The cosmological constant from the semiclassical S4 partition function: supporting analysis and extended framework

This is the companion paper to Ref. [1], which obtains a zero-parameter formula for the cosmological constant as a conditional theorem from three premises: (P1) instanton dominance of the round S4 at Planck curvature, (P2) Born-reciprocal evaluation scale H2 = mpMP, and (P3) anomaly extraction via the scheme-independent Weyl response. Here we provide the detailed supporting analysis deferred from that work. We establish the topological dominance of S4 among compact positive-Einstein spin manifolds (ChernGaussBonnet volume bound); prove four-dimensional uniqueness of the gravitationalgauge action ratio; demonstrate stabilisation of the conformal sector by the matter trace anomaly (aSM >0); compute the one-loop finite part ΓSM = 4.773 and the full error budget; derive the infrared scale from the QCD deconnement crossover (2πTc ≈mp to 4%); provide the minimax consistency check on the evaluation scale; prove that the linear power (mp/MP)1 cannot emerge from the Euclidean sector and is uniquely selected by the modular involution; and develop the thermodynamic interpretation identifying Λ with the horizon Helmholtz free energy. Each section is self-contained and keyed to the corresponding premise or derived consequence of Ref. [1].