ZQCM: An Axiomatic Cosmological Framework from S³ Spectral Geometry, Spinor Symmetry, and a Coxeter Selection

We construct a cosmological framework from three axioms — S³ spectral geometry, a Spin(9)⊃B2×D2 spinor lock, and a B‑type Coxeter structural selection (Δ=h(B4)−h∨(B2)=5) — plus five registered constants, with zero adjustable parameters in derivation chains (inputs and declared anchors itemized in a tiered ledger). The framework yields: a closed‑universe geometry (Ωk∈(−0.01,0)); a static Einstein‑universe initial state with a proved no‑beginning theorem; an exact elastic micro‑theory of the vacuum (closed‑form order parameter, B=0 potential); a dark‑matter candidate (0.97keV) and a dark‑energy value (−2.9 from observation) from the same ladder; a pre‑registered, zero‑parameter dark‑energy dynamics w(a) testable by DESI/Euclid 2026–2028; and a constants department with every load‑bearing claim explicitly tiered (derived / reverse‑fitted / declared / immunized / external). Twenty‑two internally generated claims have been formally executed by the program's own audit. External confirmations to date: zero — stated here first. This paper presents the model; a companion deposit presents the audit.