{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:TZXMOEY3MOZBKX4EYVVBEOMEQD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b7c7a6a6eff9eea85e854fe13d26086e1b585efc618ae02abb384e82af74e26c","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-24T18:53:16Z","title_canon_sha256":"946f9550c2f15808589272b1f7ea8af60ff5a092b0c3de3b977fbfac1442328c"},"schema_version":"1.0","source":{"id":"0808.3267","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.3267","created_at":"2026-05-18T03:53:52Z"},{"alias_kind":"arxiv_version","alias_value":"0808.3267v4","created_at":"2026-05-18T03:53:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.3267","created_at":"2026-05-18T03:53:52Z"},{"alias_kind":"pith_short_12","alias_value":"TZXMOEY3MOZB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"TZXMOEY3MOZBKX4E","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"TZXMOEY3","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:4277f1ab6b64d0a7aea4e81f2f117debc9d8a6728d7f531a575063cc7fe13c03","target":"graph","created_at":"2026-05-18T03:53:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let k be a separably closed field. Let K_i=[A_i \\to B_i] (for i=1,2,3) be three 1-motives defined over k. We define the geometrical notions of extension of K_1 by K_3 and of biextension of (K_1,K_2) by K_3. We then compute the homological interpretation of these new geometrical notions: namely, the group Biext^0(K_1,K_2;K_3) of automorphisms of any biextension of (K_1,K_2) by K_3 is canonically isomorphic to the cohomology group Ext^0(K_1 \\otimes K_2,K_3), and the group Biext^1(K_1,K_2;K_3) of isomorphism classes of biextensions of (K_1,K_2) by K_3 is canonically isomorphic to the cohomology g","authors_text":"Cristiana Bertolin","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-24T18:53:16Z","title":"Homological interpretation of extensions and biextensions of 1-motives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.3267","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:07d7b8f5d5205c75621b294ca6ef826d063cdda555954f079a59921d9b815c0b","target":"record","created_at":"2026-05-18T03:53:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b7c7a6a6eff9eea85e854fe13d26086e1b585efc618ae02abb384e82af74e26c","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-08-24T18:53:16Z","title_canon_sha256":"946f9550c2f15808589272b1f7ea8af60ff5a092b0c3de3b977fbfac1442328c"},"schema_version":"1.0","source":{"id":"0808.3267","kind":"arxiv","version":4}},"canonical_sha256":"9e6ec7131b63b2155f84c56a12398480cee75a8987625610a654e2a87041386d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e6ec7131b63b2155f84c56a12398480cee75a8987625610a654e2a87041386d","first_computed_at":"2026-05-18T03:53:52.757476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:52.757476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IJM9/bbKY/TnIw7pGcVkySWDx1LbgJ6wxyvjBgY+BWoOeIocQqMFeCD2tQ5UNEziONbQgXZdEIY4uthjydOZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:52.758326Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.3267","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07d7b8f5d5205c75621b294ca6ef826d063cdda555954f079a59921d9b815c0b","sha256:4277f1ab6b64d0a7aea4e81f2f117debc9d8a6728d7f531a575063cc7fe13c03"],"state_sha256":"215127be2731171e957ae2593e2fc86e869d820af72daf0931c09f88f04dd49a"}