{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NJLNGDBFE2KOM4JKE3JKOWKQ7R","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":"d48806b8ef1ca18e5eda1ec39dcfc7690c90494f4961f99cb0f04aec66580a29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-14T07:35:09Z","title_canon_sha256":"31ea9b0023e8a428692da6a6d1c3c6ebb5232ea388afbc0c315233771082e525"},"schema_version":"1.0","source":{"id":"1211.3227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3227","created_at":"2026-05-18T03:40:50Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3227v1","created_at":"2026-05-18T03:40:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3227","created_at":"2026-05-18T03:40:50Z"},{"alias_kind":"pith_short_12","alias_value":"NJLNGDBFE2KO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NJLNGDBFE2KOM4JK","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NJLNGDBF","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:e4aebc19de179bce931f5fd7b87abd21da79a74ffb4726cad9303bd474dc7950","target":"graph","created_at":"2026-05-18T03:40:50Z","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":"It is hereby established that, in Euclidean spaces of finite dimension, bounded self-contracted curves have finite length. This extends the main result of Daniilidis, Ley, and Sabourau (J. Math. Pures Appl. 2010) concerning continuous planar self-contracted curves to any dimension, and dispenses entirely with the continuity requirement. The proof borrows heavily from a geometric idea of Manselli and Pucci (Geom. Dedicata 1991) employed for the study of regular enough curves, and can be seen as a nonsmooth adaptation of the latter, albeit a nontrivial one. Applications to continuous and discret","authors_text":"Antoine Lemenant (LJLL), Aris Daniilidis, Estibalitz Durand-Cartagena, Guy David (LM-Orsay)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-14T07:35:09Z","title":"Rectifiability of Self-contracted curves in the Euclidean space and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3227","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":"sha256:5a6e7dceebab4156b8531b7178032a746666a3b39ac71386b47d36d79ffd5a1d","target":"record","created_at":"2026-05-18T03:40:50Z","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":"d48806b8ef1ca18e5eda1ec39dcfc7690c90494f4961f99cb0f04aec66580a29","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-11-14T07:35:09Z","title_canon_sha256":"31ea9b0023e8a428692da6a6d1c3c6ebb5232ea388afbc0c315233771082e525"},"schema_version":"1.0","source":{"id":"1211.3227","kind":"arxiv","version":1}},"canonical_sha256":"6a56d30c252694e6712a26d2a75950fc54ee129351af21f9e9ab0fab848e920a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a56d30c252694e6712a26d2a75950fc54ee129351af21f9e9ab0fab848e920a","first_computed_at":"2026-05-18T03:40:50.531415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:50.531415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qlhJyrtxz4pwQWDldfkwxqyZjsIYLa3dFNG54+JOZwnvfUpGxzM0rXSqDf7isQyrO2de95BW3AtfYan1hkeqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:50.532059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a6e7dceebab4156b8531b7178032a746666a3b39ac71386b47d36d79ffd5a1d","sha256:e4aebc19de179bce931f5fd7b87abd21da79a74ffb4726cad9303bd474dc7950"],"state_sha256":"dc3c0d400a0b47e19755815b4b0e39db83194698d35c57c998d8e115cc823148"}