{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:V7RHNBC4QHVQ2SB2UIYGCAJU3V","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":"5722f688a93ee0e9d925df038683f940e210e9c2919f6296253b00ce08934d5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-08T07:39:51Z","title_canon_sha256":"c49700c73218f3cedddc3242026f3dfc7a0ac1872911ea98daad33aa5be4146c"},"schema_version":"1.0","source":{"id":"0903.1393","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.1393","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"arxiv_version","alias_value":"0903.1393v3","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.1393","created_at":"2026-05-18T03:40:37Z"},{"alias_kind":"pith_short_12","alias_value":"V7RHNBC4QHVQ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"V7RHNBC4QHVQ2SB2","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"V7RHNBC4","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:98ab890b72a5f75132626cdedb33a127fd1658cb06716cea0dfc209d583ca4fa","target":"graph","created_at":"2026-05-18T03:40:37Z","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":"We show how to construct certain homogeneous deformations for rational normal varieties with codimension one torus action. This can then be used to construct homogeneous deformations of any toric variety in arbitrary degree. For locally trivial deformations coming from this construction, we calculate the image of the Kodaira-Spencer map. We then show that for a smooth complete toric variety, our homogeneous deformations span the space of first-order deformations.","authors_text":"Nathan Owen Ilten, Robert Vollmert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-08T07:39:51Z","title":"Deformations of Rational T-Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1393","kind":"arxiv","version":3},"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":"sha256:426c900cd1bf2c1d3be32ca60b031b155a2ea929559bc0eb287729d4904f9d33","target":"record","created_at":"2026-05-18T03:40:37Z","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":"5722f688a93ee0e9d925df038683f940e210e9c2919f6296253b00ce08934d5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-03-08T07:39:51Z","title_canon_sha256":"c49700c73218f3cedddc3242026f3dfc7a0ac1872911ea98daad33aa5be4146c"},"schema_version":"1.0","source":{"id":"0903.1393","kind":"arxiv","version":3}},"canonical_sha256":"afe276845c81eb0d483aa230610134dd73260e796ce8dbb33fa8ee4bf94f652d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afe276845c81eb0d483aa230610134dd73260e796ce8dbb33fa8ee4bf94f652d","first_computed_at":"2026-05-18T03:40:37.141959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:37.141959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PwZ+ObrKJhUejddCtuiFt/AwUjyL13StiOJt2dAzeR4iCJTxbV+9ttPldpk65hZ3aLkOqJGZRy1UcJy2yLK8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:37.142729Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.1393","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:426c900cd1bf2c1d3be32ca60b031b155a2ea929559bc0eb287729d4904f9d33","sha256:98ab890b72a5f75132626cdedb33a127fd1658cb06716cea0dfc209d583ca4fa"],"state_sha256":"43cc264ed6336a775385987d4a466141e3c93a2e091564cecb11ddae15a8445e"}