{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QVXIBDG2SFWEO4G7DS2ULG4BSK","short_pith_number":"pith:QVXIBDG2","schema_version":"1.0","canonical_sha256":"856e808cda916c4770df1cb5459b8192a217be6152621419827a08b44070bc5f","source":{"kind":"arxiv","id":"1304.4426","version":2},"attestation_state":"computed","paper":{"title":"Submaximal metric projective and metric affine structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Boris Kruglikov, Vladimir Matveev","submitted_at":"2013-04-16T13:06:22Z","abstract_excerpt":"We prove that the next possible dimension after the maximal $n^2+2n$ for the Lie algebra of local projective symmetries of a metric on a manifold of dimension $n>1$ is $n^2-3n+5$ if the signature is Riemannian or $n=2$, $n^2-3n+6$ if the signature is Lorentzian and $n>2$, and $n^2-3n+8$ elsewise. We also prove that the Lie algebra of local affine symmetries of a metric has the same submaximal dimensions (after the maximal $n^2+n$) unless the signature is Riemannian and $n=3,4$, in which case the submaximal dimension is $n^2-3n+6$."},"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":"1304.4426","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-16T13:06:22Z","cross_cats_sorted":[],"title_canon_sha256":"30dabfc4281d0eaa6231b045523d5b7c1c6cbe0bc5a82eb0373098d7d1ab4086","abstract_canon_sha256":"50bbf8fa453dceffcfddb498de595d50b56ec2177d978a82fcbf5544088d8a07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:45.005429Z","signature_b64":"isGbWcRviEj5Xg4GMIYRBE8RPcHegWpudoMVGNy7ibZ6+ECRKx2oz7PSu0e7RXimtCOnxXwbB7JpILc9bU4jBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"856e808cda916c4770df1cb5459b8192a217be6152621419827a08b44070bc5f","last_reissued_at":"2026-05-18T03:20:45.004672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:45.004672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Submaximal metric projective and metric affine structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Boris Kruglikov, Vladimir Matveev","submitted_at":"2013-04-16T13:06:22Z","abstract_excerpt":"We prove that the next possible dimension after the maximal $n^2+2n$ for the Lie algebra of local projective symmetries of a metric on a manifold of dimension $n>1$ is $n^2-3n+5$ if the signature is Riemannian or $n=2$, $n^2-3n+6$ if the signature is Lorentzian and $n>2$, and $n^2-3n+8$ elsewise. We also prove that the Lie algebra of local affine symmetries of a metric has the same submaximal dimensions (after the maximal $n^2+n$) unless the signature is Riemannian and $n=3,4$, in which case the submaximal dimension is $n^2-3n+6$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4426","kind":"arxiv","version":2},"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":"1304.4426","created_at":"2026-05-18T03:20:45.004807+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.4426v2","created_at":"2026-05-18T03:20:45.004807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4426","created_at":"2026-05-18T03:20:45.004807+00:00"},{"alias_kind":"pith_short_12","alias_value":"QVXIBDG2SFWE","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QVXIBDG2SFWEO4G7","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QVXIBDG2","created_at":"2026-05-18T12:27:57.521954+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/QVXIBDG2SFWEO4G7DS2ULG4BSK","json":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK.json","graph_json":"https://pith.science/api/pith-number/QVXIBDG2SFWEO4G7DS2ULG4BSK/graph.json","events_json":"https://pith.science/api/pith-number/QVXIBDG2SFWEO4G7DS2ULG4BSK/events.json","paper":"https://pith.science/paper/QVXIBDG2"},"agent_actions":{"view_html":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK","download_json":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK.json","view_paper":"https://pith.science/paper/QVXIBDG2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.4426&json=true","fetch_graph":"https://pith.science/api/pith-number/QVXIBDG2SFWEO4G7DS2ULG4BSK/graph.json","fetch_events":"https://pith.science/api/pith-number/QVXIBDG2SFWEO4G7DS2ULG4BSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK/action/storage_attestation","attest_author":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK/action/author_attestation","sign_citation":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK/action/citation_signature","submit_replication":"https://pith.science/pith/QVXIBDG2SFWEO4G7DS2ULG4BSK/action/replication_record"}},"created_at":"2026-05-18T03:20:45.004807+00:00","updated_at":"2026-05-18T03:20:45.004807+00:00"}