{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DP7XZ6ZCVPJ7BYKPPGMYYXHTNM","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":"8f413699a4f8da2d4b291a94158efc75f22f92f37f3b0e4b649fdf0f5dedb9a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-12T13:42:46Z","title_canon_sha256":"f1cc02fddb2a30325c44249369c43c61f4bf1d767777d96351a4265ce05494e5"},"schema_version":"1.0","source":{"id":"1405.2753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2753","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2753v1","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2753","created_at":"2026-05-18T02:52:04Z"},{"alias_kind":"pith_short_12","alias_value":"DP7XZ6ZCVPJ7","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DP7XZ6ZCVPJ7BYKP","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DP7XZ6ZC","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:2fafaf0a635580c23a9da5148a7ff6be5c80b120384f056af97a9c725ce5dc0c","target":"graph","created_at":"2026-05-18T02:52:04Z","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 give an explicit parametrization of the Hilbert schemes of rational curves C in P^n having a given splitting type of the restricted tangent bundle from P^n to C. The adopted technique uses the description of such curves as projections of a rational normal curve from a suitable linear vertex and a classification of those vertices that correspond to the required splitting type of the restricted tangent bundle. This classification involves the study of a suitable PGL(2) action on the relevant Grassmannian variety.","authors_text":"Alberto Alzati, Riccardo Re","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-12T13:42:46Z","title":"PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2753","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:af732554998263adc96e11b5e23e57adf26e0734548624976287b558a0ea1811","target":"record","created_at":"2026-05-18T02:52:04Z","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":"8f413699a4f8da2d4b291a94158efc75f22f92f37f3b0e4b649fdf0f5dedb9a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-12T13:42:46Z","title_canon_sha256":"f1cc02fddb2a30325c44249369c43c61f4bf1d767777d96351a4265ce05494e5"},"schema_version":"1.0","source":{"id":"1405.2753","kind":"arxiv","version":1}},"canonical_sha256":"1bff7cfb22abd3f0e14f79998c5cf36b22bd0974cd8bf280fe048ceb8860e1ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bff7cfb22abd3f0e14f79998c5cf36b22bd0974cd8bf280fe048ceb8860e1ac","first_computed_at":"2026-05-18T02:52:04.838638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:04.838638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qyiu2/Ms/EgxjhAs+XHJ8+Bxx4Yi++4HuO2IrrekT11BTd2h/qRonWFILnE59JcNHIv8FgaEPJkM3sAzfBlxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:04.839114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af732554998263adc96e11b5e23e57adf26e0734548624976287b558a0ea1811","sha256:2fafaf0a635580c23a9da5148a7ff6be5c80b120384f056af97a9c725ce5dc0c"],"state_sha256":"d2ed4dd352974df115d7a5386786b8d371beffb2736d3f1cbc38512e6220343c"}