{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GLSA5UUQNS6WRSWXV46L4W45ZV","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":"6c7cb51282f41bf42f8f6f4b104d5bde19e2c7f44434ec9fe789b386e9537e01","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-02-19T17:06:23Z","title_canon_sha256":"1753a4e0e7d58109f7878258db8967d6ce7ca2c0ccc2d28ebd664e9dd77199ea"},"schema_version":"1.0","source":{"id":"1602.06222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06222","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06222v1","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06222","created_at":"2026-05-18T01:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"GLSA5UUQNS6W","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GLSA5UUQNS6WRSWX","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GLSA5UUQ","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:049056d3f816395a7de4c3068976319d9d2d3bd3b464d60644e9119e59cd8858","target":"graph","created_at":"2026-05-18T01:20:18Z","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"},"paper":{"abstract_excerpt":"For any complex scheme X or any dg category, there is an associated K-theory presheaf on the category of complex affine schemes. We study real smooth functions on this presheaf, defined by Kan extension, and show that they are closely related to real Deligne cohomology. When X is quasi-compact and semi-separated, and for various non-commutative derived schemes, these smooth functions on K-theory are dual to the homotopy fibre of the Chern character from Blanc's semi-topological K-theory to cyclic homology.","authors_text":"J.P.Pridham","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-02-19T17:06:23Z","title":"Smooth functions on algebraic K-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06222","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":"sha256:8438ed8327d4c687b8a4405790732a9ba68e2f26dc8c6c6d511678717a762288","target":"record","created_at":"2026-05-18T01:20:18Z","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":"6c7cb51282f41bf42f8f6f4b104d5bde19e2c7f44434ec9fe789b386e9537e01","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2016-02-19T17:06:23Z","title_canon_sha256":"1753a4e0e7d58109f7878258db8967d6ce7ca2c0ccc2d28ebd664e9dd77199ea"},"schema_version":"1.0","source":{"id":"1602.06222","kind":"arxiv","version":1}},"canonical_sha256":"32e40ed2906cbd68cad7af3cbe5b9dcd60fe077d47efc14f67f83d10e36c8992","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32e40ed2906cbd68cad7af3cbe5b9dcd60fe077d47efc14f67f83d10e36c8992","first_computed_at":"2026-05-18T01:20:18.369327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:18.369327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y+zTZc1qFPx07KQj9sujfhxBMu9co4lujymuLAU+VxlQQSFmoaLjyKVZCMAIwTeZaC+on2rct0J4z76rwgB5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:18.369850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8438ed8327d4c687b8a4405790732a9ba68e2f26dc8c6c6d511678717a762288","sha256:049056d3f816395a7de4c3068976319d9d2d3bd3b464d60644e9119e59cd8858"],"state_sha256":"ceef0d75e2c15c452f7520343eeb692b6e44c0b0fda847b741081ad11b9c0b65"}