{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:RVNO2AW5VKXVS7A6VBSBH4GD7D","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":"ca52ce9fa43edc4376ec1a3ac2406a3dbba4cd7b3cc3f054bb70a884e733c110","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-05-27T01:15:42Z","title_canon_sha256":"2dca1995b7e22ed435bf7978c0c854f4acb2f8bc5d3d287f75c5a07ff8f5eef4"},"schema_version":"1.0","source":{"id":"math/0605694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605694","created_at":"2026-07-04T15:35:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605694v2","created_at":"2026-07-04T15:35:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605694","created_at":"2026-07-04T15:35:21Z"},{"alias_kind":"pith_short_12","alias_value":"RVNO2AW5VKXV","created_at":"2026-07-04T15:35:21Z"},{"alias_kind":"pith_short_16","alias_value":"RVNO2AW5VKXVS7A6","created_at":"2026-07-04T15:35:21Z"},{"alias_kind":"pith_short_8","alias_value":"RVNO2AW5","created_at":"2026-07-04T15:35:21Z"}],"graph_snapshots":[{"event_id":"sha256:f15ec03380e4b10a1edfe6759645e5b4e3af4ecc560bfad75b9312035cca382a","target":"graph","created_at":"2026-07-04T15:35:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0605694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce differentiable stacks and explain the relationship with Lie groupoids. Then we study $S^1$-bundles and $S^1$-gerbes over differentiable stacks. In particular, we establish the relationship between $S^1$-gerbes and groupoid $S^1$-central extensions. We define connections and curvings for groupoid $S^1$-central extensions extending the corresponding notions of Brylinski, Hitchin and Murray for\n  $S^1$-gerbes over manifolds. We develop a Chern-Weil theory of characteristic classes in this general setting by presenting a construction of Chern classes and Dixmier-Douady classes in term","authors_text":"Kai Behrend, Ping Xu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-05-27T01:15:42Z","title":"Differentiable Stacks and Gerbes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605694","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":"sha256:7af8369159ce8ae4054e1e8ca2726888f7c78068bab1e3cb9b9f235d478bd77b","target":"record","created_at":"2026-07-04T15:35:21Z","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":"ca52ce9fa43edc4376ec1a3ac2406a3dbba4cd7b3cc3f054bb70a884e733c110","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2006-05-27T01:15:42Z","title_canon_sha256":"2dca1995b7e22ed435bf7978c0c854f4acb2f8bc5d3d287f75c5a07ff8f5eef4"},"schema_version":"1.0","source":{"id":"math/0605694","kind":"arxiv","version":2}},"canonical_sha256":"8d5aed02ddaaaf597c1ea86413f0c3f8f696747a3a96ce7bb99de17fa8e1f641","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d5aed02ddaaaf597c1ea86413f0c3f8f696747a3a96ce7bb99de17fa8e1f641","first_computed_at":"2026-07-04T15:35:21.214765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:35:21.214765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xOHB8e7foY3sR8yHq76SN7ACqGaPP+Leuip0uWcVHU7rSu/eytcN6rIiPQWxr6IGkUQDA46IlxHTMTuRU0YxDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:35:21.215266Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7af8369159ce8ae4054e1e8ca2726888f7c78068bab1e3cb9b9f235d478bd77b","sha256:f15ec03380e4b10a1edfe6759645e5b4e3af4ecc560bfad75b9312035cca382a"],"state_sha256":"463b980a0acaaab397b009f25ba43af6a5967ff265eec47d995b92a2476ee9cc"}