{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3UCRXUOAYZBCYPRFF7Q3VBT34H","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":"e961603f40317544317f72326bf0cccc38cd397231e70ddec7d0402b89e58fe0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-27T18:43:47Z","title_canon_sha256":"12e8de7a647b20fc63a26cb89f1e15852bb636baaa6dcb9183bf748dfc0fcf84"},"schema_version":"1.0","source":{"id":"2606.29044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29044","created_at":"2026-06-30T01:17:50Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29044v1","created_at":"2026-06-30T01:17:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29044","created_at":"2026-06-30T01:17:50Z"},{"alias_kind":"pith_short_12","alias_value":"3UCRXUOAYZBC","created_at":"2026-06-30T01:17:50Z"},{"alias_kind":"pith_short_16","alias_value":"3UCRXUOAYZBCYPRF","created_at":"2026-06-30T01:17:50Z"},{"alias_kind":"pith_short_8","alias_value":"3UCRXUOA","created_at":"2026-06-30T01:17:50Z"}],"graph_snapshots":[{"event_id":"sha256:22995df3c150df267591ff70029ec5415fbed436be8ae20b29cbac278ebb5871","target":"graph","created_at":"2026-06-30T01:17:50Z","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/2606.29044/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let \\(S_b\\) be the class of birational morphisms between smooth varieties over a field \\(F\\), and let \\(L_n=S_b^{-1}d_{\\leq n}\\Sm(F)\\). Kahn and Sujatha asked whether the natural functor \\(L_n\\to S_b^{-1}\\Sm(F)\\) is fully faithful. We prove that it is fully faithful exactly for \\(n=0\\). More strongly, for every \\(n\\geq1\\) and every \\(N\\geq n+1\\), the transition functor \\(L_n\\to L_N\\) has an infinite fibre on an endomorphism set. The proof identifies a sharp dimension threshold: if \\(\\dim X+r\\leq n\\), then \\(X\\times\\mathbb A^r\\to X\\) is invertible in \\(L_n\\) precisely when \\(\\dim X+r\\leq n-1\\).","authors_text":"David Kumallagov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-27T18:43:47Z","title":"Dimension filtrations in birational localisation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29044","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":"sha256:4867a02478024a83bd0788939a4222551671f481efa4bb697e6ca8b08ee2b7a9","target":"record","created_at":"2026-06-30T01:17:50Z","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":"e961603f40317544317f72326bf0cccc38cd397231e70ddec7d0402b89e58fe0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-27T18:43:47Z","title_canon_sha256":"12e8de7a647b20fc63a26cb89f1e15852bb636baaa6dcb9183bf748dfc0fcf84"},"schema_version":"1.0","source":{"id":"2606.29044","kind":"arxiv","version":1}},"canonical_sha256":"dd051bd1c0c6422c3e252fe1ba867be1ea80e1956b8038b3b6b424d9cfd1516a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd051bd1c0c6422c3e252fe1ba867be1ea80e1956b8038b3b6b424d9cfd1516a","first_computed_at":"2026-06-30T01:17:50.542449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:17:50.542449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FtTOBblFl9P+cykI8GhYlNi+xEu3Hq9JZO0UaJPj0ahfAQxO04MTpKr9pTWcL3ZrO3iIjStjdRlo3pDXubVwCA==","signature_status":"signed_v1","signed_at":"2026-06-30T01:17:50.543284Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4867a02478024a83bd0788939a4222551671f481efa4bb697e6ca8b08ee2b7a9","sha256:22995df3c150df267591ff70029ec5415fbed436be8ae20b29cbac278ebb5871"],"state_sha256":"5de01d9fa6e8727608f509d8698b7caeea095a16b47ea704d78394916d87946a"}