{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:RCYEHDYQZ3WWH5SV3J32CUBFWV","short_pith_number":"pith:RCYEHDYQ","canonical_record":{"source":{"id":"1107.3687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-19T11:38:12Z","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP","math.SG"],"title_canon_sha256":"2d4238e448f2184c9b627b8be8efcd3fda4fa9f68de48c7e02f5727b790a193f","abstract_canon_sha256":"b24d7119ed6888ae30dbc1e1a8504fe41cf66947ed572c1fd05a45eaf510e0d4"},"schema_version":"1.0"},"canonical_sha256":"88b0438f10ceed63f655da77a15025b57ba5682cc6595a675aac2dd0747de452","source":{"kind":"arxiv","id":"1107.3687","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3687","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3687v2","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3687","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"pith_short_12","alias_value":"RCYEHDYQZ3WW","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCYEHDYQZ3WWH5SV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCYEHDYQ","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:RCYEHDYQZ3WWH5SV3J32CUBFWV","target":"record","payload":{"canonical_record":{"source":{"id":"1107.3687","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-19T11:38:12Z","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP","math.SG"],"title_canon_sha256":"2d4238e448f2184c9b627b8be8efcd3fda4fa9f68de48c7e02f5727b790a193f","abstract_canon_sha256":"b24d7119ed6888ae30dbc1e1a8504fe41cf66947ed572c1fd05a45eaf510e0d4"},"schema_version":"1.0"},"canonical_sha256":"88b0438f10ceed63f655da77a15025b57ba5682cc6595a675aac2dd0747de452","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:26.171778Z","signature_b64":"C9WX8rr0Fx37IugeHg57kPcdh5l2eR4bD1kcab7f+11RL4+hX/XiZup01l+waUaD/9S1hRYVewsqp9wmFVCLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88b0438f10ceed63f655da77a15025b57ba5682cc6595a675aac2dd0747de452","last_reissued_at":"2026-05-18T04:01:26.171043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:26.171043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.3687","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":"2026-05-18T04:01:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oz7Wvwy0/NX+d+5/5cRDdM7qdHkp358PcfxIRZzOxWXG/VsZqdTvqgIBW16nmNt37y+hcFJM0lY00lPWu3mIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T17:36:23.440067Z"},"content_sha256":"0056e48ab7bae0c8f3008f0b6570f18b198b455e061c7127e4c33c65f802c0b6","schema_version":"1.0","event_id":"sha256:0056e48ab7bae0c8f3008f0b6570f18b198b455e061c7127e4c33c65f802c0b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:RCYEHDYQZ3WWH5SV3J32CUBFWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bundle gerbes and moduli spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.GT","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"Peter Bouwknegt, Siye Wu, Varghese Mathai","submitted_at":"2011-07-19T11:38:12Z","abstract_excerpt":"In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3687","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":"2026-05-18T04:01:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tUje+GrXmTf/7cBJLw5lolPR0lRAM8XQsxgPVJPRBg1LEMqkDe+Kro/fU9vbg246LQ6z94RaEFMwSisvOX64Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T17:36:23.440551Z"},"content_sha256":"2af1d29b3d3caf83db9aae20d3c484dba835e7877db4d7fa223bb27c35e07933","schema_version":"1.0","event_id":"sha256:2af1d29b3d3caf83db9aae20d3c484dba835e7877db4d7fa223bb27c35e07933"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCYEHDYQZ3WWH5SV3J32CUBFWV/bundle.json","state_url":"https://pith.science/pith/RCYEHDYQZ3WWH5SV3J32CUBFWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCYEHDYQZ3WWH5SV3J32CUBFWV/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":"2026-08-20T17:36:23Z","links":{"resolver":"https://pith.science/pith/RCYEHDYQZ3WWH5SV3J32CUBFWV","bundle":"https://pith.science/pith/RCYEHDYQZ3WWH5SV3J32CUBFWV/bundle.json","state":"https://pith.science/pith/RCYEHDYQZ3WWH5SV3J32CUBFWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCYEHDYQZ3WWH5SV3J32CUBFWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RCYEHDYQZ3WWH5SV3J32CUBFWV","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":"b24d7119ed6888ae30dbc1e1a8504fe41cf66947ed572c1fd05a45eaf510e0d4","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-19T11:38:12Z","title_canon_sha256":"2d4238e448f2184c9b627b8be8efcd3fda4fa9f68de48c7e02f5727b790a193f"},"schema_version":"1.0","source":{"id":"1107.3687","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3687","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3687v2","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3687","created_at":"2026-05-18T04:01:26Z"},{"alias_kind":"pith_short_12","alias_value":"RCYEHDYQZ3WW","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCYEHDYQZ3WWH5SV","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCYEHDYQ","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:2af1d29b3d3caf83db9aae20d3c484dba835e7877db4d7fa223bb27c35e07933","target":"graph","created_at":"2026-05-18T04:01:26Z","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":"In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analytically constructed index bundle gerbe. We apply these constructions to certain moduli spaces associated to compact Riemann surfaces, constructing on these moduli spaces, natural bundle gerbes with connection and curving, whose 3-curvature represent Dixmier-Douady classes that are","authors_text":"Peter Bouwknegt, Siye Wu, Varghese Mathai","cross_cats":["hep-th","math-ph","math.GT","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-19T11:38:12Z","title":"Bundle gerbes and moduli spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3687","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":"sha256:0056e48ab7bae0c8f3008f0b6570f18b198b455e061c7127e4c33c65f802c0b6","target":"record","created_at":"2026-05-18T04:01:26Z","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":"b24d7119ed6888ae30dbc1e1a8504fe41cf66947ed572c1fd05a45eaf510e0d4","cross_cats_sorted":["hep-th","math-ph","math.GT","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-19T11:38:12Z","title_canon_sha256":"2d4238e448f2184c9b627b8be8efcd3fda4fa9f68de48c7e02f5727b790a193f"},"schema_version":"1.0","source":{"id":"1107.3687","kind":"arxiv","version":2}},"canonical_sha256":"88b0438f10ceed63f655da77a15025b57ba5682cc6595a675aac2dd0747de452","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88b0438f10ceed63f655da77a15025b57ba5682cc6595a675aac2dd0747de452","first_computed_at":"2026-05-18T04:01:26.171043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:26.171043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C9WX8rr0Fx37IugeHg57kPcdh5l2eR4bD1kcab7f+11RL4+hX/XiZup01l+waUaD/9S1hRYVewsqp9wmFVCLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:26.171778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3687","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0056e48ab7bae0c8f3008f0b6570f18b198b455e061c7127e4c33c65f802c0b6","sha256:2af1d29b3d3caf83db9aae20d3c484dba835e7877db4d7fa223bb27c35e07933"],"state_sha256":"d18c2d860f0c048bf2832e65d6f35ebf56c9f2b99b8fdc098f2ccc2f6bd15422"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2kEl/pbuW6IXiS1YzCZKAJdiS5KJv4KdwQT5vTmzh8RdwfKilgm7QLcwVTJSA4Xo8zeiezXCqvWQ19qQpBdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T17:36:23.444485Z","bundle_sha256":"0b05f0cdf812c274b9cce49d1284bf105ea88acacab8c609f4e910e7372d60c0"}}