{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2EYWILLAYXAIFTVETLDJXE5KCU","short_pith_number":"pith:2EYWILLA","canonical_record":{"source":{"id":"2507.08220","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-10T23:54:27Z","cross_cats_sorted":[],"title_canon_sha256":"dbad9eff0595fcc443ba2b4e507303def46306491127f3ec3deca2ce05c04b11","abstract_canon_sha256":"0e112a5d0d3b312faff7f937c5f4e593b912a18634eb4b17167221bb7f175f08"},"schema_version":"1.0"},"canonical_sha256":"d131642d60c5c082cea49ac69b93aa1532813577826b60d18410d5d403e660c8","source":{"kind":"arxiv","id":"2507.08220","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.08220","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"arxiv_version","alias_value":"2507.08220v2","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.08220","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"pith_short_12","alias_value":"2EYWILLAYXAI","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"pith_short_16","alias_value":"2EYWILLAYXAIFTVE","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"pith_short_8","alias_value":"2EYWILLA","created_at":"2026-07-05T11:38:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2EYWILLAYXAIFTVETLDJXE5KCU","target":"record","payload":{"canonical_record":{"source":{"id":"2507.08220","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-10T23:54:27Z","cross_cats_sorted":[],"title_canon_sha256":"dbad9eff0595fcc443ba2b4e507303def46306491127f3ec3deca2ce05c04b11","abstract_canon_sha256":"0e112a5d0d3b312faff7f937c5f4e593b912a18634eb4b17167221bb7f175f08"},"schema_version":"1.0"},"canonical_sha256":"d131642d60c5c082cea49ac69b93aa1532813577826b60d18410d5d403e660c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:31.432027Z","signature_b64":"TcYiOWsJf+u68eqrrixzYWLyoDuhZS7AAK8CTTVMkKzR7hYnC6mWS29QBOw4RG9Me1sKqBcTfHhLaIrO+GbaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d131642d60c5c082cea49ac69b93aa1532813577826b60d18410d5d403e660c8","last_reissued_at":"2026-07-05T11:38:31.431477Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:31.431477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.08220","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":"2026-07-05T11:38:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YsbFQna6F+dbna2wOwpjs5/3YCBXbqMi4aXRGY/2hW7gsj0lyYa+pbWdyYM5o9sNciVepyx+US3qkPAbg12zBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:17:11.015156Z"},"content_sha256":"5e7087d7d448eaa47e78c89a6397de66c3d41fe2509f8f12f4ff62d8e4552860","schema_version":"1.0","event_id":"sha256:5e7087d7d448eaa47e78c89a6397de66c3d41fe2509f8f12f4ff62d8e4552860"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2EYWILLAYXAIFTVETLDJXE5KCU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamentals of Lie categories and Yang-Mills theory for multiplicative Ehresmann connections","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"\\v{Z}an Grad","submitted_at":"2025-07-10T23:54:27Z","abstract_excerpt":"The first and shorter part of this thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible differentiable structure. We introduce various examples of Lie categories, examine their differences and similarities with Lie groupoids, and research the notions emerging naturally from the lack of invertibility of arrows. The aim of the second and principal part of this thesis is to provide a far-reaching generalization of Yang-Mills theory, extending it from the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08220","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.08220/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:38:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/9bNAbe6BkYjcb+xdiJStgRwPBPxnIRvLb0EuW6/e1623Q0AVOo8DxVRp8C6a+TpT1Cl7sG7GlWFLotIqVSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:17:11.015698Z"},"content_sha256":"ed4111fc48ae2870e79cf8beea85df7c5c127a2815bb269b8289b93a9212966f","schema_version":"1.0","event_id":"sha256:ed4111fc48ae2870e79cf8beea85df7c5c127a2815bb269b8289b93a9212966f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2EYWILLAYXAIFTVETLDJXE5KCU/bundle.json","state_url":"https://pith.science/pith/2EYWILLAYXAIFTVETLDJXE5KCU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