and publishing was the cheapest way to keep the record straight once the errors existed. What started as self-protection became method. The genuine change of state is that the programme now runs audits before being forced to, because the previous corrections taught it where its own errors live, and a failure mode you have named is a failure mode you can test for on schedule instead of by accident. Fourteen entries is not a shame. It is a price list, and the alternative, an unpriced corpus, is what should be embarrassing.

What follows is the computational series, the newest work and the part that does not depend on the topology, starting with novelty as a compression measurement.