{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DP7XZ6ZCVPJ7BYKPPGMYYXHTNM","short_pith_number":"pith:DP7XZ6ZC","canonical_record":{"source":{"id":"1405.2753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-12T13:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"f1cc02fddb2a30325c44249369c43c61f4bf1d767777d96351a4265ce05494e5","abstract_canon_sha256":"8f413699a4f8da2d4b291a94158efc75f22f92f37f3b0e4b649fdf0f5dedb9a3"},"schema_version":"1.0"},"canonical_sha256":"1bff7cfb22abd3f0e14f79998c5cf36b22bd0974cd8bf280fe048ceb8860e1ac","source":{"kind":"arxiv","id":"1405.2753","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DP7XZ6ZCVPJ7BYKPPGMYYXHTNM","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-05-12T13:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"f1cc02fddb2a30325c44249369c43c61f4bf1d767777d96351a4265ce05494e5","abstract_canon_sha256":"8f413699a4f8da2d4b291a94158efc75f22f92f37f3b0e4b649fdf0f5dedb9a3"},"schema_version":"1.0"},"canonical_sha256":"1bff7cfb22abd3f0e14f79998c5cf36b22bd0974cd8bf280fe048ceb8860e1ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:04.839114Z","signature_b64":"qyiu2/Ms/EgxjhAs+XHJ8+Bxx4Yi++4HuO2IrrekT11BTd2h/qRonWFILnE59JcNHIv8FgaEPJkM3sAzfBlxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bff7cfb22abd3f0e14f79998c5cf36b22bd0974cd8bf280fe048ceb8860e1ac","last_reissued_at":"2026-05-18T02:52:04.838638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:04.838638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2753","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIvhUNGQTdlH/KeOmhHcjcGpTGIf4igsVAfHQ+Uf2AQ8S5pRUzd/1jWmwmi595W65+s72DjdI3JF++gl/xzzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:25:56.076027Z"},"content_sha256":"af732554998263adc96e11b5e23e57adf26e0734548624976287b558a0ea1811","schema_version":"1.0","event_id":"sha256:af732554998263adc96e11b5e23e57adf26e0734548624976287b558a0ea1811"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DP7XZ6ZCVPJ7BYKPPGMYYXHTNM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PGL(2) actions on Grassmannians and projective construction of rational curves with given restricted tangent bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alberto Alzati, Riccardo Re","submitted_at":"2014-05-12T13:42:46Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2753","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:52:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JG6IOv1N4C+sc3Dpzz8ynm1vlro86TelNHcQZUW/F1/0Z1M7UwtQFwNwgHUb97cpLZO80OsNUYGzVSbSYQAUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:25:56.076495Z"},"content_sha256":"2fafaf0a635580c23a9da5148a7ff6be5c80b120384f056af97a9c725ce5dc0c","schema_version":"1.0","event_id":"sha256:2fafaf0a635580c23a9da5148a7ff6be5c80b120384f056af97a9c725ce5dc0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DP7XZ6ZCVPJ7BYKPPGMYYXHTNM/bundle.json","state_url":"https://pith.science/pith/DP7XZ6ZCVPJ7BYKPPGMYYXHTNM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DP7XZ6ZCVPJ7BYKPPGMYYXHTNM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T01:25:56Z","links":{"resolver":"https://pith.science/pith/DP7XZ6ZCVPJ7BYKPPGMYYXHTNM","bundle":"https://pith.science/pith/DP7XZ6ZCVPJ7BYKPPGMYYXHTNM/bundle.json","state":"https://pith.science/pith/DP7XZ6ZCVPJ7BYKPPGMYYXHTNM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DP7XZ6ZCVPJ7BYKPPGMYYXHTNM/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"enOFV1WLueQPWsR2VP4coxAAVV+FurTNP+nSHyGjHs6kyzWFWjfd0VRYodaUR3CzdRCgFTRjg/F8hjAAzxnTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T01:25:56.079542Z","bundle_sha256":"a088871e2fd6c182fb3aec5bc26310f0640dc32a8f65557fe3a9f7e8b24d0155"}}