{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FXLX6Z5GCT5XXPF3RT3WRGNTKU","short_pith_number":"pith:FXLX6Z5G","schema_version":"1.0","canonical_sha256":"2dd77f67a614fb7bbcbb8cf76899b3552b3b5c4798da38a05800b1f2e6c39d19","source":{"kind":"arxiv","id":"1207.1937","version":1},"attestation_state":"computed","paper":{"title":"On Einstein Matsumoto metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaoling Zhang, Yi-Bing Shen","submitted_at":"2012-07-09T03:55:09Z","abstract_excerpt":"In this paper, the necessary and sufficient conditions for Matsumoto metrics $F=\\frac{\\alpha^2}{\\alpha-\\beta}$ to be Einstein are given. It is shown that if the length of $\\beta$ with respect to $\\alpha$ is constant, then the Matsumoto metric $F$ is an Einstein metric if and only if $\\alpha$ is Ricci-flat and $\\beta$ is parallel with respect to $\\alpha$. A nontrivial example of Ricci flat Matsumoto metrics is given."},"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":"1207.1937","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-09T03:55:09Z","cross_cats_sorted":[],"title_canon_sha256":"cd42b84c9b70f7ac2fb5e3ad8066ba43a915bdd6feebf939c820e0a255f193d0","abstract_canon_sha256":"c07771c58e4bc73a0bcc8fe07891be00f658f78483f6dfc88c36a125629a05a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:26.566529Z","signature_b64":"DNTbAsH85NKJbe33U6qg1GMMSWyb2YM/tGliDzx5C3cQNjN7K8rdxwfXfVysWq/vDhpw0GlWUbL+F9XRs8NLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dd77f67a614fb7bbcbb8cf76899b3552b3b5c4798da38a05800b1f2e6c39d19","last_reissued_at":"2026-05-18T03:51:26.566009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:26.566009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Einstein Matsumoto metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaoling Zhang, Yi-Bing Shen","submitted_at":"2012-07-09T03:55:09Z","abstract_excerpt":"In this paper, the necessary and sufficient conditions for Matsumoto metrics $F=\\frac{\\alpha^2}{\\alpha-\\beta}$ to be Einstein are given. It is shown that if the length of $\\beta$ with respect to $\\alpha$ is constant, then the Matsumoto metric $F$ is an Einstein metric if and only if $\\alpha$ is Ricci-flat and $\\beta$ is parallel with respect to $\\alpha$. A nontrivial example of Ricci flat Matsumoto metrics is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1937","kind":"arxiv","version":1},"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":"1207.1937","created_at":"2026-05-18T03:51:26.566085+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.1937v1","created_at":"2026-05-18T03:51:26.566085+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1937","created_at":"2026-05-18T03:51:26.566085+00:00"},{"alias_kind":"pith_short_12","alias_value":"FXLX6Z5GCT5X","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FXLX6Z5GCT5XXPF3","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FXLX6Z5G","created_at":"2026-05-18T12:27:06.952714+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/FXLX6Z5GCT5XXPF3RT3WRGNTKU","json":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU.json","graph_json":"https://pith.science/api/pith-number/FXLX6Z5GCT5XXPF3RT3WRGNTKU/graph.json","events_json":"https://pith.science/api/pith-number/FXLX6Z5GCT5XXPF3RT3WRGNTKU/events.json","paper":"https://pith.science/paper/FXLX6Z5G"},"agent_actions":{"view_html":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU","download_json":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU.json","view_paper":"https://pith.science/paper/FXLX6Z5G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.1937&json=true","fetch_graph":"https://pith.science/api/pith-number/FXLX6Z5GCT5XXPF3RT3WRGNTKU/graph.json","fetch_events":"https://pith.science/api/pith-number/FXLX6Z5GCT5XXPF3RT3WRGNTKU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU/action/storage_attestation","attest_author":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU/action/author_attestation","sign_citation":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU/action/citation_signature","submit_replication":"https://pith.science/pith/FXLX6Z5GCT5XXPF3RT3WRGNTKU/action/replication_record"}},"created_at":"2026-05-18T03:51:26.566085+00:00","updated_at":"2026-05-18T03:51:26.566085+00:00"}