Quantum Mechanics from Records: Three Consistency Postulates and One Kernel Recover the Dirac–von Neumann Formalism, with the Projection Postulate as a Theorem

We give an axiom set for quantum mechanics in which measurement is derived rather than posited. The primitives are consistency constraints on observer-indexed information states: determinacy indexed to a state, informational blanks identified with superpositions, and a two-generation pruning rule whose ∃∀ form is selected by elimination within a stated class, together with one quantitative axiom, a path-pair weighting kernel over the powerset of alternatives. Two results follow. A classification theorem, proved from the postulates alone before any quantitative axiom is available, shows that a record structure induces an exact partition of the candidate superpositions over n alternatives into valid, over-specified, and pruned classes, relocating the quantum–classical boundary from scale to information. A recovery theorem then reconstructs the Dirac–von Neumann formalism: observables are the partitions records induce and the projection postulate is pruning followed by renormalization, both theorems of the postulates; the state space, superposition, composites and evolution are the kernel’s own content; and the Born statistics follow from the primitive weight law, complex amplitudes being representational reconstructions rather than ontological primitives. No measurement, projection, or observables axiom remains. The paper is a re-axiomatization, not an operational reconstruction. The kernel is posited, and its content is what the reconstruction programs seek from operational axioms; a table separates what is proved before the kernel from what is conditional on it. The formal measurement problem is resolved, while the bridge from formal invalidity to physical unrealizability remains a stated principle rather than a result.