A Kohlrausch or Weibull Exponent Below One Admits a Classical Mixture: Pollard's Criterion as a Licence Condition, Two Predictions Refutable Against Existing Literature, and a Self-Audit of the Framework That Produced Them

Abstract

Consolidated edition. This version merges the three previous papers of the programme into a single document, reordered by logical dependency rather than chronology so that the surviving core is separable from the speculation built on it. 63 pages, 26 sections in 7 parts, 8 appendices. Eloy René Becerra Daly What is established, in decreasing order of confidence [EXACT] Identities. The Λ-hierarchy reduces to τ = ℏ/E and ℓ = the reduced Compton wavelength. The accessible information satisfies IQ = (γ/τ)β exactly. A distinguished point at D/L = 1/2 carries four coincident properties — exactly one bit, the entanglement sudden-death point for C0 = 1, the maximum of D·C̄ at L²/4, and a Bures arc of π/3 — all invariant in β, τ and L. [OBS] Verification. D + C = 1 holds to machine precision across 650 circuits on two IBM backends and ~5.5×106 shots. [THM] Limits. A no-go theorem shows the temporal exponent of dephasing is independent of the pulse-sequence filter, which removes the derivation previously claimed for Axiom 3 and relabels it as an empirical postulate. [THM] The transferable result. Pollard's criterion used as a licence condition: β ≤ 1 certifies that the curve admits a positive rate density, β > 1 proves that none exists. In reliability engineering an infant-mortality exponent licenses reading the batch as heterogeneous, while a wear-out exponent forbids it under any partition. Six transfers are registered, each with the observation that would retire it. The inference this work does not license A fitted β < 1 is not evidence of quantum behaviour. The theorem establishes representability of the curve, not identification of the mechanism — the map from mechanism to curve is many-to-one — so what follows is weaker and sufficient: the data cannot be adduced as evidence of coherence, because a classical account of them exists. The decisive test, which is not performed here On a single sample, the anomalous-diffusion exponent and the stretched-relaxation exponent must satisfy β = (1 + αdiff)/2, with β ≥ 1/2 as a corollary. Both quantities are already tabulated in the NMR relaxometry and diffusion-imaging literature for overlapping sample sets. No new experiment is required to attempt this refutation. Errata to previous versions The critical qubit number is n* = 1.848, not 2.6. The LIGO ringdown significance, with the internal error scaled by √(χ²/ν) = 1.669 as the catalogue's own goodness of fit requires, is 12.5σ; we record that our first correction of it, 20.9σ, was itself wrong for neglecting that scaling, and that the originally published 13.8σ was closer to the defensible value than our correction. A reported 18 kHz emergence mode lies below the Rayleigh limit of its own data. The published comoving density of remnants corresponds to Ω = 0.063, not the 0.12 it is stated to reproduce. Endpoint, labelled CONJ throughout The programme closes with a dark-matter candidate: Planck-scale black-hole remnants at Mmin = mP/(2√π) = 6.140 µg, an exact identity rather than the approximation 0.28 mP under which it was published. Evaluating it shows the usual dismissal to be right for the wrong reason: the remnant carries 148.6 J at galactic velocity and one transit is expected per 0.86 km²·yr, so rarity is not the obstacle; but the mean free path in rock is 1023 light years and the probability of one interaction while crossing the Earth is 10-32. The candidate is cross-section-limited, not exposure-limited, and the two demand opposite experiments. Four falsifiers are given, two requiring no new instrument. Reproducibility Every numerical claim is recomputed from the equations by a dependency-free implementation: 354 regression tests and 37 published-number checks, over a registry of 138 equations each carrying source, evidence level and declared domain. Where a published number could not be reproduced it is recorded as an erratum rather than adjusted; where a correction of ours proved wrong it is recorded as such. The register documents 27 inconsistencies, of which 11 remain open, each with the observation that would close it.