{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:WZCHITMM6G5Y7GSSJNKDEWH4CK","short_pith_number":"pith:WZCHITMM","schema_version":"1.0","canonical_sha256":"b644744d8cf1bb8f9a524b543258fc129092bd6c6d33c1cc9733b3dc2a940532","source":{"kind":"arxiv","id":"math/0310060","version":1},"attestation_state":"computed","paper":{"title":"The Stable Equivalence and Cancellation Problems","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jie-Tai Yu, Leonid Makar-Limanov, Peter van Rossum, Vladimir Shpilrain","submitted_at":"2003-10-05T19:17:59Z","abstract_excerpt":"Let $K$ be an arbitrary field of characteristic 0, and $\\Aff^n$ the $n$-dimensional affine space over $K$. A well-known cancellation problem asks, given two algebraic varieties $V_1, V_2 \\subseteq \\Aff^n$ with isomorphic cylinders $V_1 \\times \\Aff^1$ and $V_2 \\times \\Aff^1$, whether $V_1$ and $V_2$ themselves are isomorphic.\n In this paper, we focus on a related problem: given two varieties with equivalent (under an automorphism of $\\Aff^{n+1}$) cylinders $V_1 \\times \\Aff^1$ and $V_2 \\times \\Aff^1$, are $V_1$ and $V_2$ equivalent under an automorphism of $\\Aff^n$? We call this stable equivalen"},"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":"math/0310060","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2003-10-05T19:17:59Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"c02c7c9047dfa980b656fa6c4d9a1482cdc644a88f1d4e0a3b5aacbf04b129c6","abstract_canon_sha256":"737d1da5c7cee3ad63008250d7967e9259533815ceef6009818465f231eed919"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:28.593486Z","signature_b64":"tR+A+crzzvBbewJuoWH69QyTzsbyU1KMDRyt0DYHKBJ+pjngbXKlYqEAiK8+5DPIe7kqhgzXC8f2BXOtz9CkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b644744d8cf1bb8f9a524b543258fc129092bd6c6d33c1cc9733b3dc2a940532","last_reissued_at":"2026-05-18T01:05:28.593056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:28.593056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Stable Equivalence and Cancellation Problems","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jie-Tai Yu, Leonid Makar-Limanov, Peter van Rossum, Vladimir Shpilrain","submitted_at":"2003-10-05T19:17:59Z","abstract_excerpt":"Let $K$ be an arbitrary field of characteristic 0, and $\\Aff^n$ the $n$-dimensional affine space over $K$. A well-known cancellation problem asks, given two algebraic varieties $V_1, V_2 \\subseteq \\Aff^n$ with isomorphic cylinders $V_1 \\times \\Aff^1$ and $V_2 \\times \\Aff^1$, whether $V_1$ and $V_2$ themselves are isomorphic.\n In this paper, we focus on a related problem: given two varieties with equivalent (under an automorphism of $\\Aff^{n+1}$) cylinders $V_1 \\times \\Aff^1$ and $V_2 \\times \\Aff^1$, are $V_1$ and $V_2$ equivalent under an automorphism of $\\Aff^n$? We call this stable equivalen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0310060","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":"math/0310060","created_at":"2026-05-18T01:05:28.593126+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0310060v1","created_at":"2026-05-18T01:05:28.593126+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0310060","created_at":"2026-05-18T01:05:28.593126+00:00"},{"alias_kind":"pith_short_12","alias_value":"WZCHITMM6G5Y","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"WZCHITMM6G5Y7GSS","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"WZCHITMM","created_at":"2026-05-18T12:25:52.051335+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/WZCHITMM6G5Y7GSSJNKDEWH4CK","json":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK.json","graph_json":"https://pith.science/api/pith-number/WZCHITMM6G5Y7GSSJNKDEWH4CK/graph.json","events_json":"https://pith.science/api/pith-number/WZCHITMM6G5Y7GSSJNKDEWH4CK/events.json","paper":"https://pith.science/paper/WZCHITMM"},"agent_actions":{"view_html":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK","download_json":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK.json","view_paper":"https://pith.science/paper/WZCHITMM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0310060&json=true","fetch_graph":"https://pith.science/api/pith-number/WZCHITMM6G5Y7GSSJNKDEWH4CK/graph.json","fetch_events":"https://pith.science/api/pith-number/WZCHITMM6G5Y7GSSJNKDEWH4CK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK/action/storage_attestation","attest_author":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK/action/author_attestation","sign_citation":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK/action/citation_signature","submit_replication":"https://pith.science/pith/WZCHITMM6G5Y7GSSJNKDEWH4CK/action/replication_record"}},"created_at":"2026-05-18T01:05:28.593126+00:00","updated_at":"2026-05-18T01:05:28.593126+00:00"}