{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YO2Q3OTQDKYLMAHJJNEMDBLKAK","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":"e8cae880b697d3a6e0c920613a180c4e562ac0dd657b9a6de695d6937d4caed3","cross_cats_sorted":["math-ph","math.CT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2023-09-11T09:55:38Z","title_canon_sha256":"d6a00705c25431c0c495b18c806156074fa9a262257d89a3a97c6ca4c3796159"},"schema_version":"1.0","source":{"id":"2309.05355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.05355","created_at":"2026-07-05T06:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"2309.05355v1","created_at":"2026-07-05T06:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.05355","created_at":"2026-07-05T06:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"YO2Q3OTQDKYL","created_at":"2026-07-05T06:49:34Z"},{"alias_kind":"pith_short_16","alias_value":"YO2Q3OTQDKYLMAHJ","created_at":"2026-07-05T06:49:34Z"},{"alias_kind":"pith_short_8","alias_value":"YO2Q3OTQ","created_at":"2026-07-05T06:49:34Z"}],"graph_snapshots":[{"event_id":"sha256:3d73af676b7f2f00345ec9b7583656743fb2542fb6cc63c48dcf8ca38ac9703e","target":"graph","created_at":"2026-07-05T06:49:34Z","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/2309.05355/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a Lie 2-group torsor version of the well-known one-one correspondence between fibered categories and pseudofunctors. Consequently, we obtain a weak version of the principal Lie group bundle over a Lie groupoid. The correspondence also enables us to extend a particular class of principal 2-bundles to be defined over differentiable stacks. We show that the differential geometric connection structures introduced in the authors' previous work, combine nicely with the underlying fibration structure of a principal 2-bundle over a Lie groupoid. This interrelation allows us to derive a notion","authors_text":"Adittya Chaudhuri, Saikat Chatterjee","cross_cats":["math-ph","math.CT","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2023-09-11T09:55:38Z","title":"Parallel transport on a Lie 2-group bundle over a Lie groupoid along Haefliger paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.05355","kind":"arxiv","version":1},"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:d49c2d08e03b7c5ea7f200a7e1d55ace2bc7febd304c2b82f21a52991772232c","target":"record","created_at":"2026-07-05T06:49:34Z","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":"e8cae880b697d3a6e0c920613a180c4e562ac0dd657b9a6de695d6937d4caed3","cross_cats_sorted":["math-ph","math.CT","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2023-09-11T09:55:38Z","title_canon_sha256":"d6a00705c25431c0c495b18c806156074fa9a262257d89a3a97c6ca4c3796159"},"schema_version":"1.0","source":{"id":"2309.05355","kind":"arxiv","version":1}},"canonical_sha256":"c3b50dba701ab0b600e94b48c1856a02b76a5b2931c0f572dc3301de49ae9bad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3b50dba701ab0b600e94b48c1856a02b76a5b2931c0f572dc3301de49ae9bad","first_computed_at":"2026-07-05T06:49:34.304744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:49:34.304744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vwzeh+asqOOyEuMLbFOjdN7Ift8P8LktCQVPMMxFX8cCGkZet+xGqJgQlZc8WvEF55GsoTp8jvVPMOgF9TovBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:49:34.305219Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.05355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d49c2d08e03b7c5ea7f200a7e1d55ace2bc7febd304c2b82f21a52991772232c","sha256:3d73af676b7f2f00345ec9b7583656743fb2542fb6cc63c48dcf8ca38ac9703e"],"state_sha256":"b63cf7243b37600aa7944c8ed6df666f1f64a9a8353fc958968cbf8327462bf4"}