{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QSADWOVGMTM3L4OYI6E6CAA2ZV","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":"0c54fefbc215f1ad6b29c1d1f39d848483dd29f1d61ed28e5d65cffacf8421ef","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-09T16:28:01Z","title_canon_sha256":"051f7e3a3d3b30f7c8f3432d2d1e68ef869ccd4262e881674f8f071eba5fb2e4"},"schema_version":"1.0","source":{"id":"2412.06635","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.06635","created_at":"2026-07-05T11:40:32Z"},{"alias_kind":"arxiv_version","alias_value":"2412.06635v2","created_at":"2026-07-05T11:40:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.06635","created_at":"2026-07-05T11:40:32Z"},{"alias_kind":"pith_short_12","alias_value":"QSADWOVGMTM3","created_at":"2026-07-05T11:40:32Z"},{"alias_kind":"pith_short_16","alias_value":"QSADWOVGMTM3L4OY","created_at":"2026-07-05T11:40:32Z"},{"alias_kind":"pith_short_8","alias_value":"QSADWOVG","created_at":"2026-07-05T11:40:32Z"}],"graph_snapshots":[{"event_id":"sha256:e38ce5f7967be812edfd0f23ba462b1fe391492515924720813200a23158b68c","target":"graph","created_at":"2026-07-05T11:40:32Z","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/2412.06635/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a theory of motivic cohomology for quasi-compact quasi-separated schemes, which generalises the construction of Elmanto--Morrow in the case of schemes over a field. Our construction is non-$\\mathbb{A}^1$-invariant in general, but it uses the classical $\\mathbb{A}^1$-invariant motivic cohomology of smooth $\\mathbb{Z}$-schemes as an input. The main new input of our construction is a global filtration on topological cyclic homology, whose graded pieces provide an integral refinement of derived de Rham cohomology and Bhatt--Morrow--Scholze's syntomic cohomology. Our theory satisfies v","authors_text":"Tess Bouis","cross_cats":["math.KT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-09T16:28:01Z","title":"Motivic cohomology of mixed characteristic schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06635","kind":"arxiv","version":2},"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":"sha256:6e3ec102ac9efe8843ee05ce2236a9ebde4f5316ee0484a867ec3dab38d2036e","target":"record","created_at":"2026-07-05T11:40:32Z","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":"0c54fefbc215f1ad6b29c1d1f39d848483dd29f1d61ed28e5d65cffacf8421ef","cross_cats_sorted":["math.KT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-12-09T16:28:01Z","title_canon_sha256":"051f7e3a3d3b30f7c8f3432d2d1e68ef869ccd4262e881674f8f071eba5fb2e4"},"schema_version":"1.0","source":{"id":"2412.06635","kind":"arxiv","version":2}},"canonical_sha256":"84803b3aa664d9b5f1d84789e1001acd5dbde0b77fc49fa86512d37d25150323","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84803b3aa664d9b5f1d84789e1001acd5dbde0b77fc49fa86512d37d25150323","first_computed_at":"2026-07-05T11:40:32.041650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:32.041650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8knC+Oe97djZ3JWraJTICo/jwTk3v+/072F2ABnX80ESenEd+3TuAAn70pwJH+KFp1nkdxnM4QbfBfHHf9sLCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:32.042147Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.06635","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e3ec102ac9efe8843ee05ce2236a9ebde4f5316ee0484a867ec3dab38d2036e","sha256:e38ce5f7967be812edfd0f23ba462b1fe391492515924720813200a23158b68c"],"state_sha256":"a595f6491237cc79f110871289e5f46c70d02c7217b06046e550e151d42192df"}