{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B54QSVJTGMRL7P2CSBBEDFOSAT","short_pith_number":"pith:B54QSVJT","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"},"canonical_sha256":"0f790955333322bfbf4290424195d204cbfb5107babf6451e78ccaff15d76255","source":{"kind":"arxiv","id":"1401.6685","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6685","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6685v2","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6685","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"B54QSVJTGMRL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B54QSVJTGMRL7P2C","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B54QSVJT","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B54QSVJTGMRL7P2CSBBEDFOSAT","target":"record","payload":{"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"},"canonical_sha256":"0f790955333322bfbf4290424195d204cbfb5107babf6451e78ccaff15d76255","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"},"source_kind":"arxiv","source_id":"1401.6685","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hsXGbFYYRt4LiBcv5GQ8Te7UXcmP9iwVzBEuCKjBWa3nHJ3vCizryfpEOsPtD57+R2K/uu/+KLQcHZ+FOXedDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:38:12.490470Z"},"content_sha256":"0834d813680c3a9b6c9b4b5806a3e14214a0d2670a3111ca04edb48ab391eea6","schema_version":"1.0","event_id":"sha256:0834d813680c3a9b6c9b4b5806a3e14214a0d2670a3111ca04edb48ab391eea6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B54QSVJTGMRL7P2CSBBEDFOSAT","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2LNwyH9Y56odG2aa1onOfgs/hV6wmYS3G9lDQ40wo5I+F0+JZDYk7kIRhE3z2V3sPzBKMN9EWB43DC5oLmktDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:38:12.491339Z"},"content_sha256":"7ae5098c103c92e9fdc5d52347afcbf411d2e0f77b3a42528fb6020a8b20301c","schema_version":"1.0","event_id":"sha256:7ae5098c103c92e9fdc5d52347afcbf411d2e0f77b3a42528fb6020a8b20301c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/bundle.json","state_url":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T22:38:12Z","links":{"resolver":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT","bundle":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/bundle.json","state":"https://pith.science/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B54QSVJTGMRL7P2CSBBEDFOSAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B54QSVJTGMRL7P2CSBBEDFOSAT","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":"961121beaeb6e9706ef143e632909f81d837e991a4ba0580e9b075f13951da43","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-01-26T20:19:16Z","title_canon_sha256":"c88a318fa14ecdb7ef248109dea2682204ac9bbbbb18bb1c240cd3779be03ec0"},"schema_version":"1.0","source":{"id":"1401.6685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6685","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6685v2","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6685","created_at":"2026-05-18T00:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"B54QSVJTGMRL","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B54QSVJTGMRL7P2C","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B54QSVJT","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:7ae5098c103c92e9fdc5d52347afcbf411d2e0f77b3a42528fb6020a8b20301c","target":"graph","created_at":"2026-05-18T00:21:38Z","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 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","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":"2014-01-26T20:19:16Z","title":"Higher-dimensional study of extensions via torsors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6685","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":"sha256:0834d813680c3a9b6c9b4b5806a3e14214a0d2670a3111ca04edb48ab391eea6","target":"record","created_at":"2026-05-18T00:21:38Z","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":"961121beaeb6e9706ef143e632909f81d837e991a4ba0580e9b075f13951da43","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-01-26T20:19:16Z","title_canon_sha256":"c88a318fa14ecdb7ef248109dea2682204ac9bbbbb18bb1c240cd3779be03ec0"},"schema_version":"1.0","source":{"id":"1401.6685","kind":"arxiv","version":2}},"canonical_sha256":"0f790955333322bfbf4290424195d204cbfb5107babf6451e78ccaff15d76255","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f790955333322bfbf4290424195d204cbfb5107babf6451e78ccaff15d76255","first_computed_at":"2026-05-18T00:21:38.156912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:38.156912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Yi2uucWuyIxRkCB1B2e9+EAjjgJljYjQOVucjOcgZ0+xcO0ZmYf+2dQ3UBr5gN11rgfvBujxAcvjHjJMOMIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:38.157618Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0834d813680c3a9b6c9b4b5806a3e14214a0d2670a3111ca04edb48ab391eea6","sha256:7ae5098c103c92e9fdc5d52347afcbf411d2e0f77b3a42528fb6020a8b20301c"],"state_sha256":"36ded8832ec4283611c7734139e92b0ad63440e167bb7418c88afb0bda514d46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwLZ7bJHpXC2EvD/Eh/FATMt/wRYBdeVMcCatE5or1WLkmv0KAHKiSjGunTNfVsLoPGguHiH2NDa7Fh14gC2CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:38:12.495566Z","bundle_sha256":"d7d975ba75736fc47930a74bcee4477ab8613e8ea7d717d48c29c073ff1b97e8"}}