{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7RJAYTEDGVEAFIJKGCR4CW3QYS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b5e84a0975c6ad67526dfd8eefd581fd12b14ced1233cda4ca98e477c35f1e54","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-05T12:58:35Z","title_canon_sha256":"3b7bc623d0ce5582a51a7f94d1419dd702d4b6e52d35723420894959386fed54"},"schema_version":"1.0","source":{"id":"2608.04793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04793","created_at":"2026-08-06T01:47:07Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04793v1","created_at":"2026-08-06T01:47:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04793","created_at":"2026-08-06T01:47:07Z"},{"alias_kind":"pith_short_12","alias_value":"7RJAYTEDGVEA","created_at":"2026-08-06T01:47:07Z"},{"alias_kind":"pith_short_16","alias_value":"7RJAYTEDGVEAFIJK","created_at":"2026-08-06T01:47:07Z"},{"alias_kind":"pith_short_8","alias_value":"7RJAYTED","created_at":"2026-08-06T01:47:07Z"}],"graph_snapshots":[{"event_id":"sha256:5b03ed3047ada16632f5f33fbb62599b6e0197f20642643805aeb822981b2517","target":"graph","created_at":"2026-08-06T01:47:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.04793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We promote the $n$-birational motivic homotopy category $S\\mapsto \\mathcal{H}^n(S)$ to a $Pr^L$-valued presheaf on $Corr(\\mathrm{Sch})_{uglt,sm}$. 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","authors_text":"Dipankar Maity","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-05T12:58:35Z","title":"Schematic Functorialities of Birational Motivic Homotopy Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04793","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dd3f4e226cf112c11b243582deb6dfb6fd45669c5ac49f3e0dcbb16573063a89","target":"record","created_at":"2026-08-06T01:47:07Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b5e84a0975c6ad67526dfd8eefd581fd12b14ced1233cda4ca98e477c35f1e54","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-05T12:58:35Z","title_canon_sha256":"3b7bc623d0ce5582a51a7f94d1419dd702d4b6e52d35723420894959386fed54"},"schema_version":"1.0","source":{"id":"2608.04793","kind":"arxiv","version":1}},"canonical_sha256":"fc520c4c83354802a12a30a3c15b70c49f06c5a0dc4b31a820b77636ef7fdea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc520c4c83354802a12a30a3c15b70c49f06c5a0dc4b31a820b77636ef7fdea3","first_computed_at":"2026-08-06T01:47:07.450961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:47:07.450961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2ovNXZIn5/lrePoAOD3graEAVEpLljVWJgNSaMOtwvTm5ptLw1OPIl8isRIIO1T6JAqd3bV96q5KWknlYz3BA==","signature_status":"signed_v1","signed_at":"2026-08-06T01:47:07.452429Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd3f4e226cf112c11b243582deb6dfb6fd45669c5ac49f3e0dcbb16573063a89","sha256:5b03ed3047ada16632f5f33fbb62599b6e0197f20642643805aeb822981b2517"],"state_sha256":"e8c99ed0c49b260c00f5db43c54f7990a108dc3dcc16ae904e91a9ea74d84997"}