Persistence Logic

Latest version note (Section 17 addition). This version adds Section 17 (Dissolution, Persistent Structure, and the Forced Core), which addresses the permissiveness objection without introducing a new primitive. A null class of dissolving distinctions is derived from the existing reconstructibility predicate; the forced core — the distinctions no admissible variation can render non-reconstructible — is identified as the structure the calculus forces regardless of admissibility choice. The section adds an inclusion preorder on admissibility classes, a monotonicity result for dissolution, and a supporting lemma establishing that reconstructibility entails reversibility (used contrapositively in the forced-core argument). Three local corrections from peer review were applied: the quotient Π(V) is now typed as a structured quotient with N = [0] anchored to the flat corner; the forced core is typed at the distinction level Π⋆ = D ∖ ⋃_V N(V); and admissibility classes are presented as objects of comparison via the preorder rather than as parameters. A forward reference in Section 4 makes the structural dependency explicit in the body. Formal verification of the core results in Lean 4 is planned.