Quantum Mechanics from Records: Measurement Structure on a Finite Path-Kernel Domain

Abstract

We give a finite path-kernel representation of record-conditioned quantum statistics, with a qualitative admissibility classification and an explicit restriction operation. The primitives are consistency constraints on observer-indexed information states: determinacy indexed to a state, informational blanks identified with superpositions, and a two-quantifier pruning rule, the third postulate, under which a state is valid when some declared refinement of it has no contradictionreaching descendant. Under a complete and persistent record structure the rule classifies every subset of a space of paths as valid, over-specified or consistency-pruned, drawing the quantumclassical boundary as the record partition before any weight exists. One quantitative axiom, the path kernel, then yields on a fixed finite domain a Hilbert representation of the admissible clusters with the Born statistics, record observables as self-adjoint operators by a soundness result, and the projection postulate as the representation of a stipulated record-compatible restriction, realized as L¨uders conditioning and not selected by the validity postulate alone; completeness is excluded on any one finite domain. The two-tag configuration exhibits both composition regimes in one apparatus and meets the quantitative predictions, and the same admissibility criterion governs an unread which-path record and an unread friend’s laboratory, with the condition still to be established for a whole laboratory stated as a physical premise. What records physically are, and the framework’s divergence from universal unitarity, are the companion’s.