{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IGM2ZLG7RI5OIYX76IGTWR6WIB","short_pith_number":"pith:IGM2ZLG7","canonical_record":{"source":{"id":"1805.11436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-29T13:28:11Z","cross_cats_sorted":["cs.CG","math.NA"],"title_canon_sha256":"23d2c553e1873819bb78e927e8bb342d23733e9d73e3b02b37572cd237d4d7a7","abstract_canon_sha256":"d0cc6fd1cf0c6e0418b97ca80e950cfc041b2ae1f9b5c8bc09ca78ec17fce4f0"},"schema_version":"1.0"},"canonical_sha256":"4199acacdf8a3ae462fff20d3b47d6407fb97d44ecfd40901b07157bba4691d8","source":{"kind":"arxiv","id":"1805.11436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11436","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11436v1","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11436","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"pith_short_12","alias_value":"IGM2ZLG7RI5O","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IGM2ZLG7RI5OIYX7","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IGM2ZLG7","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IGM2ZLG7RI5OIYX76IGTWR6WIB","target":"record","payload":{"canonical_record":{"source":{"id":"1805.11436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-29T13:28:11Z","cross_cats_sorted":["cs.CG","math.NA"],"title_canon_sha256":"23d2c553e1873819bb78e927e8bb342d23733e9d73e3b02b37572cd237d4d7a7","abstract_canon_sha256":"d0cc6fd1cf0c6e0418b97ca80e950cfc041b2ae1f9b5c8bc09ca78ec17fce4f0"},"schema_version":"1.0"},"canonical_sha256":"4199acacdf8a3ae462fff20d3b47d6407fb97d44ecfd40901b07157bba4691d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:42.569199Z","signature_b64":"fx78clGobRi10knWpzgDZq62oVO3eKvZ6tw5IxKvh1kzPjcbwXHVEEmZFu1k6n9ODybgmhU2FAebpX+c/AORAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4199acacdf8a3ae462fff20d3b47d6407fb97d44ecfd40901b07157bba4691d8","last_reissued_at":"2026-05-18T00:14:42.568674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:42.568674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.11436","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Yg6xib98Tt+bXUorG3M4NtI8384R3l2wxd/h+wdoyAB+rL0ODdLiKOB2O8lKPLPAElpyQMjVTxDct2p2WYKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:55:37.727260Z"},"content_sha256":"b78bc0f20dfd28b095b59397c3cce26e6b7a6610a8928af14b6e4980e560f9da","schema_version":"1.0","event_id":"sha256:b78bc0f20dfd28b095b59397c3cce26e6b7a6610a8928af14b6e4980e560f9da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IGM2ZLG7RI5OIYX76IGTWR6WIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parallel Transport with Pole Ladder: a Third Order Scheme in Affine Connection Spaces which is Exact in Affine Symmetric Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.NA"],"primary_cat":"math.DG","authors_text":"UCA), Xavier Pennec (EPIONE","submitted_at":"2018-05-29T13:28:11Z","abstract_excerpt":"Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are currently used in geometric data processing. In this last class,  pole ladder is a simplification of Schild's ladder for the parallel transport along geodesics that was shown to be particularly simple and numerically  stable in Lie groups. So far, these methods were shown to be first order approximations of the Riemannian parallel transport, but higher order error terms are difficult to establish. In this paper, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11436","kind":"arxiv","version":1},"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":"2026-05-18T00:14:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oqKOE83Q7iTFhCnXj93onM7ZcH9WOEiN7iTGDdLOMbRgxoSpE4uO/HgHSjZpIli1tMDpvDpjbefS0ovvle42Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:55:37.727938Z"},"content_sha256":"eff3c69a274cb1fc7bdaf3aa5384ea8b95c03da9a3d6222adcce2d558e43501e","schema_version":"1.0","event_id":"sha256:eff3c69a274cb1fc7bdaf3aa5384ea8b95c03da9a3d6222adcce2d558e43501e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGM2ZLG7RI5OIYX76IGTWR6WIB/bundle.json","state_url":"https://pith.science/pith/IGM2ZLG7RI5OIYX76IGTWR6WIