{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PVNCLCWKOV76VHRKWB5FRHIM5G","short_pith_number":"pith:PVNCLCWK","schema_version":"1.0","canonical_sha256":"7d5a258aca757fea9e2ab07a589d0ce9b716d968d802bd16c9e5aa729dfff7b9","source":{"kind":"arxiv","id":"1602.08873","version":3},"attestation_state":"computed","paper":{"title":"A long exact sequence for homology of FI-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Wee Liang Gan","submitted_at":"2016-02-29T09:19:21Z","abstract_excerpt":"We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo-Mumford regularity of an FI-module which is generated and related in finite degree. We also prove that for an FI-module which is generated and related in finite degree, if it has a nonzero higher homology, then its homological degrees are strictly increasing (starting from the first homological degree)."},"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":"1602.08873","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-02-29T09:19:21Z","cross_cats_sorted":[],"title_canon_sha256":"66f7d5339a8acd81845fce54938459584acdaf904306537660ed205c57c69ef6","abstract_canon_sha256":"0960748262e65e62750b6f2d3e525abc9dd3ad60e21625a64f08836ea630f437"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:17.127453Z","signature_b64":"IukonzAy6aYea66imIhPlawl4xIX4PysuzzcIB0dVwDoPwtW24ewjWdVseiV7a3yU7pYSWZ2VlNDUoH+eV34DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d5a258aca757fea9e2ab07a589d0ce9b716d968d802bd16c9e5aa729dfff7b9","last_reissued_at":"2026-05-18T01:17:17.126694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:17.126694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A long exact sequence for homology of FI-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Wee Liang Gan","submitted_at":"2016-02-29T09:19:21Z","abstract_excerpt":"We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo-Mumford regularity of an FI-module which is generated and related in finite degree. We also prove that for an FI-module which is generated and related in finite degree, if it has a nonzero higher homology, then its homological degrees are strictly increasing (starting from the first homological degree)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08873","kind":"arxiv","version":3},"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":"1602.08873","created_at":"2026-05-18T01:17:17.126773+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.08873v3","created_at":"2026-05-18T01:17:17.126773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08873","created_at":"2026-05-18T01:17:17.126773+00:00"},{"alias_kind":"pith_short_12","alias_value":"PVNCLCWKOV76","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PVNCLCWKOV76VHRK","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PVNCLCWK","created_at":"2026-05-18T12:30:39.010887+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/PVNCLCWKOV76VHRKWB5FRHIM5G","json":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G.json","graph_json":"https://pith.science/api/pith-number/PVNCLCWKOV76VHRKWB5FRHIM5G/graph.json","events_json":"https://pith.science/api/pith-number/PVNCLCWKOV76VHRKWB5FRHIM5G/events.json","paper":"https://pith.science/paper/PVNCLCWK"},"agent_actions":{"view_html":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G","download_json":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G.json","view_paper":"https://pith.science/paper/PVNCLCWK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.08873&json=true","fetch_graph":"https://pith.science/api/pith-number/PVNCLCWKOV76VHRKWB5FRHIM5G/graph.json","fetch_events":"https://pith.science/api/pith-number/PVNCLCWKOV76VHRKWB5FRHIM5G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G/action/storage_attestation","attest_author":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G/action/author_attestation","sign_citation":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G/action/citation_signature","submit_replication":"https://pith.science/pith/PVNCLCWKOV76VHRKWB5FRHIM5G/action/replication_record"}},"created_at":"2026-05-18T01:17:17.126773+00:00","updated_at":"2026-05-18T01:17:17.126773+00:00"}