A Conditional Closure Theorem for the CIFT-CMM-CUP Chronometric Programme: Chronometric Algebra, Stationary-Dressing Recovery, and Controlled Low-Residual Limits

This manuscript presents a conditional theoretical closure theorem for the low-residual sector of the CIFT-CMM-CUP chronometric research programme. The paper does not claim empirical confirmation, an unconditional theory of everything, a derivation of the Standard Model gauge group, a UV-complete theory of quantum gravity, or a full nonlinear strong-field stability theorem. Its contribution is conditional and mathematical.

The manuscript first reconstructs the chronometric algebra from a common modular record-state structure. Given an admissible record subalgebra, a faithful normal state, a record-degradation channel, an admissible record-transition map, and a modular-compatible coarse-graining, the record factor, distinguishability factor, local chronometric scalar, and maintenance operator are recovered as linked functionals of the same algebraic structure.

Second, the paper proves a stationary-dressing recovery theorem. If there exists a positive recovery point satisfying the stationary-dressing and stability conditions, then in the low-residual limit the chronometric effective system recovers Einstein gravity with an effective cosmological constant, ordinary quantum field theory on the recovered background, and a ΛCDM-like Friedmann limit, with deviations bounded by a closure-error functional.

The manuscript further supplies support results on the existence of the stationary point through an even recovery symmetry, a naturalness criterion for stationary dressing, conservation bookkeeping compatible with the Bianchi identity, a unified closure-error bound, and local recovery-point stability. A gravitational-collapse/decoherence feedback channel is included only as a conditional candidate mechanism, not as evidence for the theory.

The final status claimed is that the CIFT-CMM-CUP programme is conditionally theoretically closed in its low-residual recovery sector. The paper explicitly defers empirical confirmation, Standard Model gauge selection, UV completion, strong-field gravity, and quantum cosmogony as bounded future sectors.