{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:X43M5ECH7QOGCGWIEM6AIK37HX","short_pith_number":"pith:X43M5ECH","schema_version":"1.0","canonical_sha256":"bf36ce9047fc1c611ac8233c042b7f3ddd5bbfa080acf2bceff902164bf63c53","source":{"kind":"arxiv","id":"1104.1647","version":3},"attestation_state":"computed","paper":{"title":"The Binet-Legendre Metric in Finsler Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Marc Troyanov, Vladimir S. Matveev","submitted_at":"2011-04-07T16:44:07Z","abstract_excerpt":"For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \\mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions. The Riemannian metric $g_F$ also behaves nicely under conformal or bilipshitz deformation of the Finsler metric $F$. These properties makes it a powerful tool in Finsler geometry and we illustrate that by solving a number of named Finslerian geometric problems. We also generalize and give new and shorter proofs of a number of known results. In particular we answer a q"},"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":"1104.1647","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-07T16:44:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"3c336bc38b925598b6224e8abf86219cda739cc62d7c563a1e4f964f95829dba","abstract_canon_sha256":"2b1fa389879b47a08cf4712a1a4171c2a77aa103e85bd1615c1cbc26fad13381"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:18.186060Z","signature_b64":"rRVoaRkWcQylhMPFDtHWfU+x1fz/+heeDUZij8SKTaHHBRc+FotD2MbsSa8+DHyAz8VovmhZyH8CCJ3E4kcfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf36ce9047fc1c611ac8233c042b7f3ddd5bbfa080acf2bceff902164bf63c53","last_reissued_at":"2026-05-18T02:38:18.185290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:18.185290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Binet-Legendre Metric in Finsler Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Marc Troyanov, Vladimir S. Matveev","submitted_at":"2011-04-07T16:44:07Z","abstract_excerpt":"For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \\mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions. The Riemannian metric $g_F$ also behaves nicely under conformal or bilipshitz deformation of the Finsler metric $F$. These properties makes it a powerful tool in Finsler geometry and we illustrate that by solving a number of named Finslerian geometric problems. We also generalize and give new and shorter proofs of a number of known results. In particular we answer a q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1647","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":"1104.1647","created_at":"2026-05-18T02:38:18.185429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.1647v3","created_at":"2026-05-18T02:38:18.185429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1647","created_at":"2026-05-18T02:38:18.185429+00:00"},{"alias_kind":"pith_short_12","alias_value":"X43M5ECH7QOG","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"X43M5ECH7QOGCGWI","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"X43M5ECH","created_at":"2026-05-18T12:26:44.992195+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/X43M5ECH7QOGCGWIEM6AIK37HX","json":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX.json","graph_json":"https://pith.science/api/pith-number/X43M5ECH7QOGCGWIEM6AIK37HX/graph.json","events_json":"https://pith.science/api/pith-number/X43M5ECH7QOGCGWIEM6AIK37HX/events.json","paper":"https://pith.science/paper/X43M5ECH"},"agent_actions":{"view_html":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX","download_json":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX.json","view_paper":"https://pith.science/paper/X43M5ECH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.1647&json=true","fetch_graph":"https://pith.science/api/pith-number/X43M5ECH7QOGCGWIEM6AIK37HX/graph.json","fetch_events":"https://pith.science/api/pith-number/X43M5ECH7QOGCGWIEM6AIK37HX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX/action/storage_attestation","attest_author":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX/action/author_attestation","sign_citation":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX/action/citation_signature","submit_replication":"https://pith.science/pith/X43M5ECH7QOGCGWIEM6AIK37HX/action/replication_record"}},"created_at":"2026-05-18T02:38:18.185429+00:00","updated_at":"2026-05-18T02:38:18.185429+00:00"}