The Spectral Admissibility Sub-Programme

Abstract

The spectral admissibility sub-programme of the Cosmochrony corpus addresses a single central question: which sectors of a supplied finite Heisenberg carrier and its associated Weil action survive the Born–Infeld bounded-flux constraint? The investigation organises the entire O-series (papers O1 and O3–O33, five precursor papers, and the Span-Growth and Critical Coverage companion notes) along a single chain: \[ \text{bounded flux} \;\Longrightarrow\; \text{admissibility envelope} \;\Longrightarrow\; \text{Weil-sector capacity} \;\Longrightarrow\; {\delta_{\mathrm{pair}}}. \] Its fibre-structure conditionality is closed by O24 for the segment ${c_{\mathrm{BI}}} \to {\delta_{\mathrm{pair}}}$, under a supplied carrier. The further step to the cascade exponent ${\beta^*}$ is not part of the chain: the reciprocal prescription ${\beta^*} \approx 1/({\delta_{\mathrm{pair}}} + \tfrac{1}{2})$ has no carrier on the Heisenberg measurement substrate, and the Span-Growth Note establishes that the expander-derived conversion does not transfer there, so the agreement of ${\beta^*} \approx 0.126$ with the charged-lepton window is a coincidence check and not a derivation. On the SU(2) side the carrier is supplied conditionally rather than derived, and on the SU(3) side the O31 record is a withdrawal notice, so the colour group and the Standard Model gauge group are open. This note maps the constituent papers, identifies the internal phases, records the status of their principal results as proved, structural, numerical, conditional, or open, and states the open deliverables: hypothesis $[\mathrm{H\text{-}color}]$, of which the two levels established in O32 stand while those that rested on O31 are not currently asserted; the identification of the spin-$\tfrac{1}{2}$ sector; and a full-breadth numerical campaign beyond $q = 211$. Interpretive status. This map distinguishes internal mathematical results from supplied carriers and open bridges; it does not derive a physical gauge or matter sector.