{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HT3C6AR6CPWWCWBNRF2D7H4ONX","short_pith_number":"pith:HT3C6AR6","schema_version":"1.0","canonical_sha256":"3cf62f023e13ed61582d89743f9f8e6dd9f75e25c0f0b2091af59c8594175413","source":{"kind":"arxiv","id":"1208.0483","version":2},"attestation_state":"computed","paper":{"title":"A Counter-example to the Cancellation Problem for the Affine Space A^3 in characteristic p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Neena Gupta","submitted_at":"2012-08-02T13:52:51Z","abstract_excerpt":"We show that the Cancellation Conjecture does not hold for the affine space A^3_k over any field k of positive characteristic. We prove that an example of T. Asanuma provides a three-dimensional k-algebra A for which A is not isomorphic to k[X_1,X_2,X_3] although A[T] is isomorphic to k[X_1, X_2, X_3, X_4]."},"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":"1208.0483","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-02T13:52:51Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"edb934eb7fcd521c439ea7615f46bce553aa1de3f26d8da96ee75638912d6214","abstract_canon_sha256":"f17d5d71fef3a6a2391e61f31bf456caee6e39013fe1529057c38c18d50031a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:40.964831Z","signature_b64":"fBezKQ87dzb1V/BrsRozN0g0ivtkxeiYVSZKZysll95CqC9QfGFV5kJuhCDS0kwxpk4uynDCX/12AK/R+7kcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cf62f023e13ed61582d89743f9f8e6dd9f75e25c0f0b2091af59c8594175413","last_reissued_at":"2026-05-18T03:35:40.963955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:40.963955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Counter-example to the Cancellation Problem for the Affine Space A^3 in characteristic p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Neena Gupta","submitted_at":"2012-08-02T13:52:51Z","abstract_excerpt":"We show that the Cancellation Conjecture does not hold for the affine space A^3_k over any field k of positive characteristic. We prove that an example of T. Asanuma provides a three-dimensional k-algebra A for which A is not isomorphic to k[X_1,X_2,X_3] although A[T] is isomorphic to k[X_1, X_2, X_3, X_4]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0483","kind":"arxiv","version":2},"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":"1208.0483","created_at":"2026-05-18T03:35:40.964102+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.0483v2","created_at":"2026-05-18T03:35:40.964102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0483","created_at":"2026-05-18T03:35:40.964102+00:00"},{"alias_kind":"pith_short_12","alias_value":"HT3C6AR6CPWW","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HT3C6AR6CPWWCWBN","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HT3C6AR6","created_at":"2026-05-18T12:27:09.501522+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/HT3C6AR6CPWWCWBNRF2D7H4ONX","json":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX.json","graph_json":"https://pith.science/api/pith-number/HT3C6AR6CPWWCWBNRF2D7H4ONX/graph.json","events_json":"https://pith.science/api/pith-number/HT3C6AR6CPWWCWBNRF2D7H4ONX/events.json","paper":"https://pith.science/paper/HT3C6AR6"},"agent_actions":{"view_html":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX","download_json":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX.json","view_paper":"https://pith.science/paper/HT3C6AR6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.0483&json=true","fetch_graph":"https://pith.science/api/pith-number/HT3C6AR6CPWWCWBNRF2D7H4ONX/graph.json","fetch_events":"https://pith.science/api/pith-number/HT3C6AR6CPWWCWBNRF2D7H4ONX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX/action/storage_attestation","attest_author":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX/action/author_attestation","sign_citation":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX/action/citation_signature","submit_replication":"https://pith.science/pith/HT3C6AR6CPWWCWBNRF2D7H4ONX/action/replication_record"}},"created_at":"2026-05-18T03:35:40.964102+00:00","updated_at":"2026-05-18T03:35:40.964102+00:00"}