{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:32YC4F7MO52MLOKMRCYWAZXHOE","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":"a041ff9293b84ff39a16432043aaa45802adddb23c78aabd7f3b250d73b42f9a","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-29T09:20:29Z","title_canon_sha256":"60805791d965f1d585aaaa104f6eece8162bd1beb3e57175453a59f9448d81ea"},"schema_version":"1.0","source":{"id":"1205.6308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6308","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6308v2","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6308","created_at":"2026-05-18T03:00:37Z"},{"alias_kind":"pith_short_12","alias_value":"32YC4F7MO52M","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"32YC4F7MO52MLOKM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"32YC4F7M","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:c14b17fe80962f56a8c2ae0c2075592f6ca7dcc8fbe8848778784d2cda06b46a","target":"graph","created_at":"2026-05-18T03:00:37Z","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":"The aim of this paper is to define and study the 3-category of extensions of Picard 2-stacks over a site S and to furnish a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves. More precisely, our main Theorem furnishes\n  (1) a parametrization of the equivalence classes of objects, 1-arrows, 2-arrows, and 3-arrows of the 3-category of extensions of Picard 2-stacks by the cohomology groups Ext^i, and\n  (2) a geometrical description of the cohomology groups Ext^i of length 3 complexes of abelian sheaves via extensions of Picard 2-stacks.\n  To this end,","authors_text":"Ahmet Emin Tatar, Cristiana Bertolin","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-29T09:20:29Z","title":"Extensions of Picard 2-Stacks and the cohomology groups Ext^i of length 3 complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6308","kind":"arxiv","version":2},"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":"sha256:3d2885fa9c63c6fcef5290642d3717e2824e4fb4d5468e1b3b97839cbc126f43","target":"record","created_at":"2026-05-18T03:00:37Z","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":"a041ff9293b84ff39a16432043aaa45802adddb23c78aabd7f3b250d73b42f9a","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-29T09:20:29Z","title_canon_sha256":"60805791d965f1d585aaaa104f6eece8162bd1beb3e57175453a59f9448d81ea"},"schema_version":"1.0","source":{"id":"1205.6308","kind":"arxiv","version":2}},"canonical_sha256":"deb02e17ec7774c5b94c88b16066e7712341e2678ba316d1290f33f250c104d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"deb02e17ec7774c5b94c88b16066e7712341e2678ba316d1290f33f250c104d1","first_computed_at":"2026-05-18T03:00:37.514818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:37.514818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dDaLufeWm3EewRLdWZMzedCdO2JkAOiTaxpqFvbnVGZ8qhZsBvjaLJSYXXtKy7DKDRbLsp0bjNp0Cn4FtBWACA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:37.515649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d2885fa9c63c6fcef5290642d3717e2824e4fb4d5468e1b3b97839cbc126f43","sha256:c14b17fe80962f56a8c2ae0c2075592f6ca7dcc8fbe8848778784d2cda06b46a"],"state_sha256":"94e0e9de57486b64e20b1b6b84a5147ab81518c4053980a35d406064fc24bdf7"}