Prediction, fit, and numerology are three different things

The three most important words in this archive are prediction, fit, and numerology, and the entire corrections series exists because I confused them, repeatedly, for years. This post is the checklist I now use to keep them apart, and the test cases are the archive’s own.

The definitions that matter

A prediction is a number computed from inputs fixed before the number was known, by a route stated before the comparison. A fit is a number chosen to match data, with the choice visible in the method. A numerological claim is a number whose route terminates at the answer: the inputs were selected because of the target, so the agreement carries no information, but the structure pretends otherwise.

The definitions are epistemic, not mathematical. The same formula can be all three, depending on ordering. The coefficient that was a fit can become a prediction, if its derivation is later found and the derivation does not use the data. The prediction can degrade into a fit, if the derivation quietly used the target. Ordering and provenance are everything, which is why the checklist is about history, not algebra.

The checklist

Five questions, in order. One: what were the inputs, and were they fixed before the target was known? Two: could the route have produced any other answer, or was there a choice, of channel, normalisation, or free integer, made with the target visible? Three: if the route had failed, would I have published the failure? Four: does the agreement’s precision exceed what the route’s inputs could support, which is the signature of back-derivation? Five: is there an independent route to the same number that does not touch the target?

Applying the five to the archive’s cases. The Z6 congruence: inputs fixed early, no choices, the failure question answers yes, precision is exact rather than suspicious, independent route exists through the anomaly calculation. Verdict, prediction-strength theorem. The modular phase: input chosen with the target visible, route admitted alternatives. Verdict, fit. The neutrino coefficient: precision far exceeds its inputs’ support, no independent route, route terminates at the answer. Verdict, numerology, now labelled back-solved. The instanton exponent: inputs, the central charge, fixed by independent arguments years before the vacuum application; route admits no freedom; the failure question answers yes, with a named kill criterion. Verdict, the strongest available: a candidate prediction.

Why the distinction is expensive to keep

Because the temptation is structural. A fit that works feels like evidence, and the feeling is stronger when the fit is yours. The five questions are designed to be answerable by someone who does not share the feeling, which is the point: they are audit questions, not introspection questions. The programme’s version of honesty is not a feeling of rigour. It is that every number on the shelf has a file, the file records its provenance history, and the checklist’s verdicts are written next to the number where a reader can see them. When the ordering changes, as when a derivation is found for a fit, the file changes, and the label changes with it. That maintenance, unglamorous and perpetual, is what keeps the three words from drifting back into one.

The next post is the reader’s manual for the badges this archive puts on its claims: how to read a status badge.