{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:VZNH2NTQ4TIF44DDCX2DALR6TT","short_pith_number":"pith:VZNH2NTQ","canonical_record":{"source":{"id":"2003.12379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-03-27T12:43:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bdceab957010d7b251fd235adae637f14ce2ad0d387c311bff5b24133153469a","abstract_canon_sha256":"06427bc8754c98ad29e9757479d01acc2ef63df701216e8c07aca67352b036d7"},"schema_version":"1.0"},"canonical_sha256":"ae5a7d3670e4d05e706315f4302e3e9cdeb9f76e27b4e7d0f710994381dba496","source":{"kind":"arxiv","id":"2003.12379","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.12379","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"2003.12379v1","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.12379","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"VZNH2NTQ4TIF","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"pith_short_16","alias_value":"VZNH2NTQ4TIF44DD","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"pith_short_8","alias_value":"VZNH2NTQ","created_at":"2026-07-05T00:50:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:VZNH2NTQ4TIF44DDCX2DALR6TT","target":"record","payload":{"canonical_record":{"source":{"id":"2003.12379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-03-27T12:43:04Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bdceab957010d7b251fd235adae637f14ce2ad0d387c311bff5b24133153469a","abstract_canon_sha256":"06427bc8754c98ad29e9757479d01acc2ef63df701216e8c07aca67352b036d7"},"schema_version":"1.0"},"canonical_sha256":"ae5a7d3670e4d05e706315f4302e3e9cdeb9f76e27b4e7d0f710994381dba496","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:50:57.804571Z","signature_b64":"Pn8aCmQTvhXstncP3R3XqW3aP/gJD60G92tGmwsJwv2F81Rhnaf8IHxj+30UtAEAVdm7EDVwhcD6CVwdl6isCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae5a7d3670e4d05e706315f4302e3e9cdeb9f76e27b4e7d0f710994381dba496","last_reissued_at":"2026-07-05T00:50:57.804229Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:50:57.804229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.12379","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":"2026-07-05T00:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E31pRdUpfED4Z/nga1CCWhsnUQWRYquCAM0mc3A1MRSaGWHBljbflvo1zwIbfcAKCAkdclSZgyRbcuHJBGGdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:47:54.930715Z"},"content_sha256":"07aaad3f763d47d8a9d0c8876030380e5e11b4f58cc4373f3038c19da7555966","schema_version":"1.0","event_id":"sha256:07aaad3f763d47d8a9d0c8876030380e5e11b4f58cc4373f3038c19da7555966"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:VZNH2NTQ4TIF44DDCX2DALR6TT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Kosuke Shibata, Naoki Terai, Seyed Amin Seyed Fakhari, Siamak Yassemi","submitted_at":"2020-03-27T12:43:04Z","abstract_excerpt":"We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs which have unmixed and non-Cohen-Macaulay vertex-weighted edge ideals, while the edge ideal of their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes and Toledo."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.12379","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.12379/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:50:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CFmMFs6u1dtywa6dIITpRQ/pF7o4Zim+JCLRj/qE+O0KLg0g2am6Uu47RgCVUo1IF9RcNzl9k8NSCOdDp/6eAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:47:54.931089Z"},"content_sha256":"0240a07d19a5cf68e1a9889b5a3c899dd007513a764af260f9f72072142b8cfc","schema_version":"1.0","event_id":"sha256:0240a07d19a5cf68e1a9889b5a3c899dd007513a764af260f9f72072142b8cfc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZNH2NTQ4TIF44DDCX2DALR6TT/bundle.json","state_url":"https://pith.science/pith/VZNH2NTQ4TIF44DDCX2DALR6TT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZNH2NTQ4TIF44DDCX2DALR6TT/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":"2026-07-06T10:47:54Z","links":{"resolver":"https://pith.science/pith/VZNH2NTQ4TIF44DDCX2DALR6TT","bundle":"https://pith.science/pith/VZNH2NTQ4TIF44DDCX2DALR6TT/bundle.json","state":"https://pith.science/pith/VZNH2NTQ4TIF44DDCX2DALR6TT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZNH2NTQ4TIF44DDCX2DALR6TT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:VZNH2NTQ4TIF44DDCX2DALR6TT","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":"06427bc8754c98ad29e9757479d01acc2ef63df701216e8c07aca67352b036d7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-03-27T12:43:04Z","title_canon_sha256":"bdceab957010d7b251fd235adae637f14ce2ad0d387c311bff5b24133153469a"},"schema_version":"1.0","source":{"id":"2003.12379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.12379","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"2003.12379v1","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.12379","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"VZNH2NTQ4TIF","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"pith_short_16","alias_value":"VZNH2NTQ4TIF44DD","created_at":"2026-07-05T00:50:57Z"},{"alias_kind":"pith_short_8","alias_value":"VZNH2NTQ","created_at":"2026-07-05T00:50:57Z"}],"graph_snapshots":[{"event_id":"sha256:0240a07d19a5cf68e1a9889b5a3c899dd007513a764af260f9f72072142b8cfc","target":"graph","created_at":"2026-07-05T00:50:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2003.12379/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. We also provide examples of oriented graphs which have unmixed and non-Cohen-Macaulay vertex-weighted edge ideals, while the edge ideal of their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes and Toledo.","authors_text":"Kosuke Shibata, Naoki Terai, Seyed Amin Seyed Fakhari, Siamak Yassemi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-03-27T12:43:04Z","title":"Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.12379","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":"sha256:07aaad3f763d47d8a9d0c8876030380e5e11b4f58cc4373f3038c19da7555966","target":"record","created_at":"2026-07-05T00:50:57Z","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":"06427bc8754c98ad29e9757479d01acc2ef63df701216e8c07aca67352b036d7","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-03-27T12:43:04Z","title_canon_sha256":"bdceab957010d7b251fd235adae637f14ce2ad0d387c311bff5b24133153469a"},"schema_version":"1.0","source":{"id":"2003.12379","kind":"arxiv","version":1}},"canonical_sha256":"ae5a7d3670e4d05e706315f4302e3e9cdeb9f76e27b4e7d0f710994381dba496","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae5a7d3670e4d05e706315f4302e3e9cdeb9f76e27b4e7d0f710994381dba496","first_computed_at":"2026-07-05T00:50:57.804229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:50:57.804229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pn8aCmQTvhXstncP3R3XqW3aP/gJD60G92tGmwsJwv2F81Rhnaf8IHxj+30UtAEAVdm7EDVwhcD6CVwdl6isCw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:50:57.804571Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.12379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07aaad3f763d47d8a9d0c8876030380e5e11b4f58cc4373f3038c19da7555966","sha256:0240a07d19a5cf68e1a9889b5a3c899dd007513a764af260f9f72072142b8cfc"],"state_sha256":"5d58d20a02069d1b5263af661c9bcef651df7518cc7d305ccb2a2a3d388e16c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l0JWFz18vFTQQbYnDcaOad3hZYueM3v9QyX9mYTWcAaNmtcFNiudaNb3kv+UfxchWmaoCXnmQaORTb0lu0r0DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T10:47:54.932994Z","bundle_sha256":"f74c5d13b9d109e505546e3b28427a21065b89c534a03dc56b702e05be749763"}}