{"paper":{"title":"Local Uniqueness of the Born Rule on Categories with Complex-Weighted Morphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Tayfun Ustun","submitted_at":"2026-08-04T15:13:05Z","abstract_excerpt":"I prove a local uniqueness theorem for the Born rule in the setting of small categories equipped with complex morphism weights and path-amplitude probability functionals. Given (i) non-negativity, (ii) polynomiality of bounded total degree, (iii) global U(1) invariance, (iv) classical-limit additivity over mutually exclusive paths, and (v) normalization, I show that the probability assignment P: C -> R>=0 is uniquely determined to be P(z) = |z|^2. The notion of mutually exclusive paths is given a precise categorical formulation as the absence of a shared factorization through any common morphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05197","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.05197/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}