{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:O4MXYJ42HTNXRGDWVTUAIWEKR7","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":"68c8157dac28b51de7a0d86720208f67ee6059175b8a14d18d697a25310bc3ee","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-31T22:23:17Z","title_canon_sha256":"f5a3b4b053281a9e4767201cc49a686092662164eb37ace3e8839b001d4ba0e4"},"schema_version":"1.0","source":{"id":"0811.0031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0031","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0031v2","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0031","created_at":"2026-05-18T04:15:06Z"},{"alias_kind":"pith_short_12","alias_value":"O4MXYJ42HTNX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"O4MXYJ42HTNXRGDW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"O4MXYJ42","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:ac790d5dac60551cebd3889aad4eeb3100c3f0ecdee4d4a71a8de6080ca8526b","target":"graph","created_at":"2026-05-18T04:15:06Z","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":"In Theorem 1, we generalize the results of Szabo for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F. As an application we show (Corollary 3) that every Berwald projectively flat metric is a Minkowski metric; this statement is a \"Berwald\" version of Hilbert's 4th problem.\n  Further, we investigate geodesic equivalence of Berwald metrics. Theorem 2 gives a system of PDE that has a (nontrivial) solution if and only if the given essentially Berwald metric admits a Riemannian metric that ","authors_text":"Vladimir S. Matveev","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-31T22:23:17Z","title":"Riemannian metrics having common geodesics with Berwald metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0031","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:faa5fe3a321c7c917d7b556cbabd1fd3a57ff86b581c40c716e944b86f7c31e8","target":"record","created_at":"2026-05-18T04:15:06Z","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":"68c8157dac28b51de7a0d86720208f67ee6059175b8a14d18d697a25310bc3ee","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-10-31T22:23:17Z","title_canon_sha256":"f5a3b4b053281a9e4767201cc49a686092662164eb37ace3e8839b001d4ba0e4"},"schema_version":"1.0","source":{"id":"0811.0031","kind":"arxiv","version":2}},"canonical_sha256":"77197c279a3cdb789876ace804588a8fd7472e68a2f79d38667830f5f9bbf4c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77197c279a3cdb789876ace804588a8fd7472e68a2f79d38667830f5f9bbf4c1","first_computed_at":"2026-05-18T04:15:06.850485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:06.850485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wEdFTl8Qs3wKhSGwZZWGjYYEJXjymi0Ccx6dYoJLb7KX8hqUiNW7MUBSlvnlGsYJ56QNpamPNgUdZNmsKn16CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:06.850982Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.0031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:faa5fe3a321c7c917d7b556cbabd1fd3a57ff86b581c40c716e944b86f7c31e8","sha256:ac790d5dac60551cebd3889aad4eeb3100c3f0ecdee4d4a71a8de6080ca8526b"],"state_sha256":"068ff4b1baff2ad2a32fe46c5823a7eef56f02ff6eb8bcc1e8e49a5708acf04d"}