The Spectral Admissibility Sub-Programme

Abstract

The spectral admissibility sub-programme of the Cosmochrony corpus addresses a single central question: which spectral sectors of the Weil representation of ${\mathrm{Heis}}_3(\mathbb{Z}/q\mathbb{Z})$ survive the Born–Infeld bounded-flux constraint? The answer organises the entire O-series (papers O1–O32 and five precursor papers) into a logically closed derivation chain: \[ \text{bounded flux} \;\Longrightarrow\; \text{admissibility envelope} \;\Longrightarrow\; \text{Weil-sector capacity} \;\Longrightarrow\; {\delta_{\mathrm{pair}}} \;\Longrightarrow\; {\beta^*} \approx 0.126. \] This note maps the constituent papers, identifies four internal phases, records the status of every result as proved, structural, or open, and states the two remaining open deliverables: the pointwise analytical proof of hypothesis $[\mathrm{H\text{-}color}]$ (partially resolved at three levels in O32) and the extension of the numerical campaign to $q = 401$.