{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O6FZPIMZSBWJZ7B6BA6L6DP5YP","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":"f512c2cef3735822441b8fc7da37838dfa224d1a2618855da839de1ceb22aa57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T12:37:22Z","title_canon_sha256":"d6181ab743ef7649796fa8e8a74a5cf577378f73a7f9747c339ff55ada53bd85"},"schema_version":"1.0","source":{"id":"1311.5039","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5039","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5039v2","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5039","created_at":"2026-05-18T02:24:28Z"},{"alias_kind":"pith_short_12","alias_value":"O6FZPIMZSBWJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6FZPIMZSBWJZ7B6","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6FZPIMZ","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:29e053dd86631e24f923072e373c5460b5b1fe0bdaa69e2b2ca9732974340b93","target":"graph","created_at":"2026-05-18T02:24:28Z","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":"We compare various viewpoints on down-sets (simplicial complexes), illustrating how the combinatorial inclusion-exclusion principle may serve as an alternative to more advanced methods of studying their face numbers.","authors_text":"Michal Adamaszek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T12:37:22Z","title":"Face numbers of down-sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5039","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:ad0bd729db1f8cd911a73f7738898d7bff40e6658683e0bdd5b670f31cadaf17","target":"record","created_at":"2026-05-18T02:24:28Z","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":"f512c2cef3735822441b8fc7da37838dfa224d1a2618855da839de1ceb22aa57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-20T12:37:22Z","title_canon_sha256":"d6181ab743ef7649796fa8e8a74a5cf577378f73a7f9747c339ff55ada53bd85"},"schema_version":"1.0","source":{"id":"1311.5039","kind":"arxiv","version":2}},"canonical_sha256":"778b97a199906c9cfc3e083cbf0dfdc3ee719ff3ab4710494f7c540cb1b45176","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"778b97a199906c9cfc3e083cbf0dfdc3ee719ff3ab4710494f7c540cb1b45176","first_computed_at":"2026-05-18T02:24:28.814374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:28.814374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hWuJs/ICPcYoVOsEFRvFLbRQWdWGlI3z/6wh5xGTVJ+BfrpS81UlH1t4nFXtcRLnzFEY2KRkhSgRuECm/Nz4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:28.815036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5039","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad0bd729db1f8cd911a73f7738898d7bff40e6658683e0bdd5b670f31cadaf17","sha256:29e053dd86631e24f923072e373c5460b5b1fe0bdaa69e2b2ca9732974340b93"],"state_sha256":"e43d06c06e2541ad8e7b5f37f27dfa8eabe393a2d04ce0671934c8525e1a5835"}