{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D7M4THPVTUG2LKZAMXJGQPLUS3","short_pith_number":"pith:D7M4THPV","canonical_record":{"source":{"id":"1004.0170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T16:16:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4ab78e49718901f497b3653dbd485e90855b210d43ef36ca5af70ec1da4249ef","abstract_canon_sha256":"f7ae79b137c03dfa640176e662067819dbc3935b9070797d0fbc202af336d64e"},"schema_version":"1.0"},"canonical_sha256":"1fd9c99df59d0da5ab2065d2683d7496cb70869db657bc458ceed8d2e0f6b308","source":{"kind":"arxiv","id":"1004.0170","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0170","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0170v2","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0170","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"D7M4THPVTUG2","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D7M4THPVTUG2LKZA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D7M4THPV","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D7M4THPVTUG2LKZAMXJGQPLUS3","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0170","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T16:16:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4ab78e49718901f497b3653dbd485e90855b210d43ef36ca5af70ec1da4249ef","abstract_canon_sha256":"f7ae79b137c03dfa640176e662067819dbc3935b9070797d0fbc202af336d64e"},"schema_version":"1.0"},"canonical_sha256":"1fd9c99df59d0da5ab2065d2683d7496cb70869db657bc458ceed8d2e0f6b308","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:56.506923Z","signature_b64":"FjEXpVpcd6z881gghsjrQe+Z/EmlZSLak4z9kGCjhhcG65tM4I3+hDJbqyhEL0aE7D3yY/RQSGXW84EVFrCUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fd9c99df59d0da5ab2065d2683d7496cb70869db657bc458ceed8d2e0f6b308","last_reissued_at":"2026-05-18T04:12:56.506284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:56.506284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0170","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrkcJ0pubomBzNKkkB+lloOrC+ORVRQamkTM/8xLEEHja5OI/LjTAE9djRu9OSc7fFKzLbLIki9fgyVvSWYJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:32:59.337342Z"},"content_sha256":"29b77e83e2e5ef901bcb92cd50148941f424a9448fd5c8310b31eef7e34ac2d0","schema_version":"1.0","event_id":"sha256:29b77e83e2e5ef901bcb92cd50148941f424a9448fd5c8310b31eef7e34ac2d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D7M4THPVTUG2LKZAMXJGQPLUS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the h-vectors of Cohen-Macaulay Flag Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Alexandru Constantinescu, Matteo Varbaro","submitted_at":"2010-04-01T16:16:08Z","abstract_excerpt":"Starting from an unpublished conjecture of Kalai and from a conjecture of Eisenbud, Green and Harris, we study several problems relating h-vectors of Cohen-Macaulay, flag simplicial complexes and face vectors of simplicial complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0170","kind":"arxiv","version":2},"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":"2026-05-18T04:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OR+y+SWt+mofkUJXTbmCCVRzQuCUNhTh2Dq/qc7xe8TEQid+FFAj0JB28uHZdrtDQoBc6yRepRi4EL89sX4YAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:32:59.337706Z"},"content_sha256":"92b4221e7ba44b4e318f64891133c6e886e702c58b51d00e8622cfa228174e1a","schema_version":"1.0","event_id":"sha256:92b4221e7ba44b4e318f64891133c6e886e702c58b51d00e8622cfa228174e1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D7M4THPVTUG2LKZAMXJGQPLUS3/bundle.json","state_url":"https://pith.science/pith/D7M4THPVTUG2LKZAMXJGQPLUS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D7M4THPVTUG2LKZAMXJGQPLUS3/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":"2026-05-26T21:32:59Z","links":{"resolver":"https://pith.science/pith/D7M4THPVTUG2LKZAMXJGQPLUS3","bundle":"https://pith.science/pith/D7M4THPVTUG2LKZAMXJGQPLUS3/bundle.json","state":"https://pith.science/pith/D7M4THPVTUG2LKZAMXJGQPLUS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D7M4THPVTUG2LKZAMXJGQPLUS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D7M4THPVTUG2LKZAMXJGQPLUS3","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":"f7ae79b137c03dfa640176e662067819dbc3935b9070797d0fbc202af336d64e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T16:16:08Z","title_canon_sha256":"4ab78e49718901f497b3653dbd485e90855b210d43ef36ca5af70ec1da4249ef"},"schema_version":"1.0","source":{"id":"1004.0170","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0170","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0170v2","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0170","created_at":"2026-05-18T04:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"D7M4THPVTUG2","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D7M4THPVTUG2LKZA","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D7M4THPV","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:92b4221e7ba44b4e318f64891133c6e886e702c58b51d00e8622cfa228174e1a","target":"graph","created_at":"2026-05-18T04:12:56Z","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":"Starting from an unpublished conjecture of Kalai and from a conjecture of Eisenbud, Green and Harris, we study several problems relating h-vectors of Cohen-Macaulay, flag simplicial complexes and face vectors of simplicial complexes.","authors_text":"Alexandru Constantinescu, Matteo Varbaro","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T16:16:08Z","title":"On the h-vectors of Cohen-Macaulay Flag Complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0170","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":"sha256:29b77e83e2e5ef901bcb92cd50148941f424a9448fd5c8310b31eef7e34ac2d0","target":"record","created_at":"2026-05-18T04:12:56Z","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":"f7ae79b137c03dfa640176e662067819dbc3935b9070797d0fbc202af336d64e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T16:16:08Z","title_canon_sha256":"4ab78e49718901f497b3653dbd485e90855b210d43ef36ca5af70ec1da4249ef"},"schema_version":"1.0","source":{"id":"1004.0170","kind":"arxiv","version":2}},"canonical_sha256":"1fd9c99df59d0da5ab2065d2683d7496cb70869db657bc458ceed8d2e0f6b308","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fd9c99df59d0da5ab2065d2683d7496cb70869db657bc458ceed8d2e0f6b308","first_computed_at":"2026-05-18T04:12:56.506284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:56.506284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FjEXpVpcd6z881gghsjrQe+Z/EmlZSLak4z9kGCjhhcG65tM4I3+hDJbqyhEL0aE7D3yY/RQSGXW84EVFrCUAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:56.506923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0170","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29b77e83e2e5ef901bcb92cd50148941f424a9448fd5c8310b31eef7e34ac2d0","sha256:92b4221e7ba44b4e318f64891133c6e886e702c58b51d00e8622cfa228174e1a"],"state_sha256":"29987470bd675efc0940babac17bbcf668eb7b26cca9f7380b1b866426792915"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U9CSx9CHaVDsiiBoYP/6jLg0oKWESJ+5pZy5GUgzH62hSpHkp4zKi8jR8QgcoiJcJPOurYdQ4caxX+8m8ojRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:32:59.340041Z","bundle_sha256":"509004fcf7e7decc638cfb97e1b190ea462e0b4c119101ad9745fd740d97ee10"}}