{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3D4GOMX3GNFVXTCZIJRMZTOY6M","short_pith_number":"pith:3D4GOMX3","canonical_record":{"source":{"id":"1504.04062","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-15T22:28:38Z","cross_cats_sorted":[],"title_canon_sha256":"f02bb6cafcf7066f9bd91385eab6f7bca4c67aab99dcd5cc2869e111d1654497","abstract_canon_sha256":"3e82cd8facfd5c8ec15f4812f84726a5bc9d8dcfa1d0f25e4d472d57c711c580"},"schema_version":"1.0"},"canonical_sha256":"d8f86732fb334b5bcc594262cccdd8f32f42788a5f191601626d10f3e096b26e","source":{"kind":"arxiv","id":"1504.04062","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04062","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04062v3","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04062","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"3D4GOMX3GNFV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3D4GOMX3GNFVXTCZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3D4GOMX3","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3D4GOMX3GNFVXTCZIJRMZTOY6M","target":"record","payload":{"canonical_record":{"source":{"id":"1504.04062","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-15T22:28:38Z","cross_cats_sorted":[],"title_canon_sha256":"f02bb6cafcf7066f9bd91385eab6f7bca4c67aab99dcd5cc2869e111d1654497","abstract_canon_sha256":"3e82cd8facfd5c8ec15f4812f84726a5bc9d8dcfa1d0f25e4d472d57c711c580"},"schema_version":"1.0"},"canonical_sha256":"d8f86732fb334b5bcc594262cccdd8f32f42788a5f191601626d10f3e096b26e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:23.936544Z","signature_b64":"8SI+lMVaMXElt6G6P6YMtQylhazzswgBf0t0Kznjts9tqDVpQ3LceAvJx+CWbHstoEYQHJ/NVpllqxOB10haDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8f86732fb334b5bcc594262cccdd8f32f42788a5f191601626d10f3e096b26e","last_reissued_at":"2026-05-18T01:27:23.935997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:23.935997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.04062","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u/xKyVJIADTlNFw4NaM6ROc1T395g4PbHZP1LK8fj7cY9vpa3ZWavJPut1Ku/cK4c71mOYxSON/KHxMwW+aiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:37:57.555484Z"},"content_sha256":"dddb68849a5103136481c0bc2d7747cae468528b1f73eab0ca0d7ffbae93b383","schema_version":"1.0","event_id":"sha256:dddb68849a5103136481c0bc2d7747cae468528b1f73eab0ca0d7ffbae93b383"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3D4GOMX3GNFVXTCZIJRMZTOY6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edgewise Cohen-Macaulay connectivity of partially ordered sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christos A. Athanasiadis, Myrto Kallipoliti","submitted_at":"2015-04-15T22:28:38Z","abstract_excerpt":"The proper parts of face lattices of convex polytopes are shown to satisfy a strong form of the Cohen--Macaulay property, namely that removing from their Hasse diagram all edges in any closed interval results in a Cohen--Macaulay poset of the same rank. A corresponding notion of edgewise Cohen--Macaulay connectivity for partially ordered sets is investigated. Examples and open questions are discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04062","kind":"arxiv","version":3},"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":"2026-05-18T01:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4WcIARiudIYePyzJMCs17JgRFov91jYqT8V+WH5POb4+43hzVjU67L7Amja6NziGASAGiZ/a0fgEvCt9Qs1lCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T14:37:57.556108Z"},"content_sha256":"6a7c7d0adf11bd3198931d9e6c33b563dcf30785a2be8c253b18af2a10dbf545","schema_version":"1.0","event_id":"sha256:6a7c7d0adf11bd3198931d9e6c33b563dcf30785a2be8c253b18af2a10dbf545"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3D4GOMX3GNFVXTCZIJRMZTOY6M/bundle.json","state_url":"https://pith.science/pith/3D4GOMX3GNFVXTCZIJRMZTOY6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3D4GOMX3GNFVXTCZIJRMZTOY6M/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":"2026-06-09T14:37:57Z","links":{"resolver":"https://pith.science/pith/3D4GOMX3GNFVXTCZIJRMZTOY6M","bundle":"https://pith.science/pith/3D4GOMX3GNFVXTCZIJRMZTOY6M/bundle.json","state":"https://pith.science/pith/3D4GOMX3GNFVXTCZIJRMZTOY6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3D4GOMX3GNFVXTCZIJRMZTOY6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3D4GOMX3GNFVXTCZIJRMZTOY6M","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":"3e82cd8facfd5c8ec15f4812f84726a5bc9d8dcfa1d0f25e4d472d57c711c580","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-15T22:28:38Z","title_canon_sha256":"f02bb6cafcf7066f9bd91385eab6f7bca4c67aab99dcd5cc2869e111d1654497"},"schema_version":"1.0","source":{"id":"1504.04062","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.04062","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1504.04062v3","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04062","created_at":"2026-05-18T01:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"3D4GOMX3GNFV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3D4GOMX3GNFVXTCZ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3D4GOMX3","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:6a7c7d0adf11bd3198931d9e6c33b563dcf30785a2be8c253b18af2a10dbf545","target":"graph","created_at":"2026-05-18T01:27:23Z","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":"The proper parts of face lattices of convex polytopes are shown to satisfy a strong form of the Cohen--Macaulay property, namely that removing from their Hasse diagram all edges in any closed interval results in a Cohen--Macaulay poset of the same rank. A corresponding notion of edgewise Cohen--Macaulay connectivity for partially ordered sets is investigated. Examples and open questions are discussed.","authors_text":"Christos A. Athanasiadis, Myrto Kallipoliti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-15T22:28:38Z","title":"Edgewise Cohen-Macaulay connectivity of partially ordered sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04062","kind":"arxiv","version":3},"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:dddb68849a5103136481c0bc2d7747cae468528b1f73eab0ca0d7ffbae93b383","target":"record","created_at":"2026-05-18T01:27:23Z","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":"3e82cd8facfd5c8ec15f4812f84726a5bc9d8dcfa1d0f25e4d472d57c711c580","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-15T22:28:38Z","title_canon_sha256":"f02bb6cafcf7066f9bd91385eab6f7bca4c67aab99dcd5cc2869e111d1654497"},"schema_version":"1.0","source":{"id":"1504.04062","kind":"arxiv","version":3}},"canonical_sha256":"d8f86732fb334b5bcc594262cccdd8f32f42788a5f191601626d10f3e096b26e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8f86732fb334b5bcc594262cccdd8f32f42788a5f191601626d10f3e096b26e","first_computed_at":"2026-05-18T01:27:23.935997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:23.935997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8SI+lMVaMXElt6G6P6YMtQylhazzswgBf0t0Kznjts9tqDVpQ3LceAvJx+CWbHstoEYQHJ/NVpllqxOB10haDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:23.936544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.04062","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dddb68849a5103136481c0bc2d7747cae468528b1f73eab0ca0d7ffbae93b383","sha256:6a7c7d0adf11bd3198931d9e6c33b563dcf30785a2be8c253b18af2a10dbf545"],"state_sha256":"cc4334310e73d0172c876cd4a5c4915003ff459fe4a7a97c5226774b0b8af005"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uGQfOdD1l8TkuZdimiTIi/lsMcu2bMdWB9z9kYlmAQDqngOmUWmm/nTnbTW4GS2A/FCCfosDyIuNEDPNzaflBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T14:37:57.558143Z","bundle_sha256":"16cdee3b45da530a44cddd899b95f42ffafc0561722f9582c6a2191339f437c2"}}