{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MOOV4LT36D4PUBKVO4IS76TDKW","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":"1f9f9851b5ebc911b29159f9edfd13f1fc02e65228de32129fdd80c24ac4c240","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T05:58:08Z","title_canon_sha256":"b4534eb438782768f0637d56c05790679f5959258662e64d6f09fa43331d1ebf"},"schema_version":"1.0","source":{"id":"2606.22887","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22887","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22887v1","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22887","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_12","alias_value":"MOOV4LT36D4P","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_16","alias_value":"MOOV4LT36D4PUBKV","created_at":"2026-06-23T03:14:03Z"},{"alias_kind":"pith_short_8","alias_value":"MOOV4LT3","created_at":"2026-06-23T03:14:03Z"}],"graph_snapshots":[{"event_id":"sha256:ed95224eb5a71eaaa9b9b12db1ec1ac1f2e0671aa11ee3bf7ce3859b2cbc8422","target":"graph","created_at":"2026-06-23T03:14:03Z","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/2606.22887/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Over a qcqs scheme $S$, we analyze the birational localization $L_{\\mathrm{bir}}\\mathcal{H}^{\\mathbb{A}^1}(S)$ of the motivic $\\infty$-category. As introduced in [\\cite{bachmann2019voevodsky}], this is obtained by localizing $\\mathcal{H}^{\\mathbb{A}^1}(S)$ at all dense open immersions in $Sm_S$. We establish that the associated localization functor $L_{bir}$ commutes with the bar construction, and thus preserves connectivity. Over a perfect field $k$, we demonstrate that a sheaf of groups is birational exactly when it is strongly $\\mathbb{A}^1$-invariant and has trivial $\\mathbb{G}_m$-contract","authors_text":"Dipankar Maity","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T05:58:08Z","title":"Birational Algebraic Topology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22887","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:a1918319c7f07c42310df86b5f5cc92e1f17be8f4b6e081584b0e55d3d09d78c","target":"record","created_at":"2026-06-23T03:14:03Z","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":"1f9f9851b5ebc911b29159f9edfd13f1fc02e65228de32129fdd80c24ac4c240","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-22T05:58:08Z","title_canon_sha256":"b4534eb438782768f0637d56c05790679f5959258662e64d6f09fa43331d1ebf"},"schema_version":"1.0","source":{"id":"2606.22887","kind":"arxiv","version":1}},"canonical_sha256":"639d5e2e7bf0f8fa055577112ffa63559388de285029c61538e4d026a5757396","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"639d5e2e7bf0f8fa055577112ffa63559388de285029c61538e4d026a5757396","first_computed_at":"2026-06-23T03:14:03.277648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:03.277648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r7Cv5akSJY9vktajux3TGACkuuaVmafNahV31R+fecmZcNAr5PH+k1+ZauxLj/Xj/PS9CY7Ws20aeRRdAJyODA==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:03.278041Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22887","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1918319c7f07c42310df86b5f5cc92e1f17be8f4b6e081584b0e55d3d09d78c","sha256:ed95224eb5a71eaaa9b9b12db1ec1ac1f2e0671aa11ee3bf7ce3859b2cbc8422"],"state_sha256":"ab2046c76fb1672ddf243de74849de557737cec867ba4ac8acb11b13f94f3772"}