{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:N7RGY5NTM7SDJB5JRA72ZV73NG","short_pith_number":"pith:N7RGY5NT","schema_version":"1.0","canonical_sha256":"6fe26c75b367e43487a9883facd7fb69bd9a255d6140ab29ae84b91fd860fdb5","source":{"kind":"arxiv","id":"1004.5476","version":1},"attestation_state":"computed","paper":{"title":"Topological Constructions for Multigraded Squarefree Module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hara Charalambous","submitted_at":"2010-04-30T09:05:54Z","abstract_excerpt":"Let $R=\\Bbbk[x_1,\\..., x_n]$ and $M=R^s/I$ a multigraded squarefree module. We discuss the construction of cochain complexes associated to $M$ and we show how to interpret homological invariants of $M$ in terms of topological computations. This is a generalization of the well studied  case of squarefree monomial ideals."},"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":"1004.5476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-04-30T09:05:54Z","cross_cats_sorted":[],"title_canon_sha256":"0352b21116cbc511e5649952c747bdd2eca7a586bc62f5757be73d16c19bb632","abstract_canon_sha256":"3a4558aa277194db409fbdd6eba17fdb6d28e6dfd02aafb776fdcb4a91628feb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:10.002490Z","signature_b64":"XXENNBT8JqnEOs2pAbsB3QSGs1SZSMPmATMj4muEcrWfjOJPBQgpdOZTJdyirMp0kB4EqFIuvPgapAThPqwFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fe26c75b367e43487a9883facd7fb69bd9a255d6140ab29ae84b91fd860fdb5","last_reissued_at":"2026-05-18T02:24:10.001836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:10.001836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topological Constructions for Multigraded Squarefree Module","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hara Charalambous","submitted_at":"2010-04-30T09:05:54Z","abstract_excerpt":"Let $R=\\Bbbk[x_1,\\..., x_n]$ and $M=R^s/I$ a multigraded squarefree module. We discuss the construction of cochain complexes associated to $M$ and we show how to interpret homological invariants of $M$ in terms of topological computations. This is a generalization of the well studied  case of squarefree monomial ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.5476","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":"1004.5476","created_at":"2026-05-18T02:24:10.001926+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.5476v1","created_at":"2026-05-18T02:24:10.001926+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.5476","created_at":"2026-05-18T02:24:10.001926+00:00"},{"alias_kind":"pith_short_12","alias_value":"N7RGY5NTM7SD","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"N7RGY5NTM7SDJB5J","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"N7RGY5NT","created_at":"2026-05-18T12:26:10.704358+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/N7RGY5NTM7SDJB5JRA72ZV73NG","json":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG.json","graph_json":"https://pith.science/api/pith-number/N7RGY5NTM7SDJB5JRA72ZV73NG/graph.json","events_json":"https://pith.science/api/pith-number/N7RGY5NTM7SDJB5JRA72ZV73NG/events.json","paper":"https://pith.science/paper/N7RGY5NT"},"agent_actions":{"view_html":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG","download_json":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG.json","view_paper":"https://pith.science/paper/N7RGY5NT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.5476&json=true","fetch_graph":"https://pith.science/api/pith-number/N7RGY5NTM7SDJB5JRA72ZV73NG/graph.json","fetch_events":"https://pith.science/api/pith-number/N7RGY5NTM7SDJB5JRA72ZV73NG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG/action/storage_attestation","attest_author":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG/action/author_attestation","sign_citation":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG/action/citation_signature","submit_replication":"https://pith.science/pith/N7RGY5NTM7SDJB5JRA72ZV73NG/action/replication_record"}},"created_at":"2026-05-18T02:24:10.001926+00:00","updated_at":"2026-05-18T02:24:10.001926+00:00"}