{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YJYG7DF7FZ5MNX7PFH3BWJKAF4","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":"875a0c2d7e63fed9461389a8a878a8254c26560b55aabb6507d95ac3ccd46cef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-03-31T13:05:49Z","title_canon_sha256":"370d239622e310fd9fda10d40db39bd8ebd50984c91e9db73daafad452505bb1"},"schema_version":"1.0","source":{"id":"1604.02673","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02673","created_at":"2026-05-18T01:17:22Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02673v1","created_at":"2026-05-18T01:17:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02673","created_at":"2026-05-18T01:17:22Z"},{"alias_kind":"pith_short_12","alias_value":"YJYG7DF7FZ5M","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YJYG7DF7FZ5MNX7P","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YJYG7DF7","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:ea07bb47f021da660c2c4b30d06d6e68decff125b6440ea19c3e9df868f1095d","target":"graph","created_at":"2026-05-18T01:17:22Z","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":"We prove that any self-contracted curve in R 2 endowed with a C 2 and strictly convex norm, has finite length. The proof follows from the study of the curve bisector of two points in R 2 for a general norm together with an adaptation of the argument used in [2].","authors_text":"Antoine Lemenant (LJLL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-03-31T13:05:49Z","title":"Rectifiability of non Euclidean planar self-contracted curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02673","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":"sha256:235633897d6cc508e0ead1e5285bda3c84428ba64b64fcac1a747a17803ece36","target":"record","created_at":"2026-05-18T01:17:22Z","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":"875a0c2d7e63fed9461389a8a878a8254c26560b55aabb6507d95ac3ccd46cef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-03-31T13:05:49Z","title_canon_sha256":"370d239622e310fd9fda10d40db39bd8ebd50984c91e9db73daafad452505bb1"},"schema_version":"1.0","source":{"id":"1604.02673","kind":"arxiv","version":1}},"canonical_sha256":"c2706f8cbf2e7ac6dfef29f61b25402f25a043bf5262d82d753ce36ef8e01cdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2706f8cbf2e7ac6dfef29f61b25402f25a043bf5262d82d753ce36ef8e01cdc","first_computed_at":"2026-05-18T01:17:22.459336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:22.459336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SzQmLrsovzw3/kOc219MyQZ6XjeRWOJk1d5iW+E8FJH52dspL1DbziOlGOvjUZV/8oo6FvwHrWM829PfvY40CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:22.459748Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02673","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:235633897d6cc508e0ead1e5285bda3c84428ba64b64fcac1a747a17803ece36","sha256:ea07bb47f021da660c2c4b30d06d6e68decff125b6440ea19c3e9df868f1095d"],"state_sha256":"ae87026c6d082f3f2624c95aa93be82c43ac876c39ee21d904f3296d0bd0ab47"}