Glass Is an Unclosed Layer: Kovacs Memory as Predictive-Quotient Residue

Abstract

Glass Is an Unclosed Layer: Kovacs Memory as Predictive-Quotient Residue asks, on finite Markov models small enough to settle it by exact computation, whether a declared readout forms a closed description: whether its present value fixes its own future statistics. Kovacs's 1963 crossover experiment is the laboratory form of the question: at the moment an aged sample's volume equals its equilibrium value, the volume moves away again. The models are the East and Fredrickson–Andersen kinetically constrained spin chains and a Bouchaud-type trap family. The bookkeeping comes from the certificate-based closure calculus of Six Birds Theory, which the paper cites rather than re-derives; every object is also defined in ordinary probabilistic terms. The results, each stated at its declared finite scope: the energy readout of an aging East chain has a closure deficit at least 3/2 times its constrained-equilibrium value at every tested horizon, certified in exact rational arithmetic, and the equilibrium value is itself provably nonzero (GT1); the Kovacs protocol yields two preparations with the same mean energy now and different mean energies later (GT2); all 512 yes/no functions of the energy agree on a constructed pair that one structural coordinate separates (GT3); a kill-test panel rejects five look-alike regimes (GT4); one added coordinate resolves the Kovacs pair (GT5); two randomized stops of one aging run share the entire energy distribution, exactly, yet their mean energies separate at each of 21 later horizons, so no function of the current energy law, a fictive-temperature-like index included, predicts the future on that shell (GT6); and aging constants frozen on East and scored mechanically on Fredrickson–Andersen pass 8 of 22 predictions, with the trap column empty for a reason the paper proves (GT7). The paper also reports what does not hold: the fixed-point route to a full strict-extension filing fails on the audited shell, and a positive infinite-time conditional pressure gap is provably zero there. Lean machine-checks the abstract theorems and the exported witness tables; a legacy formal core is proved unable to express any witness. Every claim is pinned by content hash to its evidence, and the full ledger of what is not claimed is printed unabridged. Version 2 follows an independent mathematical and Lean audit of every certificate. It rebuilds the GT6 result around a new same-shell full-energy-law witness, certifies the GT1 margin in exact arithmetic, mechanizes the numeric witness tables in Lean, corrects the GB1 stationary bound, and rewrites the exposition throughout; an appendix lists the changes. This work is part of the Six Birds Theory programme and is substantially AI-assisted.