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If a Finsler metric has the group of almost isometries of dimension greater than $\\frac{n^2 -n}{2} +1$, then the Finsler metric is Randers, i.e., $F(x,y)= \\sqrt{g_x(y,y)} + \\tau(y)$. Moreover, if $n\\ne 4$, the Riemannian metric $g$ has constant sectional curvature and, if in addition $n\\ne 2$, the 1-form $\\tau$ is closed, so (locally) the metric admits the group of local isometries of the maximal"},"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":"1207.6922","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-30T12:54:08Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"59e67721a1961c0f6eaf39078836dcb06f4f6443d3077bcd3a92af683ca77685","abstract_canon_sha256":"a7fb4c91587bebf275322251e82e1ba960c5d3107fb785d66466827906dff47e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:48.229740Z","signature_b64":"ybF55Nqnq4lr1b4/EeG71B7/ODNtHp2ju2K3Jg/8d5nsv8xvuK9NfWPkFG3cu65GX++y5DR8Zuy1CtkFpQvQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3467cdf48b46b93f7d2d290da0c181079c33a17fc9666c7d1bb46ee0ea99542a","last_reissued_at":"2026-05-18T03:49:48.228787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:48.228787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On submaximal dimension of the group of almost isometries of Finsler metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Vladimir S. Matveev","submitted_at":"2012-07-30T12:54:08Z","abstract_excerpt":"We show that the second greatest possible dimension of the group of (local) almost isometries of a Finsler metric is $\\frac{n^2 -n}{2} +1$ for $n= dim(M)\\ne 4 $ and $\\frac{n^2 -n}{2} +2 =8$ for $n=4$. If a Finsler metric has the group of almost isometries of dimension greater than $\\frac{n^2 -n}{2} +1$, then the Finsler metric is Randers, i.e., $F(x,y)= \\sqrt{g_x(y,y)} + \\tau(y)$. Moreover, if $n\\ne 4$, the Riemannian metric $g$ has constant sectional curvature and, if in addition $n\\ne 2$, the 1-form $\\tau$ is closed, so (locally) the metric admits the group of local isometries of the maximal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6922","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":"1207.6922","created_at":"2026-05-18T03:49:48.228934+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.6922v1","created_at":"2026-05-18T03:49:48.228934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6922","created_at":"2026-05-18T03:49:48.228934+00:00"},{"alias_kind":"pith_short_12","alias_value":"GRT435ELI24T","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GRT435ELI24T67JN","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GRT435EL","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/GRT435ELI24T67JNFEG2BQMBA6","json":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6.json","graph_json":"https://pith.science/api/pith-number/GRT435ELI24T67JNFEG2BQMBA6/graph.json","events_json":"https://pith.science/api/pith-number/GRT435ELI24T67JNFEG2BQMBA6/events.json","paper":"https://pith.science/paper/GRT435EL"},"agent_actions":{"view_html":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6","download_json":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6.json","view_paper":"https://pith.science/paper/GRT435EL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.6922&json=true","fetch_graph":"https://pith.science/api/pith-number/GRT435ELI24T67JNFEG2BQMBA6/graph.json","fetch_events":"https://pith.science/api/pith-number/GRT435ELI24T67JNFEG2BQMBA6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6/action/storage_attestation","attest_author":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6/action/author_attestation","sign_citation":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6/action/citation_signature","submit_replication":"https://pith.science/pith/GRT435ELI24T67JNFEG2BQMBA6/action/replication_record"}},"created_at":"2026-05-18T03:49:48.228934+00:00","updated_at":"2026-05-18T03:49:48.228934+00:00"}