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 110 papers across three theory branches. Branch I (Foundation track) builds the axiomatic base: four axioms suffice to derive the Heisenberg group ${\mathrm{Heis}}_3(\mathbb{Z}/q\mathbb{Z})$ and its Weil representation as theorems, without any background substrate or relaxation mechanism. Branch II (O-series) develops the spectral admissibility sub-programme, deriving and numerically validating the transfer chain $c_{\mathrm{BI}} \to \delta_{\mathrm{pair}} \to \beta^* \approx 0.126$ that connects the Born–Infeld saturation constant to the charged-lepton mass hierarchy, and identifies the Standard Model gauge group $G_{\mathrm{SM}} = {\mathrm{SU}}(3)\times{\mathrm{SU}}(2)\times\mathrm{U}(1)$ (unconditional at the pointwise level on the standard graph). Branch III (Q-series and companion papers) derives quantum mechanics, spacetime geometry, and gauge dynamics from the Branch I axioms and Branch II spectral data: the universal singlet correlator and Born rule (paper Q3), the effective Lorentzian co-metric $g^{\mu\nu} = \mathrm{diag}(-2,2,2,2) \propto \eta^{\mu\nu}$ under the continuum-limit hypotheses (the geometric-emergence papers, with $A_\tau = 2$ from paper Q11), and the spectral derivation of the Einstein ($a_2$) and local Yang–Mills ($a_4$) sectors from a single spectral-entropy functional (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.