{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JPQTNIEP6WRS4WMWSBF6OVUJBY","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":"a03d497159944fb1aaa085287f983ec65b34de6dd14ca1344d3d6635805b2e24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-11T14:50:36Z","title_canon_sha256":"908d3f95a32c223202d9a736d10a19fc554c9cdf1bb6aa073f5a483877c6b972"},"schema_version":"1.0","source":{"id":"1302.3256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3256","created_at":"2026-05-18T03:33:39Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3256v1","created_at":"2026-05-18T03:33:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3256","created_at":"2026-05-18T03:33:39Z"},{"alias_kind":"pith_short_12","alias_value":"JPQTNIEP6WRS","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JPQTNIEP6WRS4WMW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JPQTNIEP","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:39275dfc0580dd0d2fdb9eab5d32b1aecdc38e78e93dcdbaefd59b3cc0cf772f","target":"graph","created_at":"2026-05-18T03:33:39Z","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 this paper, we characterize locally dually flat generalized m-th root Finsler metrics. Then we find a condition under which a generalized m-th root metric is projectively related to a m-th root metric. Finally, we prove that if a generalized m-th root metric is conformal to a m-th root metric, then both of them reduce to Riemannian metrics.","authors_text":"A. Tayebi, E. Peyghan, M. Shahbazi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-11T14:50:36Z","title":"On Generalized m-th Root Finsler Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3256","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":"sha256:0e0540f3b7626d0e9bd5c74edc00d5240ec95e20f94cb98f083b818944987c61","target":"record","created_at":"2026-05-18T03:33:39Z","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":"a03d497159944fb1aaa085287f983ec65b34de6dd14ca1344d3d6635805b2e24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-11T14:50:36Z","title_canon_sha256":"908d3f95a32c223202d9a736d10a19fc554c9cdf1bb6aa073f5a483877c6b972"},"schema_version":"1.0","source":{"id":"1302.3256","kind":"arxiv","version":1}},"canonical_sha256":"4be136a08ff5a32e5996904be756890e386df2de124f8858f55b6571f73ae5e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4be136a08ff5a32e5996904be756890e386df2de124f8858f55b6571f73ae5e9","first_computed_at":"2026-05-18T03:33:39.423589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:39.423589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bgQ65ja2lm3Hvp3DHR6aoIoP3cla1o3nIPvNB8XEaQD3pz8ae+AfPIj9aM9sq8ACFRCA/ESoufwgGoE2+rGQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:39.424074Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e0540f3b7626d0e9bd5c74edc00d5240ec95e20f94cb98f083b818944987c61","sha256:39275dfc0580dd0d2fdb9eab5d32b1aecdc38e78e93dcdbaefd59b3cc0cf772f"],"state_sha256":"eaec83d0473d0a0d3e389e076ba149c275bf6e73298cac277e5e45f4806ee3fc"}