{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XKMJSMVOG46FL6X3GZVA25WMOT","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":"4a543d2db92b7346b6fdf1c4f5dfa7ede8d23d4970caeeb089cd33c762979d1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-12T18:16:52Z","title_canon_sha256":"74b2d4c602c94b121a7c01548931c43dc1942ce3ac594b01ffa7bd395edf79c9"},"schema_version":"1.0","source":{"id":"1307.3533","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3533","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3533v2","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3533","created_at":"2026-05-18T02:39:09Z"},{"alias_kind":"pith_short_12","alias_value":"XKMJSMVOG46F","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XKMJSMVOG46FL6X3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XKMJSMVO","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3e7c3f58fb9ebabe60cefe3eb62623eac69487e201f3eaa064138e20771434e1","target":"graph","created_at":"2026-05-18T02:39:09Z","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":"Assuming GCH, we construct an atomic boolean algebra whose pi-weight is strictly less than the least size of a maximal irredundant family.","authors_text":"Kenneth Kunen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-12T18:16:52Z","title":"Irredundant Sets in Atomic Boolean Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3533","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":"sha256:90f4fef7a3be15a9ee8883182eb8b312fa6c4cff48b240f534ecafef77368586","target":"record","created_at":"2026-05-18T02:39:09Z","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":"4a543d2db92b7346b6fdf1c4f5dfa7ede8d23d4970caeeb089cd33c762979d1e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-12T18:16:52Z","title_canon_sha256":"74b2d4c602c94b121a7c01548931c43dc1942ce3ac594b01ffa7bd395edf79c9"},"schema_version":"1.0","source":{"id":"1307.3533","kind":"arxiv","version":2}},"canonical_sha256":"ba989932ae373c55fafb366a0d76cc74c884bd5edad3361e94fc11a3c55347de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba989932ae373c55fafb366a0d76cc74c884bd5edad3361e94fc11a3c55347de","first_computed_at":"2026-05-18T02:39:09.155890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:09.155890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IrCEMv1dG0CNAk4k8bkY8rKFJwD187nES/vetO6SFQZR2UrT5yQn1L9p65ledquztvYq+gUmAzB6rOYUh0gpAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:09.156962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3533","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90f4fef7a3be15a9ee8883182eb8b312fa6c4cff48b240f534ecafef77368586","sha256:3e7c3f58fb9ebabe60cefe3eb62623eac69487e201f3eaa064138e20771434e1"],"state_sha256":"8e3e912cdc3b6bdd1f4b3be02684d6542bf20bb462f72de41dd356eaa7bd6267"}