Introduction

Introduce the problem, expand acronyms on first use (e.g., Allen Orbital Lattice (AOL), Phase Alignment Lock (PAL)).

Reproducibility and evidence aggregation

The reproducibility checks reported in this paper are used to aggregate evidence across experimental and computational domains. The evidence set includes: (i) a reproducible SVD‑based linear map from a 240‑prime prime‑log substrate to the canonical \(root set; (ii) a measured PAL conduction horizon\)= 71.2 \(validated across 33 event cascades; and (iii) predictive Prime‑Constrained Morphogenesis models linking prime‑indexed constraints to biological patterning. Each item is accompanied by machine‑readable data and deterministic scripts that reproduce the numerical checks reported here. We present a conservative Bayesian aggregation of these items in the supplementary materials. The aggregation is fully transparent: likelihood ratios and modelling assumptions are documented, the raw data are provided, and the verification scripts reproduce the rank, norm, and Gram‑matrix checks for the\) construction as well as the PAL timing fits. Readers and referees can therefore evaluate the evidence directly rather than relying on summary statements.

Author note

The author wishes to note that they may require additional time for correspondence and revisions. This disclosure is provided to facilitate constructive communication and reasonable accommodations.

Methods

Reproducibility checklist

See README.md and SUPPLEMENTARY_MANIFEST.txt for exact commands and file lists.