{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O2WSQQHL7BRG7JVRCCLDINASFV","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":"9a1f29931fa87b85b397df0987b3aef1628ea5921a5428c3fe1a24311e84a677","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-23T12:43:37Z","title_canon_sha256":"75b41db0007f93b4ef6ce751b23fcb4c2a404c0be7d424d81023614269cc522c"},"schema_version":"1.0","source":{"id":"1301.5486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5486","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5486v1","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5486","created_at":"2026-05-18T03:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"O2WSQQHL7BRG","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O2WSQQHL7BRG7JVR","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O2WSQQHL","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:665762629b4361160139e3d0729bf4817b83b9669d58e027a4959c79e8d92297","target":"graph","created_at":"2026-05-18T03:35:39Z","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":"Let X be an $n$-dimensional Fano manifold of Picard number 1. We study how many different ways X can compactify the complex vector group C^n equivariantly. Hassett and Tschinkel showed that when X = P^n with n \\geq 2, there are many distinct ways that X can be realized as equivariant compactifications of C^n. Our result says that projective space is an exception: among Fano manifolds of Picard number 1 with smooth VMRT, projective space is the only one compactifying C^n equivariantly in more than one ways. This answers questions raised by Hassett-Tschinkel and Arzhantsev-Sharoyko.","authors_text":"Baohua Fu, Jun-Muk Hwang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-23T12:43:37Z","title":"Uniqueness of equivariant compactifications of C^n by a Fano manifold of Picard number 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5486","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":"sha256:66b63927239385de50a88310f0cd6fed371208bd54a47c2aaae1cbf4e2e1789d","target":"record","created_at":"2026-05-18T03:35:39Z","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":"9a1f29931fa87b85b397df0987b3aef1628ea5921a5428c3fe1a24311e84a677","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-01-23T12:43:37Z","title_canon_sha256":"75b41db0007f93b4ef6ce751b23fcb4c2a404c0be7d424d81023614269cc522c"},"schema_version":"1.0","source":{"id":"1301.5486","kind":"arxiv","version":1}},"canonical_sha256":"76ad2840ebf8626fa6b110963434122d62af69225b1e2c593d0029f19db02b27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76ad2840ebf8626fa6b110963434122d62af69225b1e2c593d0029f19db02b27","first_computed_at":"2026-05-18T03:35:39.658427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:39.658427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xx7KHXk3c/+ouacXTZzB3sxcZ6eZj2VTkgLHez8LhrCFM3jg9NsYRPqln4T9j/H4hkpHxzz/ou9RZEawe1/MBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:39.659059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66b63927239385de50a88310f0cd6fed371208bd54a47c2aaae1cbf4e2e1789d","sha256:665762629b4361160139e3d0729bf4817b83b9669d58e027a4959c79e8d92297"],"state_sha256":"4f9688c03dfa666dafcd2c9f1d683b3bccc7f776af3f77f881ccc1e44b24a2e7"}