{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DQA3DTTUGQUX6AX67S7KEGRQUX","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":"8363d68d5d606e19bda45eb1f12e25d6e0e2b42e5decbde3b7813b3ad24c15fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-03T05:39:16Z","title_canon_sha256":"68de9a9a8f3b07dec2fb77dec190555bbdab7d9e856534335e6b9a4bbb9ad69a"},"schema_version":"1.0","source":{"id":"1801.00901","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00901","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00901v4","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00901","created_at":"2026-05-18T00:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"DQA3DTTUGQUX","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DQA3DTTUGQUX6AX6","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DQA3DTTU","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:4abd058f52049b742e6fd6bd3f8e1f501e8fffa061a906897774df73a531ea27","target":"graph","created_at":"2026-05-18T00:10:54Z","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 $X,Y$ 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), ","authors_text":"Tuyen Trung Truong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-03T05:39:16Z","title":"Bounded birationality and isomorphism problems are computable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00901","kind":"arxiv","version":4},"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:e588360046aa3e106e6197abc2adfec86910d0e3d5a64b8b5027363fa9ca5c86","target":"record","created_at":"2026-05-18T00:10:54Z","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":"8363d68d5d606e19bda45eb1f12e25d6e0e2b42e5decbde3b7813b3ad24c15fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-01-03T05:39:16Z","title_canon_sha256":"68de9a9a8f3b07dec2fb77dec190555bbdab7d9e856534335e6b9a4bbb9ad69a"},"schema_version":"1.0","source":{"id":"1801.00901","kind":"arxiv","version":4}},"canonical_sha256":"1c01b1ce7434297f02fefcbea21a30a5d77a4f5bee06329d83dce214215002c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c01b1ce7434297f02fefcbea21a30a5d77a4f5bee06329d83dce214215002c3","first_computed_at":"2026-05-18T00:10:54.731714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:54.731714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Kwt/VRJPvswTvzQscQg4GXiYcdDWi3/NdmecDeDX9Z1RL3E2qr5SvxogbdHXoFW+DCKIvDJIgIIFrXl989FAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:54.732443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00901","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e588360046aa3e106e6197abc2adfec86910d0e3d5a64b8b5027363fa9ca5c86","sha256:4abd058f52049b742e6fd6bd3f8e1f501e8fffa061a906897774df73a531ea27"],"state_sha256":"ead3e67eb7983a20d68fa4a27fd3cdae75c05cd4d96975c68e83e83e4e8611cb"}