{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:GEOATEI7NHJRZDH3KVT6THF6WU","short_pith_number":"pith:GEOATEI7","schema_version":"1.0","canonical_sha256":"311c09911f69d31c8cfb5567e99cbeb514e045e073b7fe3d6456633699a956d7","source":{"kind":"arxiv","id":"1112.4616","version":1},"attestation_state":"computed","paper":{"title":"On the lattice structure of probability spaces in quantum mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Angel Plastino, C\\'esar Massri, Federico Holik, Leandro Zuberman","submitted_at":"2011-12-20T09:23:26Z","abstract_excerpt":"Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets c"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1112.4616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-12-20T09:23:26Z","cross_cats_sorted":[],"title_canon_sha256":"ce80e526721314b0dac727d91d58b8d0909697c11fbcbe0c25a43443130d8eec","abstract_canon_sha256":"201bc4115a884459ea12b70070cc51f2d0aa02ba2735c1d997bbcfec9437d738"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:04.836965Z","signature_b64":"QQDA33raovJdvYjyL1H/zHlkORbIkJb38e24qqKLF2DbDEMpjzkw7+4oVodu/nHmAKCRnuGsqFNla9+74N9FAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"311c09911f69d31c8cfb5567e99cbeb514e045e073b7fe3d6456633699a956d7","last_reissued_at":"2026-05-18T01:59:04.836199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:04.836199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the lattice structure of probability spaces in quantum mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Angel Plastino, C\\'esar Massri, Federico Holik, Leandro Zuberman","submitted_at":"2011-12-20T09:23:26Z","abstract_excerpt":"Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4616","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1112.4616","created_at":"2026-05-18T01:59:04.836338+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.4616v1","created_at":"2026-05-18T01:59:04.836338+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4616","created_at":"2026-05-18T01:59:04.836338+00:00"},{"alias_kind":"pith_short_12","alias_value":"GEOATEI7NHJR","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"GEOATEI7NHJRZDH3","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"GEOATEI7","created_at":"2026-05-18T12:26:28.662955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU","json":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU.json","graph_json":"https://pith.science/api/pith-number/GEOATEI7NHJRZDH3KVT6THF6WU/graph.json","events_json":"https://pith.science/api/pith-number/GEOATEI7NHJRZDH3KVT6THF6WU/events.json","paper":"https://pith.science/paper/GEOATEI7"},"agent_actions":{"view_html":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU","download_json":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU.json","view_paper":"https://pith.science/paper/GEOATEI7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.4616&json=true","fetch_graph":"https://pith.science/api/pith-number/GEOATEI7NHJRZDH3KVT6THF6WU/graph.json","fetch_events":"https://pith.science/api/pith-number/GEOATEI7NHJRZDH3KVT6THF6WU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU/action/storage_attestation","attest_author":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU/action/author_attestation","sign_citation":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU/action/citation_signature","submit_replication":"https://pith.science/pith/GEOATEI7NHJRZDH3KVT6THF6WU/action/replication_record"}},"created_at":"2026-05-18T01:59:04.836338+00:00","updated_at":"2026-05-18T01:59:04.836338+00:00"}