{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IIXOQ3SOJTKKHNA5KIPVDP5XIQ","short_pith_number":"pith:IIXOQ3SO","schema_version":"1.0","canonical_sha256":"422ee86e4e4cd4a3b41d521f51bfb7443140c9aecfd4fa1e87adc277ab1469ed","source":{"kind":"arxiv","id":"1305.1651","version":1},"attestation_state":"computed","paper":{"title":"On the resolution of path ideals of cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ali Alilooee, Sara Faridi","submitted_at":"2013-05-07T21:27:14Z","abstract_excerpt":"We give a formula to compute all the top degree graded Betti numbers of the path ideal of a cycle. Also we will find a criterion to determine when Betti numbers of this ideal are non zero and give a formula to compute its projective dimension and regularity."},"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":"1305.1651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-05-07T21:27:14Z","cross_cats_sorted":[],"title_canon_sha256":"3bfb07800dfc61b04e5c0697c458d6e0d5adc0b7f2b0d4c325dec4202a61e075","abstract_canon_sha256":"92cca70ecbaed9f91f9c3acc2d3b0d93f4dd3eefd4fe2732ac4b51d2a60f2609"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:11.708406Z","signature_b64":"NEP3/tjRCXrC+CdzsC0yy9ASpuHH93XqQ63DJctKX9cfNWCkpsNkEiNBqV7j24siEWm47qD4BQDg4RAITDS5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"422ee86e4e4cd4a3b41d521f51bfb7443140c9aecfd4fa1e87adc277ab1469ed","last_reissued_at":"2026-05-18T03:26:11.707690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:11.707690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the resolution of path ideals of cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ali Alilooee, Sara Faridi","submitted_at":"2013-05-07T21:27:14Z","abstract_excerpt":"We give a formula to compute all the top degree graded Betti numbers of the path ideal of a cycle. Also we will find a criterion to determine when Betti numbers of this ideal are non zero and give a formula to compute its projective dimension and regularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1651","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":""},"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":"1305.1651","created_at":"2026-05-18T03:26:11.707792+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.1651v1","created_at":"2026-05-18T03:26:11.707792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1651","created_at":"2026-05-18T03:26:11.707792+00:00"},{"alias_kind":"pith_short_12","alias_value":"IIXOQ3SOJTKK","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"IIXOQ3SOJTKKHNA5","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"IIXOQ3SO","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ","json":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ.json","graph_json":"https://pith.science/api/pith-number/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/graph.json","events_json":"https://pith.science/api/pith-number/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/events.json","paper":"https://pith.science/paper/IIXOQ3SO"},"agent_actions":{"view_html":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ","download_json":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ.json","view_paper":"https://pith.science/paper/IIXOQ3SO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.1651&json=true","fetch_graph":"https://pith.science/api/pith-number/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/graph.json","fetch_events":"https://pith.science/api/pith-number/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/action/storage_attestation","attest_author":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/action/author_attestation","sign_citation":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/action/citation_signature","submit_replication":"https://pith.science/pith/IIXOQ3SOJTKKHNA5KIPVDP5XIQ/action/replication_record"}},"created_at":"2026-05-18T03:26:11.707792+00:00","updated_at":"2026-05-18T03:26:11.707792+00:00"}