{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:FQ5UL6KENDRJQO4PQYXVURULEL","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":"83bded255ff846ae1bfa43d54cd497b5b14ee50534a8fb74f8c294e0682fdc79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-09-03T02:08:11Z","title_canon_sha256":"ba2cf106017573a2dadedb0ae037efc7a3b61c6c355780636a01c1730068b1ec"},"schema_version":"1.0","source":{"id":"0809.0538","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.0538","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"0809.0538v3","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.0538","created_at":"2026-05-18T04:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"FQ5UL6KENDRJ","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FQ5UL6KENDRJQO4P","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FQ5UL6KE","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:609348b25a628fa97c2181c69c69b7939116b425be5e323457f1ccd188103694","target":"graph","created_at":"2026-05-18T04:07:06Z","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":"In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone's representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will be given using Stone's theorem from Boolean algebra.","authors_text":"Cheng Hao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-09-03T02:08:11Z","title":"Boolean Algebras and Logic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.0538","kind":"arxiv","version":3},"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:d4cdae4dcbb3f0939126878fef36e4921d9a6e579230fa3108375f026bd9c199","target":"record","created_at":"2026-05-18T04:07:06Z","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":"83bded255ff846ae1bfa43d54cd497b5b14ee50534a8fb74f8c294e0682fdc79","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-09-03T02:08:11Z","title_canon_sha256":"ba2cf106017573a2dadedb0ae037efc7a3b61c6c355780636a01c1730068b1ec"},"schema_version":"1.0","source":{"id":"0809.0538","kind":"arxiv","version":3}},"canonical_sha256":"2c3b45f94468e2983b8f862f5a468b22ec366c78c907cfb3fa365f9d271dc9b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c3b45f94468e2983b8f862f5a468b22ec366c78c907cfb3fa365f9d271dc9b0","first_computed_at":"2026-05-18T04:07:06.918169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:06.918169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ikICKYjuecRpKJ9EzAG3f8vALabrj/PCdI/Lv31dbKQ4NHoYEOW1WQxvwFMlybGNOtcoc0pa2BEgkKpZ+K3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:06.918613Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.0538","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4cdae4dcbb3f0939126878fef36e4921d9a6e579230fa3108375f026bd9c199","sha256:609348b25a628fa97c2181c69c69b7939116b425be5e323457f1ccd188103694"],"state_sha256":"07a8a64dab471312d5916093840f1cef51383b00f216f95303a0c9fa5f2a9eb3"}