{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LDC4EREBRYE44J74E4EGS5XB6H","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":"fda4529f5c848f2f0ee429db28189fbb7e8af97b10acf801c38bbd98130cf652","cross_cats_sorted":["math.AT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-31T14:59:50Z","title_canon_sha256":"e680d1aed5e941fbe3d53d4c0835f402815ece23bd99b5a9395d57bd0f8c72a9"},"schema_version":"1.0","source":{"id":"1108.0181","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0181","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0181v2","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0181","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"pith_short_12","alias_value":"LDC4EREBRYE4","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LDC4EREBRYE44J74","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LDC4EREB","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:5afc864b96f3944a552384a9d40f3ed6844f69786d735d304865a24adad4bbee","target":"graph","created_at":"2026-05-18T03:43:42Z","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":"This is the third chapter in our \"Toric Topology\" book project. Further chapters are coming. Comments and suggestions are very welcome.","authors_text":"Taras Panov, Victor Buchstaber","cross_cats":["math.AT","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-31T14:59:50Z","title":"Toric Topology. Chapter 3: Commutative and homological algebra of face rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0181","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:e6cf71143073ada6597b7250730971b867300859daf66c945b04315123e98652","target":"record","created_at":"2026-05-18T03:43:42Z","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":"fda4529f5c848f2f0ee429db28189fbb7e8af97b10acf801c38bbd98130cf652","cross_cats_sorted":["math.AT","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-07-31T14:59:50Z","title_canon_sha256":"e680d1aed5e941fbe3d53d4c0835f402815ece23bd99b5a9395d57bd0f8c72a9"},"schema_version":"1.0","source":{"id":"1108.0181","kind":"arxiv","version":2}},"canonical_sha256":"58c5c244818e09ce27fc27086976e1f1e506ad246b5e0c9fdc657f0f0032fb67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58c5c244818e09ce27fc27086976e1f1e506ad246b5e0c9fdc657f0f0032fb67","first_computed_at":"2026-05-18T03:43:42.522482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:42.522482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ulmYwyZ3rGdczlEMTTq24L28P3hf90XtPHlJnFsJNDx/T+HurWTmjc8Y+nKLTH992AH4sQZYRDe8mFRnR5LBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:42.523221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0181","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6cf71143073ada6597b7250730971b867300859daf66c945b04315123e98652","sha256:5afc864b96f3944a552384a9d40f3ed6844f69786d735d304865a24adad4bbee"],"state_sha256":"015cfa9260991c0decd1715c417ecae5f3dbe063ba39b35c71860ce4d1d29486"}