{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BRME4UEJ4BWJLR2X5BSNEBALIH","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":"55eef2db96b9e44dc97c4f7ab84a2ebb7646cf3bbb00e91fba78e629a9fb2657","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T13:14:00Z","title_canon_sha256":"736060cbd6ea2966adb96fc837aa3328b8dd6e14b228b2238ac17cd932bb708f"},"schema_version":"1.0","source":{"id":"1408.6401","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6401","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6401v2","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6401","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"BRME4UEJ4BWJ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BRME4UEJ4BWJLR2X","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BRME4UEJ","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:51939d7c23ff6dbe7368a9f549e0efa9e2d2902b6b5e09ce549a972276cfaca9","target":"graph","created_at":"2026-05-18T01:31:19Z","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":"The goal of this short paper is to give condition for the completeness of the Binet-Legendre metric in Finsler geometry. The case of the Funk and Hilbert metrics in a convex domain are discussed.","authors_text":"Marc Troyanov, Vladimir S. Matveev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T13:14:00Z","title":"Completeness and incompleteness of the Binet-Legendre Metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6401","kind":"arxiv","version":2},"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":"sha256:51ff87858a5275707532d6dc8b7748a8c0f36ad368eaef3e9b1883e71269e1f8","target":"record","created_at":"2026-05-18T01:31:19Z","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":"55eef2db96b9e44dc97c4f7ab84a2ebb7646cf3bbb00e91fba78e629a9fb2657","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-27T13:14:00Z","title_canon_sha256":"736060cbd6ea2966adb96fc837aa3328b8dd6e14b228b2238ac17cd932bb708f"},"schema_version":"1.0","source":{"id":"1408.6401","kind":"arxiv","version":2}},"canonical_sha256":"0c584e5089e06c95c757e864d2040b41ccc602784adf60876eafa67911cb6e3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c584e5089e06c95c757e864d2040b41ccc602784adf60876eafa67911cb6e3b","first_computed_at":"2026-05-18T01:31:19.942658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:19.942658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QjAOXMcopmkBdQnLRGQc+qV5qED7xBpwC7ypHFMPu9663VX4GiuLsB7/jR1n6wUeQAq654FCCwoEcS1RoQgxBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:19.943200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6401","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51ff87858a5275707532d6dc8b7748a8c0f36ad368eaef3e9b1883e71269e1f8","sha256:51939d7c23ff6dbe7368a9f549e0efa9e2d2902b6b5e09ce549a972276cfaca9"],"state_sha256":"cb308c0ecbeae1a620f221e60168d2737d78dad02ed48bc170e3af956896fdcb"}