Protocol V3.2: Evaluation Criteria for φ-Proximity Claims — Eight Failure Classes and a Multiple-Comparison Correction
Abstract
Protocol V3.1 evaluated a φ-proximity claim by a single criterion: the deviation δ = |x − φⁿ|/φⁿ, with n the nearest integer power, where δ < 0.05 marked a claim as surviving and δ > 0.10 as falsified. A corpus-wide audit conducted in July 2026 identified eight distinct ways that criterion can return a favourable verdict on a quantity carrying no φ-structure. Each was found in published FCLT papers, and each was found by the author. This document states the eight, gives a rule closing each, and applies the resulting procedure to the corpus. The most consequential correction is the last. Because n is chosen as the nearest power, the null probability of a φ-free quantity clearing δ < t is the flat lattice value P = 2t/ln φ, independent of magnitude; at t = 0.05 this is 20.8%. Across 137 registered predictions the expected number of chance passes is therefore 137 × 0.208 ≈ 28, which exceeds the number of surviving conjectures the series has claimed. Applying the Benjamini–Hochberg procedure at q = 0.05 across the corpus, no proximity row attains significance. The strongest, m_μ/m_Planck at δ = 9.4 × 10⁻⁵ and P = 3.9 × 10⁻⁴, misses the rank-one critical value of 3.6 × 10⁻⁴. Protocol V3.2 therefore retires “survives” as an evidential status. The threshold δ < 0.05 is demoted to a screening filter that admits a quantity for consideration and asserts nothing about it. Falsification at δ > 0.10 is retained unchanged, because a failure against a loose bar is informative where a pass against it is not. What FCLT retains as evidence is stated explicitly: one conditional theorem, a set of zero-parameter derivations, and a set of pre-registered forward tests that have not yet been run. The proximity corpus is not among it. This is a substantial and deliberate reduction in what the framework claims. It is made once, by rule, rather than by continued paper-by-paper attrition.
Fields of Study & Subjects
Statistical Methods in Clinical Trials
Statistical Methods and Bayesian Inference
Statistical Distribution Estimation and Applications
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 24 July 2026
- Document type
- Preprint