{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6VGOQPSYOIXJW5MGPCHWICVFRL","short_pith_number":"pith:6VGOQPSY","schema_version":"1.0","canonical_sha256":"f54ce83e58722e9b7586788f640aa58ad612411d3a94d57a1989acee30dc8a61","source":{"kind":"arxiv","id":"1710.09108","version":1},"attestation_state":"computed","paper":{"title":"Deformations of $\\mathbb{A}^1$-cylindrical varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB), Takashi Kishimoto","submitted_at":"2017-10-25T08:20:37Z","abstract_excerpt":"An algebraic variety is called $\\mathbb{A}^{1}$-cylindrical if it contains an $\\mathbb{A}^{1}$-cylinder, i.e. a Zariski open subset of the form $Z\\times\\mathbb{A}^{1}$ for some algebraic variety Z. We show that the generic fiber of a family $f:X\\rightarrow S$ of normal $\\mathbb{A}^{1}$-cylindrical varieties becomes $\\mathbb{A}^{1}$-cylindrical after a finite extension of the base. Our second result is a criterion for existence of an $\\mathbb{A}^{1}$-cylinder in X which we derive from a careful inspection of a relative Minimal Model Program ran from a suitable smooth relative projective model o"},"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":"1710.09108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-10-25T08:20:37Z","cross_cats_sorted":[],"title_canon_sha256":"cbc3b51d8b90d779f6b219d574b2d64abc6837fdbb583254229158abc45a1386","abstract_canon_sha256":"62219ee2bbf4dffb11319ec12f5468f450807a5a5badb2d2daadde577cdd1dd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:00.337715Z","signature_b64":"2+smSg44FYOn1XMUqOUQYjwi1DeF2XMJUMvy725KOqZvzllrRPoMCk0sQZJtnYyFZPhLtu26fPnEf+mWKNTVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f54ce83e58722e9b7586788f640aa58ad612411d3a94d57a1989acee30dc8a61","last_reissued_at":"2026-05-18T00:32:00.337223Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:00.337223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deformations of $\\mathbb{A}^1$-cylindrical varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB), Takashi Kishimoto","submitted_at":"2017-10-25T08:20:37Z","abstract_excerpt":"An algebraic variety is called $\\mathbb{A}^{1}$-cylindrical if it contains an $\\mathbb{A}^{1}$-cylinder, i.e. a Zariski open subset of the form $Z\\times\\mathbb{A}^{1}$ for some algebraic variety Z. We show that the generic fiber of a family $f:X\\rightarrow S$ of normal $\\mathbb{A}^{1}$-cylindrical varieties becomes $\\mathbb{A}^{1}$-cylindrical after a finite extension of the base. Our second result is a criterion for existence of an $\\mathbb{A}^{1}$-cylinder in X which we derive from a careful inspection of a relative Minimal Model Program ran from a suitable smooth relative projective model o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09108","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.09108","created_at":"2026-05-18T00:32:00.337295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.09108v1","created_at":"2026-05-18T00:32:00.337295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09108","created_at":"2026-05-18T00:32:00.337295+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VGOQPSYOIXJ","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VGOQPSYOIXJW5MG","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VGOQPSY","created_at":"2026-05-18T12:31:03.183658+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/6VGOQPSYOIXJW5MGPCHWICVFRL","json":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL.json","graph_json":"https://pith.science/api/pith-number/6VGOQPSYOIXJW5MGPCHWICVFRL/graph.json","events_json":"https://pith.science/api/pith-number/6VGOQPSYOIXJW5MGPCHWICVFRL/events.json","paper":"https://pith.science/paper/6VGOQPSY"},"agent_actions":{"view_html":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL","download_json":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL.json","view_paper":"https://pith.science/paper/6VGOQPSY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.09108&json=true","fetch_graph":"https://pith.science/api/pith-number/6VGOQPSYOIXJW5MGPCHWICVFRL/graph.json","fetch_events":"https://pith.science/api/pith-number/6VGOQPSYOIXJW5MGPCHWICVFRL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL/action/storage_attestation","attest_author":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL/action/author_attestation","sign_citation":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL/action/citation_signature","submit_replication":"https://pith.science/pith/6VGOQPSYOIXJW5MGPCHWICVFRL/action/replication_record"}},"created_at":"2026-05-18T00:32:00.337295+00:00","updated_at":"2026-05-18T00:32:00.337295+00:00"}