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As a consequence, for any unibranch scheme $X$, its (zeroth) birational motivic homotopy category $\\mathcal{H}^{b\\mathbb{A}^1}(X)$ decomposes as the product of the birational motivic homotopy categories of its function fields; in particular, for a variety $V$, $\\mathcal{H}^{b\\mathbb{A}^1}(V) \\simeq \\mathcal{H}^{b\\mathbb{A}^1}(k(V))$. This implies that birational equivalences of unibranch schemes in $Sm_S$ can be detected by the birational contractib"},"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":"2608.04793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-05T12:58:35Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"3b7bc623d0ce5582a51a7f94d1419dd702d4b6e52d35723420894959386fed54","abstract_canon_sha256":"b5e84a0975c6ad67526dfd8eefd581fd12b14ced1233cda4ca98e477c35f1e54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:47:07.452429Z","signature_b64":"W2ovNXZIn5/lrePoAOD3graEAVEpLljVWJgNSaMOtwvTm5ptLw1OPIl8isRIIO1T6JAqd3bV96q5KWknlYz3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc520c4c83354802a12a30a3c15b70c49f06c5a0dc4b31a820b77636ef7fdea3","last_reissued_at":"2026-08-06T01:47:07.450961Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:47:07.450961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Schematic Functorialities of Birational Motivic Homotopy Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.AG","authors_text":"Dipankar Maity","submitted_at":"2026-08-05T12:58:35Z","abstract_excerpt":"We promote the $n$-birational motivic homotopy category $S\\mapsto \\mathcal{H}^n(S)$ to a $Pr^L$-valued presheaf on $Corr(\\mathrm{Sch})_{uglt,sm}$. 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