{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:ALP32T5GA2EBGBNST3ER3KGL7D","short_pith_number":"pith:ALP32T5G","schema_version":"1.0","canonical_sha256":"02dfbd4fa606881305b29ec91da8cbf8f4734ac7c8d61c064de2837d524830c8","source":{"kind":"arxiv","id":"2503.08521","version":2},"attestation_state":"computed","paper":{"title":"Edge ideals whose all matching powers are bi-Cohen-Macaulay","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Antonino Ficarra, Marilena Crupi","submitted_at":"2025-03-11T15:14:27Z","abstract_excerpt":"We classify all graphs $G$ satisfying the property that all matching powers $I(G)^{[k]}$ of the edge ideal $I(G)$ are bi-Cohen-Macaulay for $1\\le k\\le\\nu(G)$, where $\\nu(G)$ is the maximum size of a matching of $G$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2503.08521","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AC","submitted_at":"2025-03-11T15:14:27Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4d64a9fa00151544ada5e06e24bdc6d34ccaf3d49823716579ccda38921dd4a6","abstract_canon_sha256":"d76c005db14121c0330254c1cef91ee008202dc7c754eeca2f5f33211ff96cdc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:47:20.130665Z","signature_b64":"e6WvcemcMJ0/PT1ku43/9lzO7Wm1PKjxOzkf8fJ04vA08Uebrcfq4wUg+RpMugiWBexqCfJ3Y023zxsA6VlaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02dfbd4fa606881305b29ec91da8cbf8f4734ac7c8d61c064de2837d524830c8","last_reissued_at":"2026-07-05T11:47:20.130174Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:47:20.130174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge ideals whose all matching powers are bi-Cohen-Macaulay","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Antonino Ficarra, Marilena Crupi","submitted_at":"2025-03-11T15:14:27Z","abstract_excerpt":"We classify all graphs $G$ satisfying the property that all matching powers $I(G)^{[k]}$ of the edge ideal $I(G)$ are bi-Cohen-Macaulay for $1\\le k\\le\\nu(G)$, where $\\nu(G)$ is the maximum size of a matching of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.08521","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.08521/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2503.08521","created_at":"2026-07-05T11:47:20.130232+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.08521v2","created_at":"2026-07-05T11:47:20.130232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.08521","created_at":"2026-07-05T11:47:20.130232+00:00"},{"alias_kind":"pith_short_12","alias_value":"ALP32T5GA2EB","created_at":"2026-07-05T11:47:20.130232+00:00"},{"alias_kind":"pith_short_16","alias_value":"ALP32T5GA2EBGBNS","created_at":"2026-07-05T11:47:20.130232+00:00"},{"alias_kind":"pith_short_8","alias_value":"ALP32T5G","created_at":"2026-07-05T11:47:20.130232+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.07022","citing_title":"Principal vector-spread Borel ideals","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D","json":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D.json","graph_json":"https://pith.science/api/pith-number/ALP32T5GA2EBGBNST3ER3KGL7D/graph.json","events_json":"https://pith.science/api/pith-number/ALP32T5GA2EBGBNST3ER3KGL7D/events.json","paper":"https://pith.science/paper/ALP32T5G"},"agent_actions":{"view_html":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D","download_json":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D.json","view_paper":"https://pith.science/paper/ALP32T5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.08521&json=true","fetch_graph":"https://pith.science/api/pith-number/ALP32T5GA2EBGBNST3ER3KGL7D/graph.json","fetch_events":"https://pith.science/api/pith-number/ALP32T5GA2EBGBNST3ER3KGL7D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D/action/storage_attestation","attest_author":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D/action/author_attestation","sign_citation":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D/action/citation_signature","submit_replication":"https://pith.science/pith/ALP32T5GA2EBGBNST3ER3KGL7D/action/replication_record"}},"created_at":"2026-07-05T11:47:20.130232+00:00","updated_at":"2026-07-05T11:47:20.130232+00:00"}