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It is proven that $\\dim \\mathfrak{aut}(X) > n(n+1)/2$ if and only if $X$ is isomorphic to $\\mathbb{P}^n, \\mathbb{Q}^n$ or ${\\rm Gr}(2,5)$. Furthermore, the equality $\\dim \\mathfrak{aut}(X) = n(n+1)/2$ holds only when $X$ is isomorphic to the 6-dimensional Lagrangian Grassmannian ${\\rm Lag}(6)$ or a general hyperplane section of ${\\rm Gr}(2,5)$."},"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":"1809.10623","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-27T16:38:51Z","cross_cats_sorted":[],"title_canon_sha256":"5190a69875cf20cd2b881baf3f06bd11b740270267e207f7820ceccf758297d7","abstract_canon_sha256":"2805006dacb2947dc05c0902d9a4aa04761bbe9b4fe0dcfa5e468010b9b97923"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:14.672521Z","signature_b64":"L8G0xk79ErzdGuRSrYVZtFbcpJri5anrIGAagNCSoP1Ja7cSFCJZFQnwa7WHS5THrTRW3aBkBo77FR9yntPlBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65de8d2dcfe735289aaf9ba7fb2586f1d79878a3b74a4db97edd77cda135326c","last_reissued_at":"2026-05-18T00:03:14.671889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:14.671889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Fano manifolds of Picard number one with big automorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Baohua Fu, Junyi Xie, Wenhao Ou","submitted_at":"2018-09-27T16:38:51Z","abstract_excerpt":"Let $X$ be an $n$-dimensional smooth Fano complex variety of Picard number one. Assume that the VMRT at a general point of $X$ is smooth irreducible and non-degenerate (which holds if $X$ is covered by lines with index $ >(n+2)/2$). It is proven that $\\dim \\mathfrak{aut}(X) > n(n+1)/2$ if and only if $X$ is isomorphic to $\\mathbb{P}^n, \\mathbb{Q}^n$ or ${\\rm Gr}(2,5)$. Furthermore, the equality $\\dim \\mathfrak{aut}(X) = n(n+1)/2$ holds only when $X$ is isomorphic to the 6-dimensional Lagrangian Grassmannian ${\\rm Lag}(6)$ or a general hyperplane section of ${\\rm Gr}(2,5)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10623","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":"1809.10623","created_at":"2026-05-18T00:03:14.671974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.10623v2","created_at":"2026-05-18T00:03:14.671974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10623","created_at":"2026-05-18T00:03:14.671974+00:00"},{"alias_kind":"pith_short_12","alias_value":"MXPI2LOP442S","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"MXPI2LOP442SRGVP","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"MXPI2LOP","created_at":"2026-05-18T12:32:40.477152+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/MXPI2LOP442SRGVPTOT7WJMG6H","json":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H.json","graph_json":"https://pith.science/api/pith-number/MXPI2LOP442SRGVPTOT7WJMG6H/graph.json","events_json":"https://pith.science/api/pith-number/MXPI2LOP442SRGVPTOT7WJMG6H/events.json","paper":"https://pith.science/paper/MXPI2LOP"},"agent_actions":{"view_html":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H","download_json":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H.json","view_paper":"https://pith.science/paper/MXPI2LOP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.10623&json=true","fetch_graph":"https://pith.science/api/pith-number/MXPI2LOP442SRGVPTOT7WJMG6H/graph.json","fetch_events":"https://pith.science/api/pith-number/MXPI2LOP442SRGVPTOT7WJMG6H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H/action/storage_attestation","attest_author":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H/action/author_attestation","sign_citation":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H/action/citation_signature","submit_replication":"https://pith.science/pith/MXPI2LOP442SRGVPTOT7WJMG6H/action/replication_record"}},"created_at":"2026-05-18T00:03:14.671974+00:00","updated_at":"2026-05-18T00:03:14.671974+00:00"}