{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:4ZKDNOVSKPFPI77B3IHY45GE2Q","short_pith_number":"pith:4ZKDNOVS","canonical_record":{"source":{"id":"1907.05696","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-06-27T14:30:04Z","cross_cats_sorted":[],"title_canon_sha256":"cadbc7ab94446220b51de126eb3cedc8c4188d041fc575e4bfed13f65014b746","abstract_canon_sha256":"035e8ab1bde91594b1a9a54436d6054efe639af0938e2bb645d686041cc8c868"},"schema_version":"1.0"},"canonical_sha256":"e65436bab253caf47fe1da0f8e74c4d41eb2e5ed2813e753417dd8a24c86265c","source":{"kind":"arxiv","id":"1907.05696","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05696","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05696v1","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05696","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"4ZKDNOVSKPFP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4ZKDNOVSKPFPI77B","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4ZKDNOVS","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:4ZKDNOVSKPFPI77B3IHY45GE2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1907.05696","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-06-27T14:30:04Z","cross_cats_sorted":[],"title_canon_sha256":"cadbc7ab94446220b51de126eb3cedc8c4188d041fc575e4bfed13f65014b746","abstract_canon_sha256":"035e8ab1bde91594b1a9a54436d6054efe639af0938e2bb645d686041cc8c868"},"schema_version":"1.0"},"canonical_sha256":"e65436bab253caf47fe1da0f8e74c4d41eb2e5ed2813e753417dd8a24c86265c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:47.246403Z","signature_b64":"mETZ2p+eirYD2XKxMC3LdLsbdHyMpVrz0zQYmwvypCjTdKIXgaaepsja30nm8omMAwwVmSUXL98BmbKN5qYkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e65436bab253caf47fe1da0f8e74c4d41eb2e5ed2813e753417dd8a24c86265c","last_reissued_at":"2026-05-17T23:40:47.245687Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:47.245687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.05696","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":"2026-05-17T23:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFo4MCjC+RiPkURg4BrVx8jvlsB6qAoz/qToeUfgYRpdS0ROvltXLceh99RS5PfoVcOPSjH4EX3m2mPtTKJaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:20:10.105742Z"},"content_sha256":"95aafe9480ebc732ab7182be5e61cbf51cfea6f4a19025868b146305260fa772","schema_version":"1.0","event_id":"sha256:95aafe9480ebc732ab7182be5e61cbf51cfea6f4a19025868b146305260fa772"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:4ZKDNOVSKPFPI77B3IHY45GE2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Visual Curve Completion and Rotational Surfaces of Constant Negative Curvature","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alvaro Pampano","submitted_at":"2019-06-27T14:30:04Z","abstract_excerpt":"If a piece of the contour of a picture is missing to the eye vision, then the brain tends to complete it using some kind of sub-Riemannian geodesics of the unit tangent bundle of the plane, R2xS1. These geodesics can be obtained by lifting extremal curves of a total curvature type energy in the plane. We completely solve this variational problem, geometrically. Moreover, we also show a way of constructing rotational surfaces of constant negative curvature in R3 by evolving these extremal curves under their associated binormal flow with prescribed velocity. Finally, we prove that, locally, all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05696","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":"2026-05-17T23:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zkB9YlaQrqrAgnK3Hou8uGIceY6Lq+tXhGeIz8chUsyTxRIvo6aTSxGt9Am+TU73i5rlEhl0kzbiRXoWxSkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:20:10.106083Z"},"content_sha256":"55f5ec60371127375467f18854b2e3a02b12320ba25416a2cafcad9e71afcbfd","schema_version":"1.0","event_id":"sha256:55f5ec60371127375467f18854b2e3a02b12320ba25416a2cafcad9e71afcbfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ZKDNOVSKPFPI77B3IHY45GE2Q/bundle.json","state_url":"https://pith.science/pith/4ZKDNOVSKPFPI77B3IHY45GE2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ZKDNOVSKPFPI77B3IHY45GE2Q/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":"2026-06-28T12:20:10Z","links":{"resolver":"https://pith.science/pith/4ZKDNOVSKPFPI77B3IHY45GE2Q","bundle":"https://pith.science/pith/4ZKDNOVSKPFPI77B3IHY45GE2Q/bundle.json","state":"https://pith.science/pith/4ZKDNOVSKPFPI77B3IHY45GE2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ZKDNOVSKPFPI77B3IHY45GE2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:4ZKDNOVSKPFPI77B3IHY45GE2Q","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":"035e8ab1bde91594b1a9a54436d6054efe639af0938e2bb645d686041cc8c868","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-06-27T14:30:04Z","title_canon_sha256":"cadbc7ab94446220b51de126eb3cedc8c4188d041fc575e4bfed13f65014b746"},"schema_version":"1.0","source":{"id":"1907.05696","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05696","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05696v1","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05696","created_at":"2026-05-17T23:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"4ZKDNOVSKPFP","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"4ZKDNOVSKPFPI77B","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"4ZKDNOVS","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:55f5ec60371127375467f18854b2e3a02b12320ba25416a2cafcad9e71afcbfd","target":"graph","created_at":"2026-05-17T23:40:47Z","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":"If a piece of the contour of a picture is missing to the eye vision, then the brain tends to complete it using some kind of sub-Riemannian geodesics of the unit tangent bundle of the plane, R2xS1. These geodesics can be obtained by lifting extremal curves of a total curvature type energy in the plane. We completely solve this variational problem, geometrically. Moreover, we also show a way of constructing rotational surfaces of constant negative curvature in R3 by evolving these extremal curves under their associated binormal flow with prescribed velocity. Finally, we prove that, locally, all ","authors_text":"Alvaro Pampano","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-06-27T14:30:04Z","title":"Visual Curve Completion and Rotational Surfaces of Constant Negative Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05696","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":"sha256:95aafe9480ebc732ab7182be5e61cbf51cfea6f4a19025868b146305260fa772","target":"record","created_at":"2026-05-17T23:40:47Z","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":"035e8ab1bde91594b1a9a54436d6054efe639af0938e2bb645d686041cc8c868","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2019-06-27T14:30:04Z","title_canon_sha256":"cadbc7ab94446220b51de126eb3cedc8c4188d041fc575e4bfed13f65014b746"},"schema_version":"1.0","source":{"id":"1907.05696","kind":"arxiv","version":1}},"canonical_sha256":"e65436bab253caf47fe1da0f8e74c4d41eb2e5ed2813e753417dd8a24c86265c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e65436bab253caf47fe1da0f8e74c4d41eb2e5ed2813e753417dd8a24c86265c","first_computed_at":"2026-05-17T23:40:47.245687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:47.245687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mETZ2p+eirYD2XKxMC3LdLsbdHyMpVrz0zQYmwvypCjTdKIXgaaepsja30nm8omMAwwVmSUXL98BmbKN5qYkBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:47.246403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.05696","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95aafe9480ebc732ab7182be5e61cbf51cfea6f4a19025868b146305260fa772","sha256:55f5ec60371127375467f18854b2e3a02b12320ba25416a2cafcad9e71afcbfd"],"state_sha256":"ecf5fd3b16654c6b196261f95d473808b1c10710ef65c823549b2aea3eb2fac0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z1x1kW7x8LBvP6OnSEwxqIo6Jz+vVtBk3GQ9O+6Y2trr7CugRaicAxj7D6+FW70UlN0Kx+/tzuArj/6a8BWTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:20:10.107930Z","bundle_sha256":"bf67850393d35738e0cb111c545b9625680f6416f9618c03b3ef445c9a2e1a99"}}