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That means that we construct hypersurfaces $H_1, H_2\\subset\\mathbb{C}^{d+1}$ whose cylinders $H_1\\times\\mathbb{C}$ and $H_2\\times\\mathbb{C}$ are equivalent hypersurfaces in $\\mathbb{C}^{d+2}$, although $H_1$ and $H_2$ themselves are not equivalent by an automorphism of $\\mathbb{C}^{d+1}$. We also give, for every $d\\geq2$, examples of two non-isomorphic algebraic varieties of dimension $d$ which are biholomorphic."},"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":"1308.2652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-08-12T19:20:34Z","cross_cats_sorted":[],"title_canon_sha256":"b934c63eaad06f402ace908b0eab40f9b6a941aa65e4a8f48be6bc9990ec929f","abstract_canon_sha256":"8aad62a7b9fa10f65391208b4018eb3815d50e37b318c333bab460a3d9ac5748"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:06.929694Z","signature_b64":"Xd+tteVIw23bCfp9YB03uo9+TF70UThPnI7WdKSXPjbjNsZMBCB5JPJysGSj/cUhwGNTuoOUfOclVhOszDMZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12222c0a58c4292a78704a2496962f2f00b6da23382643e27cecf9336275b3ea","last_reissued_at":"2026-05-18T03:16:06.929020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:06.929020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the stable equivalence problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Pierre-Marie Poloni","submitted_at":"2013-08-12T19:20:34Z","abstract_excerpt":"We provide counterexamples to the stable equivalence problem in every dimension $d\\geq2$. 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