{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T5GVOVZSJWU2HMWQBZPRYXQGBT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6a06ba539f334bc79194f91bd5bde785aa59500e1724bbee58bceb916e14e0f7","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-22T19:47:59Z","title_canon_sha256":"91e11463835574ad20def5a999cd018fb42bfe96fec069f20331397b8b79c998"},"schema_version":"1.0","source":{"id":"1305.5244","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5244","created_at":"2026-05-18T00:56:51Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5244v2","created_at":"2026-05-18T00:56:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5244","created_at":"2026-05-18T00:56:51Z"},{"alias_kind":"pith_short_12","alias_value":"T5GVOVZSJWU2","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T5GVOVZSJWU2HMWQ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T5GVOVZS","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:b656c657920cd84d3430ac689014736eae5292618a568d751354351d7ef3b0fa","target":"graph","created_at":"2026-05-18T00:56:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position -supported by E. Schrodinger- asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of solving a problem posed by Y. Manin, namely, to incorporate qu","authors_text":"Federico Holik, Newton Da Costa","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-22T19:47:59Z","title":"A formal framework for the study of the notion of undefined particle number in quantum mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5244","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7242a4c9be146bb42f0c6522c52368e3d4e6c3326937ae46345f3dde49fa005f","target":"record","created_at":"2026-05-18T00:56:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6a06ba539f334bc79194f91bd5bde785aa59500e1724bbee58bceb916e14e0f7","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-05-22T19:47:59Z","title_canon_sha256":"91e11463835574ad20def5a999cd018fb42bfe96fec069f20331397b8b79c998"},"schema_version":"1.0","source":{"id":"1305.5244","kind":"arxiv","version":2}},"canonical_sha256":"9f4d5757324da9a3b2d00e5f1c5e060cefb4f3211c3c605b5391b0373a642327","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f4d5757324da9a3b2d00e5f1c5e060cefb4f3211c3c605b5391b0373a642327","first_computed_at":"2026-05-18T00:56:51.915431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:51.915431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GRh4tKz24ctO4NSIvQy+CDjLnjJVV4T4x/Cqk4ZVyM9731ahzoZusUNgCv6lAYRjD5ok5sjTiUPfQLOLdd07Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:51.916101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5244","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7242a4c9be146bb42f0c6522c52368e3d4e6c3326937ae46345f3dde49fa005f","sha256:b656c657920cd84d3430ac689014736eae5292618a568d751354351d7ef3b0fa"],"state_sha256":"4b23127a9eab610ec1fb14a185a2c0f5e22fe623e29c3f85a730d29c881d53f7"}