The Emergent Geometry Sub-Programme

The emergent geometry sub-programme of the Cosmochrony corpus addresses a single central question: how does the admissible Weil–Heisenberg fibre give rise to an effective four-dimensional Lorentzian geometry? Starting from the admissibility filter Πq acting on the Weil representation V_ρ of Heis₃(Z/qZ), the sub-programme organises the following chain: \[ Π_q \;\; V_ρ L^2(Z/qZ) \;\; {Heis}_3(R) \;\; {Leff} \;\; {gμν} \;\; {gμν} = 2ημν. \] This note maps eleven constituent papers (Q5a, Q5a-O2, Q5b, Q6b, Q7–Q11, U1, W1, H2) across five internal phases and records the status of every result. Status revision (version 1.1). Q5a version 3.0 withdraws the first link of this chain: the canonical filtration of the admissible fibre is exactly a growing toric Fourier window, the published admissibility form converges to the zero form on it, and no common scalar normalisation produces a non-trivial toric differential operator. The existence of the spatial limit operator L_Π = -A∂ₓ² is now the explicit, unestablished hypothesis [H-L] (Q5b version 2.0), and every downstream result that consumes it is conditional on [H-L]. The geometric convergence results (Carnot limit, Dₕₒₘ = 4) and the algebraic coefficient rigidities (Q7, Q8, Q10, U1) are independent of [H-L] and stand. Question Q5 is open.