{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YXZY75D3WALRH3XPTYRUSQ47L5","short_pith_number":"pith:YXZY75D3","schema_version":"1.0","canonical_sha256":"c5f38ff47bb01713eeef9e2349439f5f689f75bb5b3147a8b0fe159cca51d6e4","source":{"kind":"arxiv","id":"1103.1299","version":2},"attestation_state":"computed","paper":{"title":"Semistability criterion for parabolic vector bundles on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ajneet Dhillon, Indranil Biswas","submitted_at":"2011-03-07T15:29:20Z","abstract_excerpt":"We give a cohomological criterion for a parabolic vector bundle on a curve to be semistable. It says that a parabolic vector bundle $E$ with rational parabolic weights is semistable if and only if there is another parabolic vector bundle $F$ with rational parabolic weights such that the cohomologies of the vector bundle underlying the para- bolic tensor product $E \\otimes F$ vanish. This criterion generalizes the known semistability criterion of Faltings for vector bundles on curves and significantly improves the result in [Bis07]."},"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":"1103.1299","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-03-07T15:29:20Z","cross_cats_sorted":[],"title_canon_sha256":"7ced0a933f4a9d0808a0caa1946d3ca12284123614a64a7aecb7b37a00669b8d","abstract_canon_sha256":"b2de332c5c0504985955a5a0128a770f120b1239d0ddc1240bc085f9bbb79749"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:34.343629Z","signature_b64":"Aq7/PWZl7umCMhomSuaw7q+4NPtlE9lJzY8xXvsq8D1ivlWuwoXEJ5UNdQAkdD58tjYzkJQvEbuxtcBUQ72TDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5f38ff47bb01713eeef9e2349439f5f689f75bb5b3147a8b0fe159cca51d6e4","last_reissued_at":"2026-05-18T04:10:34.342800Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:34.342800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semistability criterion for parabolic vector bundles on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ajneet Dhillon, Indranil Biswas","submitted_at":"2011-03-07T15:29:20Z","abstract_excerpt":"We give a cohomological criterion for a parabolic vector bundle on a curve to be semistable. It says that a parabolic vector bundle $E$ with rational parabolic weights is semistable if and only if there is another parabolic vector bundle $F$ with rational parabolic weights such that the cohomologies of the vector bundle underlying the para- bolic tensor product $E \\otimes F$ vanish. This criterion generalizes the known semistability criterion of Faltings for vector bundles on curves and significantly improves the result in [Bis07]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1299","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1103.1299","created_at":"2026-05-18T04:10:34.342929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1299v2","created_at":"2026-05-18T04:10:34.342929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1299","created_at":"2026-05-18T04:10:34.342929+00:00"},{"alias_kind":"pith_short_12","alias_value":"YXZY75D3WALR","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YXZY75D3WALRH3XP","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YXZY75D3","created_at":"2026-05-18T12:26:47.523578+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/YXZY75D3WALRH3XPTYRUSQ47L5","json":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5.json","graph_json":"https://pith.science/api/pith-number/YXZY75D3WALRH3XPTYRUSQ47L5/graph.json","events_json":"https://pith.science/api/pith-number/YXZY75D3WALRH3XPTYRUSQ47L5/events.json","paper":"https://pith.science/paper/YXZY75D3"},"agent_actions":{"view_html":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5","download_json":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5.json","view_paper":"https://pith.science/paper/YXZY75D3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1299&json=true","fetch_graph":"https://pith.science/api/pith-number/YXZY75D3WALRH3XPTYRUSQ47L5/graph.json","fetch_events":"https://pith.science/api/pith-number/YXZY75D3WALRH3XPTYRUSQ47L5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5/action/storage_attestation","attest_author":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5/action/author_attestation","sign_citation":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5/action/citation_signature","submit_replication":"https://pith.science/pith/YXZY75D3WALRH3XPTYRUSQ47L5/action/replication_record"}},"created_at":"2026-05-18T04:10:34.342929+00:00","updated_at":"2026-05-18T04:10:34.342929+00:00"}