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGM2ZLG7RI5OIYX76IGTWR6WIB/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":"2026-05-27T14:55:37Z","links":{"resolver":"https://pith.science/pith/IGM2ZLG7RI5OIYX76IGTWR6WIB","bundle":"https://pith.science/pith/IGM2ZLG7RI5OIYX76IGTWR6WIB/bundle.json","state":"https://pith.science/pith/IGM2ZLG7RI5OIYX76IGTWR6WIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGM2ZLG7RI5OIYX76IGTWR6WIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IGM2ZLG7RI5OIYX76IGTWR6WIB","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":"d0cc6fd1cf0c6e0418b97ca80e950cfc041b2ae1f9b5c8bc09ca78ec17fce4f0","cross_cats_sorted":["cs.CG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-29T13:28:11Z","title_canon_sha256":"23d2c553e1873819bb78e927e8bb342d23733e9d73e3b02b37572cd237d4d7a7"},"schema_version":"1.0","source":{"id":"1805.11436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.11436","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"arxiv_version","alias_value":"1805.11436v1","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11436","created_at":"2026-05-18T00:14:42Z"},{"alias_kind":"pith_short_12","alias_value":"IGM2ZLG7RI5O","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IGM2ZLG7RI5OIYX7","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IGM2ZLG7","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:eff3c69a274cb1fc7bdaf3aa5384ea8b95c03da9a3d6222adcce2d558e43501e","target":"graph","created_at":"2026-05-18T00:14:42Z","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":"Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are currently used in geometric data processing. In this last class,  pole ladder is a simplification of Schild's ladder for the parallel transport along geodesics that was shown to be particularly simple and numerically  stable in Lie groups. So far, these methods were shown to be first order approximations of the Riemannian parallel transport, but higher order error terms are difficult to establish. In this paper, we ","authors_text":"UCA), Xavier Pennec (EPIONE","cross_cats":["cs.CG","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-29T13:28:11Z","title":"Parallel Transport with Pole Ladder: a Third Order Scheme in Affine Connection Spaces which is Exact in Affine Symmetric Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11436","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:b78bc0f20dfd28b095b59397c3cce26e6b7a6610a8928af14b6e4980e560f9da","target":"record","created_at":"2026-05-18T00:14:42Z","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":"d0cc6fd1cf0c6e0418b97ca80e950cfc041b2ae1f9b5c8bc09ca78ec17fce4f0","cross_cats_sorted":["cs.CG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-05-29T13:28:11Z","title_canon_sha256":"23d2c553e1873819bb78e927e8bb342d23733e9d73e3b02b37572cd237d4d7a7"},"schema_version":"1.0","source":{"id":"1805.11436","kind":"arxiv","version":1}},"canonical_sha256":"4199acacdf8a3ae462fff20d3b47d6407fb97d44ecfd40901b07157bba4691d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4199acacdf8a3ae462fff20d3b47d6407fb97d44ecfd40901b07157bba4691d8","first_computed_at":"2026-05-18T00:14:42.568674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:42.568674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fx78clGobRi10knWpzgDZq62oVO3eKvZ6tw5IxKvh1kzPjcbwXHVEEmZFu1k6n9ODybgmhU2FAebpX+c/AORAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:42.569199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.11436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b78bc0f20dfd28b095b59397c3cce26e6b7a6610a8928af14b6e4980e560f9da","sha256:eff3c69a274cb1fc7bdaf3aa5384ea8b95c03da9a3d6222adcce2d558e43501e"],"state_sha256":"764428aafb8b967ac39901d084e0e84e99860b9cd4fe498880fe39b632d00a8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZZ/9MnEfbaLJtRsK+HGQZlovq5PzXPX0r3PptsHSUExi3C6T5FizbV6QVxudzs5fxadzVrMAs3jipl7OEv1Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:55:37.731392Z","bundle_sha256":"eeca419e9e63cd84da476b3f7ba372e1d8fd164db34e184d6b3fc8d4c08059d6"}}