{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SAOHGBWE674DROD33DMQPY4OF2","short_pith_number":"pith:SAOHGBWE","canonical_record":{"source":{"id":"1004.0143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T14:19:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"39c80df8d527a1c8bff829d0a1b29c39f3b42fc2b7cd287d9d6734756b279357","abstract_canon_sha256":"1b48f5fef7a72c7dc143de2ecdeda04564e02c5d8615834cffa19a77c570d493"},"schema_version":"1.0"},"canonical_sha256":"901c7306c4f7f838b87bd8d907e38e2ea3ccd2e1daed2fcfbad52c0c0dc0e5ee","source":{"kind":"arxiv","id":"1004.0143","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0143","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0143v2","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0143","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"SAOHGBWE674D","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SAOHGBWE674DROD3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SAOHGBWE","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SAOHGBWE674DROD33DMQPY4OF2","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0143","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T14:19:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"39c80df8d527a1c8bff829d0a1b29c39f3b42fc2b7cd287d9d6734756b279357","abstract_canon_sha256":"1b48f5fef7a72c7dc143de2ecdeda04564e02c5d8615834cffa19a77c570d493"},"schema_version":"1.0"},"canonical_sha256":"901c7306c4f7f838b87bd8d907e38e2ea3ccd2e1daed2fcfbad52c0c0dc0e5ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:45.113195Z","signature_b64":"DYDvZOETsG3ecPjia7fzw9KN4mVOf0xTZsBnS4x3peFareDifUcVUFb24mjALv30cejAP+mnLvCdtJCZh6vsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"901c7306c4f7f838b87bd8d907e38e2ea3ccd2e1daed2fcfbad52c0c0dc0e5ee","last_reissued_at":"2026-05-18T04:18:45.112458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:45.112458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0143","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":"2026-05-18T04:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"usK2i9Gn903h8y4A7FiHb1xX6Ec9yql5OVrLmejodsIkOKilc8IUiUeYtkdMHu8epIq2jJitytRv8pJq+gOMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:09:43.166559Z"},"content_sha256":"269cbe22ef040606b3d8301f9135152e735738b17b51dec81b306495f6f78e9e","schema_version":"1.0","event_id":"sha256:269cbe22ef040606b3d8301f9135152e735738b17b51dec81b306495f6f78e9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SAOHGBWE674DROD33DMQPY4OF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohen-Macaulay binomial edge ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Juergen Herzog, Takayuki Hibi, Viviana Ene","submitted_at":"2010-04-01T14:19:35Z","abstract_excerpt":"We study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen--Macaulay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0143","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":"2026-05-18T04:18:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2KVl7fuFY39+Pd5Gl1q4eldnlAJgvssUZnkKeYXXBJKRZQxyddKEPBGyx1CldtdjI0GrB4BJBOEnkrTrhlYZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:09:43.166890Z"},"content_sha256":"20154c710e70fe14ab07b134be29a45331c9d95d37ef2993b5409ad3ad7ff13e","schema_version":"1.0","event_id":"sha256:20154c710e70fe14ab07b134be29a45331c9d95d37ef2993b5409ad3ad7ff13e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAOHGBWE674DROD33DMQPY4OF2/bundle.json","state_url":"https://pith.science/pith/SAOHGBWE674DROD33DMQPY4OF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAOHGBWE674DROD33DMQPY4OF2/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":"2026-06-27T04:09:43Z","links":{"resolver":"https://pith.science/pith/SAOHGBWE674DROD33DMQPY4OF2","bundle":"https://pith.science/pith/SAOHGBWE674DROD33DMQPY4OF2/bundle.json","state":"https://pith.science/pith/SAOHGBWE674DROD33DMQPY4OF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAOHGBWE674DROD33DMQPY4OF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SAOHGBWE674DROD33DMQPY4OF2","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":"1b48f5fef7a72c7dc143de2ecdeda04564e02c5d8615834cffa19a77c570d493","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T14:19:35Z","title_canon_sha256":"39c80df8d527a1c8bff829d0a1b29c39f3b42fc2b7cd287d9d6734756b279357"},"schema_version":"1.0","source":{"id":"1004.0143","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0143","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0143v2","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0143","created_at":"2026-05-18T04:18:45Z"},{"alias_kind":"pith_short_12","alias_value":"SAOHGBWE674D","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SAOHGBWE674DROD3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SAOHGBWE","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:20154c710e70fe14ab07b134be29a45331c9d95d37ef2993b5409ad3ad7ff13e","target":"graph","created_at":"2026-05-18T04:18:45Z","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 study the depth of classes of binomial edge ideals and classify all closed graphs whose binomial edge ideal is Cohen--Macaulay.","authors_text":"Juergen Herzog, Takayuki Hibi, Viviana Ene","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T14:19:35Z","title":"Cohen-Macaulay binomial edge ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0143","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":"sha256:269cbe22ef040606b3d8301f9135152e735738b17b51dec81b306495f6f78e9e","target":"record","created_at":"2026-05-18T04:18:45Z","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":"1b48f5fef7a72c7dc143de2ecdeda04564e02c5d8615834cffa19a77c570d493","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-01T14:19:35Z","title_canon_sha256":"39c80df8d527a1c8bff829d0a1b29c39f3b42fc2b7cd287d9d6734756b279357"},"schema_version":"1.0","source":{"id":"1004.0143","kind":"arxiv","version":2}},"canonical_sha256":"901c7306c4f7f838b87bd8d907e38e2ea3ccd2e1daed2fcfbad52c0c0dc0e5ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"901c7306c4f7f838b87bd8d907e38e2ea3ccd2e1daed2fcfbad52c0c0dc0e5ee","first_computed_at":"2026-05-18T04:18:45.112458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:45.112458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DYDvZOETsG3ecPjia7fzw9KN4mVOf0xTZsBnS4x3peFareDifUcVUFb24mjALv30cejAP+mnLvCdtJCZh6vsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:45.113195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0143","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:269cbe22ef040606b3d8301f9135152e735738b17b51dec81b306495f6f78e9e","sha256:20154c710e70fe14ab07b134be29a45331c9d95d37ef2993b5409ad3ad7ff13e"],"state_sha256":"0c8e16e409d072e368d9c50fd8093e85817bf83c5034546e16f061f098a6342f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5vy33h1rrnIUY5gpUIxl9hJPlJOwdpyj37+dC6R/FxPpK35KW7MC0qtahA5OBH5iKqOg1cXGMdWrS1gyN7+hDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:09:43.168728Z","bundle_sha256":"631703e008346ccbcbb42f9716dbc20e0becddc225318636c4061333c5ea2b5d"}}