{"paper":{"title":"A Monty-Hall test of non-contextual determinism with a single qutrit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Deterministic hidden-variable theories require exactly 1/3 probability after a Monty Hall-style descarte on a qutrit, while quantum mechanics predicts 1/6.","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Jorge Meza-Dom\\'inguez","submitted_at":"2026-04-24T21:23:07Z","abstract_excerpt":"We present a simple equality that distinguishes non-contextual deterministic hidden-variable theories (NCHV) from standard quantum mechanics using a single three-level system. The protocol is inspired by the Monty Hall puzzle: a coherent \"discard\" procedure followed by a projective measurement. In any NCHV theory that respects the Monty Hall condition (the discard never eliminates the true state), the probability of obtaining a chosen state after the discard is exactly 1/3. In contrast, quantum mechanics predicts 1/6, due to the preparation of coherent superpositions. Quantum mechanics thus vi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"In any deterministic theory that respects the Monty Hall condition (the descarte never eliminates the real state), the probability of obtaining a chosen state after the descarte is exactly 1/3. In contrast, quantum mechanics predicts 1/6, due to the preparation of coherent superpositions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That deterministic hidden-variable theories (local or nonlocal) must respect the Monty Hall condition in which the descarte procedure never eliminates the real underlying state.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quantum mechanics violates a 1/3 probability bound required by any deterministic theory that never discards the true state in a Monty-Hall-inspired descarte protocol on a single qutrit, predicting instead 1/6.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Deterministic hidden-variable theories require exactly 1/3 probability after a Monty Hall-style descarte on a qutrit, while quantum mechanics predicts 1/6.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"57a5ab96bc42a9ea1c06a1328e561da87aa15953a98dede3945913709bf0a43a"},"source":{"id":"2604.25953","kind":"arxiv","version":2},"verdict":{"id":"a05b7f3b-f110-4c86-ba89-f202a0a1e157","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T11:38:22.019145Z","strongest_claim":"In any deterministic theory that respects the Monty Hall condition (the descarte never eliminates the real state), the probability of obtaining a chosen state after the descarte is exactly 1/3. In contrast, quantum mechanics predicts 1/6, due to the preparation of coherent superpositions.","one_line_summary":"Quantum mechanics violates a 1/3 probability bound required by any deterministic theory that never discards the true state in a Monty-Hall-inspired descarte protocol on a single qutrit, predicting instead 1/6.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That deterministic hidden-variable theories (local or nonlocal) must respect the Monty Hall condition in which the descarte procedure never eliminates the real underlying state.","pith_extraction_headline":"Deterministic hidden-variable theories require exactly 1/3 probability after a Monty Hall-style descarte on a qutrit, while quantum mechanics predicts 1/6."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.25953/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T09:40:55.429267Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:33:02.798700Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"126e26e6670a054d686c4d1c79d24d2e729d8a333506bebe8f803813a288cfc0"},"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"}