{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:R67PBMKAXT6E3JD63ABQ32MKEF","short_pith_number":"pith:R67PBMKA","canonical_record":{"source":{"id":"1602.02961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-09T12:43:42Z","cross_cats_sorted":[],"title_canon_sha256":"7bdc2936386e02cb906190d07adca26ebecaf4d8d397d37fbfb038e27acf1a19","abstract_canon_sha256":"b1bcdba44ca8b5fe775cd565ff56cb2d1b7faa570f3b0943e65ace8c51bf96df"},"schema_version":"1.0"},"canonical_sha256":"8fbef0b140bcfc4da47ed8030de98a214e22b43fdb71de0df2b41823d7f813ce","source":{"kind":"arxiv","id":"1602.02961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02961","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02961v1","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02961","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"R67PBMKAXT6E","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R67PBMKAXT6E3JD6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R67PBMKA","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:R67PBMKAXT6E3JD63ABQ32MKEF","target":"record","payload":{"canonical_record":{"source":{"id":"1602.02961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-09T12:43:42Z","cross_cats_sorted":[],"title_canon_sha256":"7bdc2936386e02cb906190d07adca26ebecaf4d8d397d37fbfb038e27acf1a19","abstract_canon_sha256":"b1bcdba44ca8b5fe775cd565ff56cb2d1b7faa570f3b0943e65ace8c51bf96df"},"schema_version":"1.0"},"canonical_sha256":"8fbef0b140bcfc4da47ed8030de98a214e22b43fdb71de0df2b41823d7f813ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:33.138616Z","signature_b64":"XqGkDUllIauxIXHgzzn48858EJKMl4i4iJ7VAvrys4fsRZhFpjweulQZthLymYQKu6eNdpOWOIgYCiFCCYqHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fbef0b140bcfc4da47ed8030de98a214e22b43fdb71de0df2b41823d7f813ce","last_reissued_at":"2026-05-18T00:42:33.137936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:33.137936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.02961","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":"2026-05-18T00:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnBYjVy/Wq3iAdq04UQUzW5qLjqKWL3Xy37a7Pm/81RYzQODiR7U43Gz8fNa2m2/TSxjcyrHItssXW3M8tGEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:03.932650Z"},"content_sha256":"d31e301a03c85d626ced80a17e2ebd9b13548d09e05f8bf5b3ed66d0d31b24d1","schema_version":"1.0","event_id":"sha256:d31e301a03c85d626ced80a17e2ebd9b13548d09e05f8bf5b3ed66d0d31b24d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:R67PBMKAXT6E3JD63ABQ32MKEF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kinetic formulation of vortex vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pierre Bochard, Radu Ignat","submitted_at":"2016-02-09T12:43:42Z","abstract_excerpt":"This article focuses on gradient vector fields of unit Euclidean norm in $\\mathbb{R}^N$ . The stream functions associated to such vector fields solve the eikonal equation and the prototype is given by the distance function to a closed set. We introduce a kinetic formulation that characterizes stream functions whose level sets are either spheres or hyperplanes in dimension $N \\geq 3$. Our main result proves that the kinetic formulation is a selection principle for the vortex vector field whose stream function is the distance function to a point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02961","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":"2026-05-18T00:42:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b9s2DRfZLsx6jNfNujKuYnby3k2/BdyU14BbcpU/edbLMITsd+QWUXHRoZJ/9erGehEqsCE4YxbkMaMIrOFgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:25:03.932985Z"},"content_sha256":"c27ff92bb87e4d7c78cf43e81b64c93894c9daefe47f930102482089a7412a42","schema_version":"1.0","event_id":"sha256:c27ff92bb87e4d7c78cf43e81b64c93894c9daefe47f930102482089a7412a42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R67PBMKAXT6E3JD63ABQ32MKEF/bundle.json","state_url":"https://pith.science/pith/R67PBMKAXT6E3JD63ABQ32MKEF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R67PBMKAXT6E3JD63ABQ32MKEF/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":"2026-06-24T22:25:03Z","links":{"resolver":"https://pith.science/pith/R67PBMKAXT6E3JD63ABQ32MKEF","bundle":"https://pith.science/pith/R67PBMKAXT6E3JD63ABQ32MKEF/bundle.json","state":"https://pith.science/pith/R67PBMKAXT6E3JD63ABQ32MKEF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R67PBMKAXT6E3JD63ABQ32MKEF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R67PBMKAXT6E3JD63ABQ32MKEF","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":"b1bcdba44ca8b5fe775cd565ff56cb2d1b7faa570f3b0943e65ace8c51bf96df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-09T12:43:42Z","title_canon_sha256":"7bdc2936386e02cb906190d07adca26ebecaf4d8d397d37fbfb038e27acf1a19"},"schema_version":"1.0","source":{"id":"1602.02961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02961","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02961v1","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02961","created_at":"2026-05-18T00:42:33Z"},{"alias_kind":"pith_short_12","alias_value":"R67PBMKAXT6E","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R67PBMKAXT6E3JD6","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R67PBMKA","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:c27ff92bb87e4d7c78cf43e81b64c93894c9daefe47f930102482089a7412a42","target":"graph","created_at":"2026-05-18T00:42:33Z","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":"This article focuses on gradient vector fields of unit Euclidean norm in $\\mathbb{R}^N$ . The stream functions associated to such vector fields solve the eikonal equation and the prototype is given by the distance function to a closed set. We introduce a kinetic formulation that characterizes stream functions whose level sets are either spheres or hyperplanes in dimension $N \\geq 3$. Our main result proves that the kinetic formulation is a selection principle for the vortex vector field whose stream function is the distance function to a point.","authors_text":"Pierre Bochard, Radu Ignat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-09T12:43:42Z","title":"Kinetic formulation of vortex vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02961","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:d31e301a03c85d626ced80a17e2ebd9b13548d09e05f8bf5b3ed66d0d31b24d1","target":"record","created_at":"2026-05-18T00:42:33Z","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":"b1bcdba44ca8b5fe775cd565ff56cb2d1b7faa570f3b0943e65ace8c51bf96df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-09T12:43:42Z","title_canon_sha256":"7bdc2936386e02cb906190d07adca26ebecaf4d8d397d37fbfb038e27acf1a19"},"schema_version":"1.0","source":{"id":"1602.02961","kind":"arxiv","version":1}},"canonical_sha256":"8fbef0b140bcfc4da47ed8030de98a214e22b43fdb71de0df2b41823d7f813ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fbef0b140bcfc4da47ed8030de98a214e22b43fdb71de0df2b41823d7f813ce","first_computed_at":"2026-05-18T00:42:33.137936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:33.137936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XqGkDUllIauxIXHgzzn48858EJKMl4i4iJ7VAvrys4fsRZhFpjweulQZthLymYQKu6eNdpOWOIgYCiFCCYqHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:33.138616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d31e301a03c85d626ced80a17e2ebd9b13548d09e05f8bf5b3ed66d0d31b24d1","sha256:c27ff92bb87e4d7c78cf43e81b64c93894c9daefe47f930102482089a7412a42"],"state_sha256":"80c2a78116d18807243badd73e178be485e35c5a4d649bb3bb456a289fe09957"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3+Wrn4Rf3N/fENwKk7xJAWx3yaL+k4us4OWY16n5nWc+U+5ajDgI3sdMV1iqdFqkF9pEPeqLGINO56dhfRBiCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:25:03.934871Z","bundle_sha256":"2879312a9717c7d48599fe4c12e903a488533fb859c1ecf14d69595ae7a3d115"}}