The Cosmochrony Research Programme: A Structural Roadmap and Paper Inventory

The Cosmochrony programme develops a pre-geometric framework in which physical structure — spacetime, quantum mechanics, gauge symmetry, and Standard Model observables — arises from a single primitive: the local structure of admissible non-injective transitions between observable states. The corpus comprises 116 papers across three theory branches. Branch I (Foundation track) develops four admissibility axioms and their consequences. A finite \(S_3\) countermodel now proves that the algebraic properties extracted from those axioms in the published carrier-selection argument do not force a central commutator, a finite Heisenberg group, or a Weil representation. The Heisenberg/Weil carrier is therefore a supplied realisation, not an axiomatic theorem. Branch II (O-series) develops the spectral admissibility sub-programme, studies the conjugate-pair fibre structure on a supplied Weil model and measures its capacity exponent $\delta_{\mathrm{pair}}$. The native Heisenberg span-growth law proves that the proposed conversion $\delta_{\mathrm{pair}} \to \beta^*$ has no derived carrier on the measurement substrate; its numerical agreement with the charged-lepton hierarchy remains a phenomenological coincidence check rather than a structural derivation. The same branch's former identification of the Standard Model gauge group has been withdrawn in O31 version 2.0; the colour factor and the complete gauge group are open. Branch III (Q-series and companion papers) develops spacetime geometry and gauge dynamics from the Branch I axioms and supplied Branch II spectral data, and states a universal singlet correlator conditional on an explicit, undemonstrated invariance hypothesis (paper Q3; the Born rule remains open), a conditional effective co-metric of rank three whose non-degenerate block is Lorentzian, under the open inputs [H-L], [H-lift] and [H-hyp] (the full-rank extension and every coefficient value remain open, and the co-metric $\mathrm{diag}(-2,2,2,2)$ still asserted by the Foundation paper and by some Lorentz-capacity and spectral-gravity consumers is pending revision); and the spectral derivation of the Einstein ($a_2$) and local Yang–Mills ($a_4$) sectors from a single spectral-entropy functional, conditional on supplied renormalized matching data (papers Q12–Q13). This paper provides a complete inventory, a logical dependency map, and a structured account of what is proved, structural, heuristic, or open, intended both as an entry point for external readers and as an internal navigation reference. Interpretive status. The programme's unifying reading — that physical structure is organised by admissibility and by spectral (Seeley–DeWitt) order rather than by an enlarged symmetry group — is offered as an interpretive outlook, not a theorem; each individual result carries the epistemic label (proved, structural, heuristic, or open) recorded in the inventory below.