{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XWDNH5XERO3HJVGQBEUVHAVNPH","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":"ddb4ba3fee9191f3eb5c63091340a334fa213cea6c029d07a492e875a16e5a81","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-26T10:15:51Z","title_canon_sha256":"f0bd366227de90fc2ecbc202b21f9a9b9d536c511aecc327fe07903b83d59db4"},"schema_version":"1.0","source":{"id":"1311.6611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6611","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6611v1","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6611","created_at":"2026-05-18T01:11:37Z"},{"alias_kind":"pith_short_12","alias_value":"XWDNH5XERO3H","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XWDNH5XERO3HJVGQ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XWDNH5XE","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:00230ffade92b7e5203e363adfae00a8eed907d46e1976c780560e3dee57fd45","target":"graph","created_at":"2026-05-18T01:11:37Z","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":"Given a principal $G$-bundle $P \\to M$ and two $C^1$ curves in $M$ with coinciding endpoints, we say that the two curves are holonomically equivalent if the parallel transport along them is identical for any smooth connection on $P$. The main result in this paper is that if $G$ is semi-simple, then the two curves are holonomically equivalent if and only if there is a thin, i.e. of rank at most one, $C^1$ homotopy linking them. Additionally, it is also demonstrated that this is equivalent to the factorizability through a tree of the loop formed from the two curves and to the reducibility of a c","authors_text":"Tamer Tlas","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-26T10:15:51Z","title":"On the Holonomic Equivalence of Two Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6611","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":"sha256:97a515d53c2b0d4e957a0910d316547af06c0a1a9c1780b48172f0843d3a59d0","target":"record","created_at":"2026-05-18T01:11:37Z","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":"ddb4ba3fee9191f3eb5c63091340a334fa213cea6c029d07a492e875a16e5a81","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-26T10:15:51Z","title_canon_sha256":"f0bd366227de90fc2ecbc202b21f9a9b9d536c511aecc327fe07903b83d59db4"},"schema_version":"1.0","source":{"id":"1311.6611","kind":"arxiv","version":1}},"canonical_sha256":"bd86d3f6e48bb674d4d009295382ad79e8da90317f2b00aac5bcf4073a358c16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd86d3f6e48bb674d4d009295382ad79e8da90317f2b00aac5bcf4073a358c16","first_computed_at":"2026-05-18T01:11:37.548474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:37.548474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ywm2XJKn2td1NCasMFqkknFsGqIM19W7b4BpY52PslxhWvfbyl8lXhil5MH+QlX4XuMqMW0FOuDlzS4Gph+cCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:37.548996Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97a515d53c2b0d4e957a0910d316547af06c0a1a9c1780b48172f0843d3a59d0","sha256:00230ffade92b7e5203e363adfae00a8eed907d46e1976c780560e3dee57fd45"],"state_sha256":"af6ecf3f630b7a2661b516348718d565d2180a559b255e939ea7ca506186e91c"}