{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TYDEQS7ITJVHPYWYSPOSBE5JG5","short_pith_number":"pith:TYDEQS7I","canonical_record":{"source":{"id":"1108.0572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-02T13:57:28Z","cross_cats_sorted":[],"title_canon_sha256":"403bb721a652394375859dd8a20682d9b82bc0729d6d24cc8c086b17454bed45","abstract_canon_sha256":"3686c402d59250255d55f9f85cf28b2f1d13fa0ed0aeee7fd397b40ce5fb6f8e"},"schema_version":"1.0"},"canonical_sha256":"9e06484be89a6a77e2d893dd2093a9377c7bbcfef98ae3fca241ab35d0171904","source":{"kind":"arxiv","id":"1108.0572","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0572","created_at":"2026-05-18T04:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0572v1","created_at":"2026-05-18T04:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0572","created_at":"2026-05-18T04:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"TYDEQS7ITJVH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TYDEQS7ITJVHPYWY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TYDEQS7I","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TYDEQS7ITJVHPYWYSPOSBE5JG5","target":"record","payload":{"canonical_record":{"source":{"id":"1108.0572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-02T13:57:28Z","cross_cats_sorted":[],"title_canon_sha256":"403bb721a652394375859dd8a20682d9b82bc0729d6d24cc8c086b17454bed45","abstract_canon_sha256":"3686c402d59250255d55f9f85cf28b2f1d13fa0ed0aeee7fd397b40ce5fb6f8e"},"schema_version":"1.0"},"canonical_sha256":"9e06484be89a6a77e2d893dd2093a9377c7bbcfef98ae3fca241ab35d0171904","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:30.181925Z","signature_b64":"NHkbT5VhVwvdEomW8OPHiYnX0e6XW8p3ST0+7bwCAXsqR+BSo83r213Ei8Cad91vj02v+R6bUbeGFVVuyAdKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e06484be89a6a77e2d893dd2093a9377c7bbcfef98ae3fca241ab35d0171904","last_reissued_at":"2026-05-18T04:16:30.181522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:30.181522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.0572","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8jgYHP0znyOK4i0VZMoEVIClewg/TlrIAL4dbI+P0utFEnlfxaypl8nG7/7OX8e8SY+Fb3LUyfGDuyj4pH+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:17:28.828864Z"},"content_sha256":"88fff71e02f864d463cc4e4eaab776750787cc25177065f3507a6201cd67e1a6","schema_version":"1.0","event_id":"sha256:88fff71e02f864d463cc4e4eaab776750787cc25177065f3507a6201cd67e1a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TYDEQS7ITJVHPYWYSPOSBE5JG5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The flag f-vectors of Gorenstein* order complexes of dimension 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eran Nevo, Satoshi Murai","submitted_at":"2011-08-02T13:57:28Z","abstract_excerpt":"We characterize the cd-indices of Gorenstein* posets of rank 5, equivalently the flag f-vectors of Gorenstein* order complexes of dimension 3. As a corollary, we characterize the f-vectors of Gorenstein* order complexes in dimensions 3 and 4. This characterization rise a speculated intimate connection between the f-vectors of flag homology spheres and the f-vectors of Gorenstein* order complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0572","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaP9SVpvx450kVIXXtj7g3KYfIW/OHu/b84m9pmLa7g5oMvj35uXzjZ7o/J66JumzfQMMgzHiD1WOIBUQaPkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:17:28.829204Z"},"content_sha256":"4bad1235a0159f42c13bfc76f4829dbab29faa258b2ed42626f88dd844632df5","schema_version":"1.0","event_id":"sha256:4bad1235a0159f42c13bfc76f4829dbab29faa258b2ed42626f88dd844632df5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYDEQS7ITJVHPYWYSPOSBE5JG5/bundle.json","state_url":"https://pith.science/pith/TYDEQS7ITJVHPYWYSPOSBE5JG5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYDEQS7ITJVHPYWYSPOSBE5JG5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T10:17:28Z","links":{"resolver":"https://pith.science/pith/TYDEQS7ITJVHPYWYSPOSBE5JG5","bundle":"https://pith.science/pith/TYDEQS7ITJVHPYWYSPOSBE5JG5/bundle.json","state":"https://pith.science/pith/TYDEQS7ITJVHPYWYSPOSBE5JG5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYDEQS7ITJVHPYWYSPOSBE5JG5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TYDEQS7ITJVHPYWYSPOSBE5JG5","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":"3686c402d59250255d55f9f85cf28b2f1d13fa0ed0aeee7fd397b40ce5fb6f8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-02T13:57:28Z","title_canon_sha256":"403bb721a652394375859dd8a20682d9b82bc0729d6d24cc8c086b17454bed45"},"schema_version":"1.0","source":{"id":"1108.0572","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0572","created_at":"2026-05-18T04:16:30Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0572v1","created_at":"2026-05-18T04:16:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0572","created_at":"2026-05-18T04:16:30Z"},{"alias_kind":"pith_short_12","alias_value":"TYDEQS7ITJVH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TYDEQS7ITJVHPYWY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TYDEQS7I","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:4bad1235a0159f42c13bfc76f4829dbab29faa258b2ed42626f88dd844632df5","target":"graph","created_at":"2026-05-18T04:16:30Z","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 characterize the cd-indices of Gorenstein* posets of rank 5, equivalently the flag f-vectors of Gorenstein* order complexes of dimension 3. As a corollary, we characterize the f-vectors of Gorenstein* order complexes in dimensions 3 and 4. This characterization rise a speculated intimate connection between the f-vectors of flag homology spheres and the f-vectors of Gorenstein* order complexes.","authors_text":"Eran Nevo, Satoshi Murai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-02T13:57:28Z","title":"The flag f-vectors of Gorenstein* order complexes of dimension 3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0572","kind":"arxiv","version":1},"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":"sha256:88fff71e02f864d463cc4e4eaab776750787cc25177065f3507a6201cd67e1a6","target":"record","created_at":"2026-05-18T04:16:30Z","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":"3686c402d59250255d55f9f85cf28b2f1d13fa0ed0aeee7fd397b40ce5fb6f8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-02T13:57:28Z","title_canon_sha256":"403bb721a652394375859dd8a20682d9b82bc0729d6d24cc8c086b17454bed45"},"schema_version":"1.0","source":{"id":"1108.0572","kind":"arxiv","version":1}},"canonical_sha256":"9e06484be89a6a77e2d893dd2093a9377c7bbcfef98ae3fca241ab35d0171904","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e06484be89a6a77e2d893dd2093a9377c7bbcfef98ae3fca241ab35d0171904","first_computed_at":"2026-05-18T04:16:30.181522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:30.181522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NHkbT5VhVwvdEomW8OPHiYnX0e6XW8p3ST0+7bwCAXsqR+BSo83r213Ei8Cad91vj02v+R6bUbeGFVVuyAdKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:30.181925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0572","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88fff71e02f864d463cc4e4eaab776750787cc25177065f3507a6201cd67e1a6","sha256:4bad1235a0159f42c13bfc76f4829dbab29faa258b2ed42626f88dd844632df5"],"state_sha256":"ef0b7f18a3a16ce49e5c0dc2bd317bb5462aa7a8685c1a9b0760cb4c24f6244b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CcJZbS+e6CcUXztNIGrTILurh6cmjqLd5XIzLD/hjp/hqxdjx3K+lfE0uIAH41WieN1DRkZmlhly440AQRwNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:17:28.831211Z","bundle_sha256":"7e5630c6b6999882dc69f5c45b62cf0517c9a6f75250ba053fd93c3d2a0b1dd7"}}