{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:C6UNCMXUZYQNGZVAQG3KTGAEPI","short_pith_number":"pith:C6UNCMXU","schema_version":"1.0","canonical_sha256":"17a8d132f4ce20d366a081b6a998047a284d91c560e994afa4adfb51a7507286","source":{"kind":"arxiv","id":"1108.5339","version":1},"attestation_state":"computed","paper":{"title":"Density conditions for quantum propositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Hans Havlicek, Karl Svozil","submitted_at":"2011-08-26T15:57:11Z","abstract_excerpt":"As has already been pointed out by Birkhoff and von Neumann, quantum logic can be formulated in terms of projective geometry. In three-dimensional Hilbert space, elementary logical propositions are associated with one-dimensional subspaces, corresponding to points of the projective plane. It is shown that, starting with three such propositions corresponding to some basis $\\{{\\vec u},{\\vec v},{\\vec w}\\}$, successive application of the binary logical operation $(x,y)\\mapsto (x\\vee y)^\\perp$ generates a set of elementary propositions which is countable infinite and dense in the projective plane i"},"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":"1108.5339","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-08-26T15:57:11Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"5a2a6a888262fe9b34d55f09daf0bebe48344038390412a2655652b56953eb2b","abstract_canon_sha256":"701e37e4e63d3684f29d1ee7b193a37986dc37a084dbedc6414ca44be2c1f883"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:38.501027Z","signature_b64":"+t69pOqpaKCpDG7GVMLtC9Z0m0mPcz2m52AKstDVc4XNi5ufpqojTolivE9xcmkxColgB5fdvDm2H6WTrJe0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a8d132f4ce20d366a081b6a998047a284d91c560e994afa4adfb51a7507286","last_reissued_at":"2026-05-18T04:14:38.500643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:38.500643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Density conditions for quantum propositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Hans Havlicek, Karl Svozil","submitted_at":"2011-08-26T15:57:11Z","abstract_excerpt":"As has already been pointed out by Birkhoff and von Neumann, quantum logic can be formulated in terms of projective geometry. In three-dimensional Hilbert space, elementary logical propositions are associated with one-dimensional subspaces, corresponding to points of the projective plane. It is shown that, starting with three such propositions corresponding to some basis $\\{{\\vec u},{\\vec v},{\\vec w}\\}$, successive application of the binary logical operation $(x,y)\\mapsto (x\\vee y)^\\perp$ generates a set of elementary propositions which is countable infinite and dense in the projective plane i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5339","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":"1108.5339","created_at":"2026-05-18T04:14:38.500695+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5339v1","created_at":"2026-05-18T04:14:38.500695+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5339","created_at":"2026-05-18T04:14:38.500695+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6UNCMXUZYQN","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6UNCMXUZYQNGZVA","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6UNCMXU","created_at":"2026-05-18T12:26:24.575870+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/C6UNCMXUZYQNGZVAQG3KTGAEPI","json":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI.json","graph_json":"https://pith.science/api/pith-number/C6UNCMXUZYQNGZVAQG3KTGAEPI/graph.json","events_json":"https://pith.science/api/pith-number/C6UNCMXUZYQNGZVAQG3KTGAEPI/events.json","paper":"https://pith.science/paper/C6UNCMXU"},"agent_actions":{"view_html":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI","download_json":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI.json","view_paper":"https://pith.science/paper/C6UNCMXU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5339&json=true","fetch_graph":"https://pith.science/api/pith-number/C6UNCMXUZYQNGZVAQG3KTGAEPI/graph.json","fetch_events":"https://pith.science/api/pith-number/C6UNCMXUZYQNGZVAQG3KTGAEPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI/action/storage_attestation","attest_author":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI/action/author_attestation","sign_citation":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI/action/citation_signature","submit_replication":"https://pith.science/pith/C6UNCMXUZYQNGZVAQG3KTGAEPI/action/replication_record"}},"created_at":"2026-05-18T04:14:38.500695+00:00","updated_at":"2026-05-18T04:14:38.500695+00:00"}