{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:XVLQJQGI3DTQVRJQWKEJK3VWYK","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":"2e146427aed42d795fee0fae9919f105309bd22e3b9eae15157b63dc25ef03ae","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2004-03-02T14:28:11Z","title_canon_sha256":"0094fb116bb67e0489b152c26d95592647ae6a3913255a9ce312ada96fb6f47f"},"schema_version":"1.0","source":{"id":"math/0403040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0403040","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0403040v2","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0403040","created_at":"2026-05-18T01:05:26Z"},{"alias_kind":"pith_short_12","alias_value":"XVLQJQGI3DTQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XVLQJQGI3DTQVRJQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XVLQJQGI","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:e76e56e29acdb36c30dcceaf03638b1ff94c3212e55657ee6d5d6b67abcc3648","target":"graph","created_at":"2026-05-18T01:05:26Z","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":"The concept of generalised (in the sense of Colombeau) connection on a principal fibre bundle is introduced. This definition is then used to extend results concerning the geometry of principal fibre bundles to those that only have a generalised connection. Some applications to singular solutions of Yang-Mills theory are given.","authors_text":"James A. Vickers, Michael Kunzinger, Roland Steinbauer","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2004-03-02T14:28:11Z","title":"Generalised Connections and Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0403040","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":"sha256:5391789753f5d4af58400387ff745dbc7d21417768c05fb210a05efa3b9faf51","target":"record","created_at":"2026-05-18T01:05:26Z","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":"2e146427aed42d795fee0fae9919f105309bd22e3b9eae15157b63dc25ef03ae","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2004-03-02T14:28:11Z","title_canon_sha256":"0094fb116bb67e0489b152c26d95592647ae6a3913255a9ce312ada96fb6f47f"},"schema_version":"1.0","source":{"id":"math/0403040","kind":"arxiv","version":2}},"canonical_sha256":"bd5704c0c8d8e70ac530b288956eb6c2bc630c5fb6028d99266824fe8061c4f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd5704c0c8d8e70ac530b288956eb6c2bc630c5fb6028d99266824fe8061c4f8","first_computed_at":"2026-05-18T01:05:26.546716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:26.546716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yxaheaWQU4pYBzi24F50B+HOLzl6sJxbz3gqQjBALTVrWXhYXrsesNNjaBt4SYDvz3BUljUgTdGgcjDIAjNXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:26.547335Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0403040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5391789753f5d4af58400387ff745dbc7d21417768c05fb210a05efa3b9faf51","sha256:e76e56e29acdb36c30dcceaf03638b1ff94c3212e55657ee6d5d6b67abcc3648"],"state_sha256":"8c90ef622b5c66e1217a6f54f7e29590f96e2b20e205bf18bc3f5c9fab75c152"}