{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DQA3DTTUGQUX6AX67S7KEGRQUX","short_pith_number":"pith:DQA3DTTU","schema_version":"1.0","canonical_sha256":"1c01b1ce7434297f02fefcbea21a30a5d77a4f5bee06329d83dce214215002c3","source":{"kind":"arxiv","id":"1801.00901","version":4},"attestation_state":"computed","paper":{"title":"Bounded birationality and isomorphism problems are computable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tuyen Trung Truong","submitted_at":"2018-01-03T05:39:16Z","abstract_excerpt":"Let $X,Y$ be two irreducible subvarieties of the projective space $\\mathbb{P}^n$, and $d\\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\\bf explicitly}, in terms of $d$ and the ideals defining $X$ and $Y$, a quasi-affine algebraic variety parametrising the set of all birational maps $f$ from $X$ onto $Y$ which can be extended to a self-rational map of $\\mathbb{P}^n$ of degree $\\leq d$.\n  Based on this result, we propose an approach towards the rationality problem (see Section 3 below), solve it for some simple cases (varieties of general type or curves), "},"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":"1801.00901","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-03T05:39:16Z","cross_cats_sorted":[],"title_canon_sha256":"68de9a9a8f3b07dec2fb77dec190555bbdab7d9e856534335e6b9a4bbb9ad69a","abstract_canon_sha256":"8363d68d5d606e19bda45eb1f12e25d6e0e2b42e5decbde3b7813b3ad24c15fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:54.732443Z","signature_b64":"/Kwt/VRJPvswTvzQscQg4GXiYcdDWi3/NdmecDeDX9Z1RL3E2qr5SvxogbdHXoFW+DCKIvDJIgIIFrXl989FAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c01b1ce7434297f02fefcbea21a30a5d77a4f5bee06329d83dce214215002c3","last_reissued_at":"2026-05-18T00:10:54.731714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:54.731714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounded birationality and isomorphism problems are computable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Tuyen Trung Truong","submitted_at":"2018-01-03T05:39:16Z","abstract_excerpt":"Let $X,Y$ be two irreducible subvarieties of the projective space $\\mathbb{P}^n$, and $d\\geq 1$ an integer number. The main result of this paper is an algorithm to construct {\\bf explicitly}, in terms of $d$ and the ideals defining $X$ and $Y$, a quasi-affine algebraic variety parametrising the set of all birational maps $f$ from $X$ onto $Y$ which can be extended to a self-rational map of $\\mathbb{P}^n$ of degree $\\leq d$.\n  Based on this result, we propose an approach towards the rationality problem (see Section 3 below), solve it for some simple cases (varieties of general type or curves), "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00901","kind":"arxiv","version":4},"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":"1801.00901","created_at":"2026-05-18T00:10:54.731834+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.00901v4","created_at":"2026-05-18T00:10:54.731834+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00901","created_at":"2026-05-18T00:10:54.731834+00:00"},{"alias_kind":"pith_short_12","alias_value":"DQA3DTTUGQUX","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DQA3DTTUGQUX6AX6","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DQA3DTTU","created_at":"2026-05-18T12:32:19.392346+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/DQA3DTTUGQUX6AX67S7KEGRQUX","json":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX.json","graph_json":"https://pith.science/api/pith-number/DQA3DTTUGQUX6AX67S7KEGRQUX/graph.json","events_json":"https://pith.science/api/pith-number/DQA3DTTUGQUX6AX67S7KEGRQUX/events.json","paper":"https://pith.science/paper/DQA3DTTU"},"agent_actions":{"view_html":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX","download_json":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX.json","view_paper":"https://pith.science/paper/DQA3DTTU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.00901&json=true","fetch_graph":"https://pith.science/api/pith-number/DQA3DTTUGQUX6AX67S7KEGRQUX/graph.json","fetch_events":"https://pith.science/api/pith-number/DQA3DTTUGQUX6AX67S7KEGRQUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX/action/storage_attestation","attest_author":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX/action/author_attestation","sign_citation":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX/action/citation_signature","submit_replication":"https://pith.science/pith/DQA3DTTUGQUX6AX67S7KEGRQUX/action/replication_record"}},"created_at":"2026-05-18T00:10:54.731834+00:00","updated_at":"2026-05-18T00:10:54.731834+00:00"}