PARTIAL CLOSURE AND THE THEORY OF DISCLOSABILITY Predictive Quotients, Residual Relevance, Backreaction, and Minimal Reclosure

Abstract

A quotient-fiber framework for lawful prediction under non-exhaustive realization, with exact descent, target- and horizon-relative predictive equivalence, projected fiber spread, closure backreaction, and minimal reclosure. Keywords: partial closure; disclosability; predictive quotient; coarse-graining; backreaction; reclosure; effective theory; model reduction Effective physical laws often predict selected variables without uniquely determining the underlying physical realization. This paper develops a quotient-fiber framework for that situation. A disclosure structure separates a realization space Ω, a disclosure space X, and a compatibility relation ω ⊨ x, inducing realization fibers and a canonical disclosure quotient. A distinct, model-dependent realization projection π : Ω → K supports autonomous effective dynamics precisely when evolution descends through the quotient. For a selected target Y and predictive horizon T, we define a canonical predictive equivalence and quotient KY,T, and introduce projected fiber spread Δπ,Y[0,T] as a quantitative measure of the future relevance of distinctions suppressed by π. Exact predictive closure corresponds to vanishing spread; positive spread witnesses closure backreaction. Refinement monotonicity motivates closure plateaus and a minimal-reclosure problem: restore only those distinctions required to meet a specified target, horizon, and tolerance. The framework is calibrated against Hamiltonian conservation, hydrodynamic moment closure, reduced quantum dynamics, and quantum error correction. We position the construction relative to Mori-Zwanzig projection, Markov lumpability, bisimulation, computational mechanics, and Koopman-invariant reduction. The broader Theory of Disclosability interprets these results through the principle that a lawful disclosure need not exhaust the realization that supports it.