Phi-Genesis
Methodology — Testing Spectral Selection Rules
This page explains the method used to test whether spectral configurations select the target indices (T={1,12,17,40}). The full versioned protocol is maintained in METHODOLOGY.md; the cumulative record is the protocol ledger.
The question and the look-elsewhere effect
The mass formula (m=A n) fits four selected masses with one scale and four integer indices. The central research question is not whether the fit can be written down, but whether a spectral rule independently selects those indices. Trying many operator configurations makes accidental matches increasingly likely.
The protocol therefore asks whether a configuration scores unusually well relative to null ensembles after taking the maximum over the tested configurations. A striking individual match is not enough.
Protocol design
- Fix the target and rule. Record the target set, index-selection rule, spectral window and tested family before evaluation.
- Define null ensembles. Use generic operators of the relevant type to estimate how often each target appears by chance.
- Weight by base rate. Common targets should contribute less evidence than rare targets.
- Correct for searching many configurations. The test statistic uses the best score across the family, not just a hand-picked configuration.
- Check power using null data alone. Confirm that the chosen statistic and threshold can be reached before evaluating the target family.
- Use a fixed decision threshold. A candidate must reach (p\le0.01) under both specified null ensembles.
- Keep a cumulative ledger. Record abandoned, exploratory and related families, and disclose dependence between them.
Why the power check matters
Protocol v1.0 was unable to reach the decision threshold even if a configuration selected all four targets. Its negative outcome therefore did not meaningfully discriminate the tested family. Later protocols changed (k) using null-only design so that the threshold could be reached. Those later tests still did not pass.
Interpretation discipline
A negative result applies to the tested family, selection rule, parameter range and null model. It does not prove that no mechanism can exist. Conversely, a numerical match after choosing targets and trying many configurations is not a prediction.
Primary records
Interactive portal · Research map · Verified results · Open problems · Reproducibility · Dissertation · Source repository