{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GXU2AQLPLINYRDAAODQTSFQUCP","short_pith_number":"pith:GXU2AQLP","schema_version":"1.0","canonical_sha256":"35e9a0416f5a1b888c0070e139161413d9929670b8812733d37ac798486923f7","source":{"kind":"arxiv","id":"1201.1546","version":3},"attestation_state":"computed","paper":{"title":"Anisotropic Fast-Marching on cartesian grids using Lattice Basis Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jean-Marie Mirebeau","submitted_at":"2012-01-07T11:37:15Z","abstract_excerpt":"We introduce a modification of the Fast Marching Algorithm, which solves the generalized eikonal equation associated to an arbitrary continuous riemannian metric, on a two or three dimensional domain. The algorithm has a logarithmic complexity in the maximum anisotropy ratio of the riemannian metric, which allows to handle extreme anisotropies for a reduced numerical cost. We prove the consistence of the algorithm, and illustrate its efficiency by numerical experiments. The algorithm relies on the computation at each grid point of a special system of coordinates: a reduced basis of the cartesi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1201.1546","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-07T11:37:15Z","cross_cats_sorted":[],"title_canon_sha256":"332b851a521b904391c7590b22b5904c7d132709a4a17c034e46623414d4b591","abstract_canon_sha256":"14bd72e75f59a2df5c4d543391f78bb8f65a8dba6c1964844f3e824b68ae86b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:52.342807Z","signature_b64":"pNlCwV1IyjlD6J4+TRsuCWX4XvVoxbYc8P6s60eSws6X2MBGs8bZ8CRjpZUs22sIe8HnIE3GsEKyo9e8z9XgDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e9a0416f5a1b888c0070e139161413d9929670b8812733d37ac798486923f7","last_reissued_at":"2026-05-18T02:37:52.342184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:52.342184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anisotropic Fast-Marching on cartesian grids using Lattice Basis Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jean-Marie Mirebeau","submitted_at":"2012-01-07T11:37:15Z","abstract_excerpt":"We introduce a modification of the Fast Marching Algorithm, which solves the generalized eikonal equation associated to an arbitrary continuous riemannian metric, on a two or three dimensional domain. The algorithm has a logarithmic complexity in the maximum anisotropy ratio of the riemannian metric, which allows to handle extreme anisotropies for a reduced numerical cost. We prove the consistence of the algorithm, and illustrate its efficiency by numerical experiments. The algorithm relies on the computation at each grid point of a special system of coordinates: a reduced basis of the cartesi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1546","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1201.1546","created_at":"2026-05-18T02:37:52.342313+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.1546v3","created_at":"2026-05-18T02:37:52.342313+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1546","created_at":"2026-05-18T02:37:52.342313+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXU2AQLPLINY","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXU2AQLPLINYRDAA","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXU2AQLP","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP","json":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP.json","graph_json":"https://pith.science/api/pith-number/GXU2AQLPLINYRDAAODQTSFQUCP/graph.json","events_json":"https://pith.science/api/pith-number/GXU2AQLPLINYRDAAODQTSFQUCP/events.json","paper":"https://pith.science/paper/GXU2AQLP"},"agent_actions":{"view_html":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP","download_json":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP.json","view_paper":"https://pith.science/paper/GXU2AQLP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.1546&json=true","fetch_graph":"https://pith.science/api/pith-number/GXU2AQLPLINYRDAAODQTSFQUCP/graph.json","fetch_events":"https://pith.science/api/pith-number/GXU2AQLPLINYRDAAODQTSFQUCP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP/action/storage_attestation","attest_author":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP/action/author_attestation","sign_citation":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP/action/citation_signature","submit_replication":"https://pith.science/pith/GXU2AQLPLINYRDAAODQTSFQUCP/action/replication_record"}},"created_at":"2026-05-18T02:37:52.342313+00:00","updated_at":"2026-05-18T02:37:52.342313+00:00"}