Chronometric Closure Paper VII: Operational Derivation and Stability of the Distinguishability Factor
Year: 2026
Type: preprint
Abstract: Chronometric Closure Paper VII addresses the foundational burden of operationally deriving and stabilizing the distinguishability factor D within the CIFT-CMM-CUP programme. The paper constructs the transition-local quantity Dk as a calibrated finite-transition distinguishability functional over admissible finite-rank record sectors, with primary form Dk = Nl dB^2(rho_k, rho_k+1), where dB is the Bures distance and Nl = 1/FQ,ref(l) is the default calibration inherited from CIFT. The central result is a conditional theorem showing that, under finite-rank admissibility, positivity and normalization, operational comparability, non-background parameterization, data-processing monotonicity, coarse-graining stability, and bounded calibration, Dk is non-negative, finite, operationally interpretable, monotone under admissible information-loss channels, compatible with Cl, and suitable for insertion into the Paper VI integrand. A further conditional refinement shows that, where an admissible local record-state assignment and transition localization are available, Dk may be read as the calibrated pullback/restriction of the local distinguishability structure along a record-transition edge. The paper does not claim a universal distinguishability-field theorem for all physical systems.
Author: zituny, tovi
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162959340
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