{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:B54QSVJTGMRL7P2CSBBEDFOSAT","short_pith_number":"pith:B54QSVJT","schema_version":"1.0","canonical_sha256":"0f790955333322bfbf4290424195d204cbfb5107babf6451e78ccaff15d76255","source":{"kind":"arxiv","id":"1401.6685","version":2},"attestation_state":"computed","paper":{"title":"Higher-dimensional study of extensions via torsors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Ahmet Emin Tatar, Cristiana Bertolin","submitted_at":"2014-01-26T20:19:16Z","abstract_excerpt":"Let S be a site. First we define the 3-category of torsors under a Picard S-2-stack and we compute its homotopy groups. Using calculus of fractions we define also a pure algebraic analogue of the 3-category of torsors under a Picard S-2-stack. Then we describe extensions of Picard S-2-stacks as torsors endowed with a group law on the fibers. As a consequence of such a description, we show that any Picard S-2-stack admits a canonical free partial left resolution that we compute explicitly. Moreover we get an explicit right resolution of the 3-category of extensions of Picard S-2-stacks in terms"},"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":"1401.6685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-01-26T20:19:16Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"c88a318fa14ecdb7ef248109dea2682204ac9bbbbb18bb1c240cd3779be03ec0","abstract_canon_sha256":"961121beaeb6e9706ef143e632909f81d837e991a4ba0580e9b075f13951da43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:38.157618Z","signature_b64":"3Yi2uucWuyIxRkCB1B2e9+EAjjgJljYjQOVucjOcgZ0+xcO0ZmYf+2dQ3UBr5gN11rgfvBujxAcvjHjJMOMIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f790955333322bfbf4290424195d204cbfb5107babf6451e78ccaff15d76255","last_reissued_at":"2026-05-18T00:21:38.156912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:38.156912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher-dimensional study of extensions via torsors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Ahmet Emin Tatar, Cristiana Bertolin","submitted_at":"2014-01-26T20:19:16Z","abstract_excerpt":"Let S be a site. First we define the 3-category of torsors under a Picard S-2-stack and we compute its homotopy groups. Using calculus of fractions we define also a pure algebraic analogue of the 3-category of torsors under a Picard S-2-stack. Then we describe extensions of Picard S-2-stacks as torsors endowed with a group law on the fibers. As a consequence of such a description, we show that any Picard S-2-stack admits a canonical free partial left resolution that we compute explicitly. Moreover we get an explicit right resolution of the 3-category of extensions of Picard S-2-stacks in terms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6685","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":"1401.6685","created_at":"2026-05-18T00:21:38.157013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.6685v2","created_at":"2026-05-18T00:21:38.157013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6685","created_at":"2026-05-18T00:21:38.157013+00:00"},{"alias_kind":"pith_short_12","alias_value":"B54QSVJTGMRL","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"B54QSVJTGMRL7P2C","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"B54QSVJT","created_at":"2026-05-18T12:28:19.803747+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/B54QSVJTGMRL7P2CSBBEDFOSAT","json":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT.json","graph_json":"https://pith.science/api/pith-number/B54QSVJTGMRL7P2CSBBEDFOSAT/graph.json","events_json":"https://pith.science/api/pith-number/B54QSVJTGMRL7P2CSBBEDFOSAT/events.json","paper":"https://pith.science/paper/B54QSVJT"},"agent_actions":{"view_html":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT","download_json":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT.json","view_paper":"https://pith.science/paper/B54QSVJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.6685&json=true","fetch_graph":"https://pith.science/api/pith-number/B54QSVJTGMRL7P2CSBBEDFOSAT/graph.json","fetch_events":"https://pith.science/api/pith-number/B54QSVJTGMRL7P2CSBBEDFOSAT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/action/storage_attestation","attest_author":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/action/author_attestation","sign_citation":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/action/citation_signature","submit_replication":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/action/replication_record"}},"created_at":"2026-05-18T00:21:38.157013+00:00","updated_at":"2026-05-18T00:21:38.157013+00:00"}