2EYWILLAYXAIFTVETLDJXE5KCU/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":"2026-08-10T22:17:11Z","links":{"resolver":"https://pith.science/pith/2EYWILLAYXAIFTVETLDJXE5KCU","bundle":"https://pith.science/pith/2EYWILLAYXAIFTVETLDJXE5KCU/bundle.json","state":"https://pith.science/pith/2EYWILLAYXAIFTVETLDJXE5KCU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2EYWILLAYXAIFTVETLDJXE5KCU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2EYWILLAYXAIFTVETLDJXE5KCU","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":"0e112a5d0d3b312faff7f937c5f4e593b912a18634eb4b17167221bb7f175f08","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-10T23:54:27Z","title_canon_sha256":"dbad9eff0595fcc443ba2b4e507303def46306491127f3ec3deca2ce05c04b11"},"schema_version":"1.0","source":{"id":"2507.08220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.08220","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"arxiv_version","alias_value":"2507.08220v2","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.08220","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"pith_short_12","alias_value":"2EYWILLAYXAI","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"pith_short_16","alias_value":"2EYWILLAYXAIFTVE","created_at":"2026-07-05T11:38:31Z"},{"alias_kind":"pith_short_8","alias_value":"2EYWILLA","created_at":"2026-07-05T11:38:31Z"}],"graph_snapshots":[{"event_id":"sha256:ed4111fc48ae2870e79cf8beea85df7c5c127a2815bb269b8289b93a9212966f","target":"graph","created_at":"2026-07-05T11:38:31Z","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/2507.08220/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The first and shorter part of this thesis deals with the structural assumption of invertibility in a Lie groupoid. When this assumption is dropped, we obtain the notion of a Lie category: a small category, endowed with a compatible differentiable structure. We introduce various examples of Lie categories, examine their differences and similarities with Lie groupoids, and research the notions emerging naturally from the lack of invertibility of arrows. The aim of the second and principal part of this thesis is to provide a far-reaching generalization of Yang-Mills theory, extending it from the ","authors_text":"\\v{Z}an Grad","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-10T23:54:27Z","title":"Fundamentals of Lie categories and Yang-Mills theory for multiplicative Ehresmann connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.08220","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":"sha256:5e7087d7d448eaa47e78c89a6397de66c3d41fe2509f8f12f4ff62d8e4552860","target":"record","created_at":"2026-07-05T11:38:31Z","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":"0e112a5d0d3b312faff7f937c5f4e593b912a18634eb4b17167221bb7f175f08","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-07-10T23:54:27Z","title_canon_sha256":"dbad9eff0595fcc443ba2b4e507303def46306491127f3ec3deca2ce05c04b11"},"schema_version":"1.0","source":{"id":"2507.08220","kind":"arxiv","version":2}},"canonical_sha256":"d131642d60c5c082cea49ac69b93aa1532813577826b60d18410d5d403e660c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d131642d60c5c082cea49ac69b93aa1532813577826b60d18410d5d403e660c8","first_computed_at":"2026-07-05T11:38:31.431477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:31.431477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TcYiOWsJf+u68eqrrixzYWLyoDuhZS7AAK8CTTVMkKzR7hYnC6mWS29QBOw4RG9Me1sKqBcTfHhLaIrO+GbaCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:31.432027Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.08220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e7087d7d448eaa47e78c89a6397de66c3d41fe2509f8f12f4ff62d8e4552860","sha256:ed4111fc48ae2870e79cf8beea85df7c5c127a2815bb269b8289b93a9212966f"],"state_sha256":"b2a90b14a9406cee46fb9ee02d1b597ac659d80022acc79a1e1c10446049d059"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOvLhvs6AyYTfePkSeOUOeWOqujCZwnQ7T8jflBY3ZNVJjaSjYJj040qMX/x2T2OUYvrQqOmiLCz+NVN/oOqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T22:17:11.024574Z","bundle_sha256":"417d676696378a294b8cfe757d17b86190cde0c4dd5abaee8fabd6e1b61d3230"}}