{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OAFBF7IKWYF3B6RMMWLGACV7MR","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":"0d550e104efd49b16e4aaed95476b05fd9c7d9a35906b64b2694af91de6f25a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-13T12:31:38Z","title_canon_sha256":"112113a5283372d26df9a489d4c13c74a5e18a62ec9972ab7ce7908e53e73fdc"},"schema_version":"1.0","source":{"id":"1409.7351","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.7351","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1409.7351v1","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.7351","created_at":"2026-05-18T02:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"OAFBF7IKWYF3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OAFBF7IKWYF3B6RM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OAFBF7IK","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:81fcb3546084b04dc729ae2e4de1976df9f2a9ad297abceb9170889b56e6fe6e","target":"graph","created_at":"2026-05-18T02:41:58Z","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 consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if it is locally Minkowskian.","authors_text":"A. Tayebi, E. Peyghan, T. Tabatabaeifar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-13T12:31:38Z","title":"On Kropina Change of m-th Root Finsler Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.7351","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:ef1029840ae32adcca0ea8cf44d534f3a296b3db1e83751293d73552c264ab26","target":"record","created_at":"2026-05-18T02:41:58Z","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":"0d550e104efd49b16e4aaed95476b05fd9c7d9a35906b64b2694af91de6f25a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-13T12:31:38Z","title_canon_sha256":"112113a5283372d26df9a489d4c13c74a5e18a62ec9972ab7ce7908e53e73fdc"},"schema_version":"1.0","source":{"id":"1409.7351","kind":"arxiv","version":1}},"canonical_sha256":"700a12fd0ab60bb0fa2c6596600abf64498f7cc87c48a51ba76cfab8eb595bd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"700a12fd0ab60bb0fa2c6596600abf64498f7cc87c48a51ba76cfab8eb595bd8","first_computed_at":"2026-05-18T02:41:58.593668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:58.593668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WRuIoNelKJODUwmlmzfU5/sPHuel2eNcSIjMeAv9AmLJ4ElxWriZAFSnjmOtAcWOyQ3AdOi3lQKmfiN/SmTIAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:58.594287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.7351","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef1029840ae32adcca0ea8cf44d534f3a296b3db1e83751293d73552c264ab26","sha256:81fcb3546084b04dc729ae2e4de1976df9f2a9ad297abceb9170889b56e6fe6e"],"state_sha256":"16cc585754e3e746ddb59b62043098b0f5a184a52c746f8343b4e7c1dc19fc29"}