{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3MVKEPPTJOVNV2QXOXXTQWQL2A","short_pith_number":"pith:3MVKEPPT","canonical_record":{"source":{"id":"1411.3933","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2014-11-14T15:16:53Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"01886209fa13daeb477c7ea3275bb16e8a695b3863bafe6aa36e988dc3c1acdf","abstract_canon_sha256":"bb7a7c4cf1cc92cc73eefa826d2d465a60e536ae0b2aa2bf9f12a445adc7303f"},"schema_version":"1.0"},"canonical_sha256":"db2aa23df34baadaea1775ef385a0bd012f87cfd258f39fca542ad6a44739418","source":{"kind":"arxiv","id":"1411.3933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3933","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3933v1","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3933","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"pith_short_12","alias_value":"3MVKEPPTJOVN","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3MVKEPPTJOVNV2QX","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3MVKEPPT","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3MVKEPPTJOVNV2QXOXXTQWQL2A","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3933","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2014-11-14T15:16:53Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"01886209fa13daeb477c7ea3275bb16e8a695b3863bafe6aa36e988dc3c1acdf","abstract_canon_sha256":"bb7a7c4cf1cc92cc73eefa826d2d465a60e536ae0b2aa2bf9f12a445adc7303f"},"schema_version":"1.0"},"canonical_sha256":"db2aa23df34baadaea1775ef385a0bd012f87cfd258f39fca542ad6a44739418","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:37.333100Z","signature_b64":"aYUA6r+v9mLaKXG1tGlkl/NpLDEbAAI/RwweAWnukxk7xGlomgBzZMvpy7Pxy6o60bk2f+/Pr/5nErPhsCcjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db2aa23df34baadaea1775ef385a0bd012f87cfd258f39fca542ad6a44739418","last_reissued_at":"2026-05-18T02:37:37.332695Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:37.332695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3933","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":"2026-05-18T02:37:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t60VjPnVniu9gUgGoIGa0O9+sfHQjQRPgpOQkYzXlB4KZXdGM+X0r/3s/6Mk+Bo7j6Xo0Yy7lmP9bl+BRk5zDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:30:41.397326Z"},"content_sha256":"9d10e6c87ed5e94132c803357759b6207f763a41d52837ac825f27a40949721f","schema_version":"1.0","event_id":"sha256:9d10e6c87ed5e94132c803357759b6207f763a41d52837ac825f27a40949721f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3MVKEPPTJOVNV2QXOXXTQWQL2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cut and conjugate points of the exponential map, with applications","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Pablo Angulo Ardoy","submitted_at":"2014-11-14T15:16:53Z","abstract_excerpt":"The goal of this thesis is to study the singularities of the exponential map of Riemannian and Finsler manifolds (a concept related to caustics and catastrophes), and the object known as the cut locus (aka ridge, medial axis or skeleton), to improve existing results about its structure, to look at it in new ways, and to derive applications to the Ambrose conjecture and the Hamilton-Jacobi equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3933","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":"2026-05-18T02:37:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yaHXB+N3UC/w3Nldw9mtxaR382jdC0AeiZlukDfSSoT/A5rvgCUHzTkZyMXUfloevvPTUTCJaj2K91qf/lqPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T03:30:41.397686Z"},"content_sha256":"f71127995786214e7ac1256562c0a9417e9540afa199994d21bbac98abb6ddda","schema_version":"1.0","event_id":"sha256:f71127995786214e7ac1256562c0a9417e9540afa199994d21bbac98abb6ddda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3MVKEPPTJOVNV2QXOXXTQWQL2A/bundle.json","state_url":"https://pith.science/pith/3MVKEPPTJOVNV2QXOXXTQWQL2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3MVKEPPTJOVNV2QXOXXTQWQL2A/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":"2026-06-22T03:30:41Z","links":{"resolver":"https://pith.science/pith/3MVKEPPTJOVNV2QXOXXTQWQL2A","bundle":"https://pith.science/pith/3MVKEPPTJOVNV2QXOXXTQWQL2A/bundle.json","state":"https://pith.science/pith/3MVKEPPTJOVNV2QXOXXTQWQL2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3MVKEPPTJOVNV2QXOXXTQWQL2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3MVKEPPTJOVNV2QXOXXTQWQL2A","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":"bb7a7c4cf1cc92cc73eefa826d2d465a60e536ae0b2aa2bf9f12a445adc7303f","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2014-11-14T15:16:53Z","title_canon_sha256":"01886209fa13daeb477c7ea3275bb16e8a695b3863bafe6aa36e988dc3c1acdf"},"schema_version":"1.0","source":{"id":"1411.3933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3933","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3933v1","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3933","created_at":"2026-05-18T02:37:37Z"},{"alias_kind":"pith_short_12","alias_value":"3MVKEPPTJOVN","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3MVKEPPTJOVNV2QX","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3MVKEPPT","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:f71127995786214e7ac1256562c0a9417e9540afa199994d21bbac98abb6ddda","target":"graph","created_at":"2026-05-18T02:37:37Z","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":"The goal of this thesis is to study the singularities of the exponential map of Riemannian and Finsler manifolds (a concept related to caustics and catastrophes), and the object known as the cut locus (aka ridge, medial axis or skeleton), to improve existing results about its structure, to look at it in new ways, and to derive applications to the Ambrose conjecture and the Hamilton-Jacobi equations.","authors_text":"Pablo Angulo Ardoy","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2014-11-14T15:16:53Z","title":"Cut and conjugate points of the exponential map, with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3933","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":"sha256:9d10e6c87ed5e94132c803357759b6207f763a41d52837ac825f27a40949721f","target":"record","created_at":"2026-05-18T02:37:37Z","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":"bb7a7c4cf1cc92cc73eefa826d2d465a60e536ae0b2aa2bf9f12a445adc7303f","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AP","submitted_at":"2014-11-14T15:16:53Z","title_canon_sha256":"01886209fa13daeb477c7ea3275bb16e8a695b3863bafe6aa36e988dc3c1acdf"},"schema_version":"1.0","source":{"id":"1411.3933","kind":"arxiv","version":1}},"canonical_sha256":"db2aa23df34baadaea1775ef385a0bd012f87cfd258f39fca542ad6a44739418","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db2aa23df34baadaea1775ef385a0bd012f87cfd258f39fca542ad6a44739418","first_computed_at":"2026-05-18T02:37:37.332695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:37.332695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aYUA6r+v9mLaKXG1tGlkl/NpLDEbAAI/RwweAWnukxk7xGlomgBzZMvpy7Pxy6o60bk2f+/Pr/5nErPhsCcjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:37.333100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d10e6c87ed5e94132c803357759b6207f763a41d52837ac825f27a40949721f","sha256:f71127995786214e7ac1256562c0a9417e9540afa199994d21bbac98abb6ddda"],"state_sha256":"2d81fe4d3a200af854aa77d94270fe37f896e83c578179655e1bad9a1eb5811d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7sQa7VCw9oBOeO6GHSmhSecIsMtftT7z203oBq99JtYXANRycpR/huwEM6TpVumYvN3XK+3/f7bRcTLCR0gCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T03:30:41.399665Z","bundle_sha256":"cba017d502a75497f80395cbbe84a6b903c6036159c085e8305f3a536baca79f"}}