Projective Temporal Ordering and Cumulative Projected Capacity: Numerical Evidence from the Spectral Admissibility Cascade

Abstract

We identify a monotone proxy for temporal ordering within the Cosmochrony spectral admissibility programme. The natural observable along the BFS cascade is not the residual capacity $\sigma_{\mathrm{pair}}(n)$, which decays by construction, but the cumulative projected capacity $I(n) = \sigma_{\mathrm{pair}}(0) - \sigma_{\mathrm{pair}}(n)$, which measures the spectral structure already projected at depth $n$. For $q \in \{29, 61, 101, 151, 211\}$, $I(n)$ is found to be strictly non-decreasing at every BFS step, for every conjugate pair $(c, q{-}c)$, with zero physically meaningful regressions observed across 274 pairs and 360 steps after burn-in. The temporal ordering is not a dynamics on the substrate $\chi$, but an induced ordering relation on admissible projections, compatible with the observable rank stability established in O24. The saturation plateau of $I(n)$ is interpreted as Born–Infeld saturation at the pair level.