Blog
A merged audit of 67 targets withdraws a roughly 10-sigma reading after enumerating the search family that made near-matches likely by chance.
PR #738 is merged in gHashTag/trinity. It audits the statistical-significance section of sacred-formulas.md with a reproducible enumeration rather than accepting the probabilities printed in the document. The audit covers 67 factual targets and the family V = n · 3^k · π^m · φ^p · e^q around each one.
The important correction is not that a few formulas moved in the last decimal place. It is that the size and local density of the search family determine how surprising a near-match can be. A narrow numerical band is not evidence by itself when the search produces many candidates for every target.
| Enumeration | Combinations | Printed probability | Recomputed probability | Corrected reading |
|---|---|---|---|---|
| Standard, m from −3 to 0 | 54,756 | 0.2% | 64.2% (minimum 33.2%) | near-matches are common |
| Extended | 123,201 | 2.9% | near 100% (minimum 88.4%) | the search is highly permissive |
For the extended enumeration, a probability near 100% per target implies roughly 67 expected hits among 67 targets. The document listed 32. Being below that chance expectation does not establish significance in either direction; it means the reported matches are not informative at the stated precision.
The audit therefore withdraws the earlier roughly 10-sigma and 3-sigma readings. For the extended family, a Šidák correction with M = 123,201 and α = 0.05 gives a threshold of 5.06σ, not 3σ. This threshold is a property of the declared multiplicity model, not a universal constant.
The merged change adds executable checks and replaces several trusted numbers with values recomputed from the underlying rows. It also corrects the count of established constants from 75 to 70 and the EXACT class from 35 to 32. These are not new measurements of nature; they are corrected readings of the repository data.
One numerical comparison shows why arithmetic precision is not the main issue here. For the proton-to-electron mass ratio, the corrected target is 1836.152673426(32), while the document’s formula misses it by 6.3·10⁷σ when expressed in measurement-uncertainty units. The audit separately checks floating-point error and finds it far below the tolerance used by the calculation, so this discrepancy is not explained by rounding.
Before asking whether a match is surprising, enumerate what was allowed to match.
That is a useful outcome for a codebase that wants its numerical claims to remain inspectable. The audit does not declare the coincidences false. It makes the stronger and narrower statement that this search procedure makes them too easy to obtain for the old significance language to survive.
Every figure above is measured, and the limits are named with it.