{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:CZZTZPNOG6SP2BFPD7GVU4BYBC","short_pith_number":"pith:CZZTZPNO","schema_version":"1.0","canonical_sha256":"16733cbdae37a4fd04af1fcd5a7038088bad4e003f9b7a037ed0bb2529abcbc6","source":{"kind":"arxiv","id":"2211.11110","version":2},"attestation_state":"computed","paper":{"title":"$K$-Theory of Truncated Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.NT"],"primary_cat":"math.KT","authors_text":"Noah Riggenbach","submitted_at":"2022-11-20T22:45:01Z","abstract_excerpt":"We study the algebraic $K$-theory of rings of the form $R[x]/x^e$. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for $R$ a perfectoid ring in terms of the big Witt vectors of $R$, for $R$ a smooth curve over a perfectoid ring in terms of the prismatic cohomology of $R$, and for $R$ a complete mixed characteristic discrete valuation rings with perfect residue field in terms of the prismatic cohomology and Hodge-Tate divisor of $R$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2211.11110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2022-11-20T22:45:01Z","cross_cats_sorted":["math.AT","math.NT"],"title_canon_sha256":"69ac25b878e5e435f8e6d21e1c4c733f7882dbcb07c86b572af40018ad56db1b","abstract_canon_sha256":"c07ab2007bbd473d025e031ab5378d202a0c0c45f2cc40fda99d9280476f7f51"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:07:09.401975Z","signature_b64":"adJFERB/+ca2HJUdzeisqJhv/x7qXT0dbe+9W2BSlAgQ812IaSz7PVr0YEbDB6edmBpmuIxPnWXvujmwIm/NCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16733cbdae37a4fd04af1fcd5a7038088bad4e003f9b7a037ed0bb2529abcbc6","last_reissued_at":"2026-07-05T06:07:09.401622Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:07:09.401622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$K$-Theory of Truncated Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.NT"],"primary_cat":"math.KT","authors_text":"Noah Riggenbach","submitted_at":"2022-11-20T22:45:01Z","abstract_excerpt":"We study the algebraic $K$-theory of rings of the form $R[x]/x^e$. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for $R$ a perfectoid ring in terms of the big Witt vectors of $R$, for $R$ a smooth curve over a perfectoid ring in terms of the prismatic cohomology of $R$, and for $R$ a complete mixed characteristic discrete valuation rings with perfect residue field in terms of the prismatic cohomology and Hodge-Tate divisor of $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.11110","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.11110/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2211.11110","created_at":"2026-07-05T06:07:09.401680+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.11110v2","created_at":"2026-07-05T06:07:09.401680+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.11110","created_at":"2026-07-05T06:07:09.401680+00:00"},{"alias_kind":"pith_short_12","alias_value":"CZZTZPNOG6SP","created_at":"2026-07-05T06:07:09.401680+00:00"},{"alias_kind":"pith_short_16","alias_value":"CZZTZPNOG6SP2BFP","created_at":"2026-07-05T06:07:09.401680+00:00"},{"alias_kind":"pith_short_8","alias_value":"CZZTZPNO","created_at":"2026-07-05T06:07:09.401680+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.19929","citing_title":"Cyclotomic synthetic spectra","ref_index":36,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC","json":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC.json","graph_json":"https://pith.science/api/pith-number/CZZTZPNOG6SP2BFPD7GVU4BYBC/graph.json","events_json":"https://pith.science/api/pith-number/CZZTZPNOG6SP2BFPD7GVU4BYBC/events.json","paper":"https://pith.science/paper/CZZTZPNO"},"agent_actions":{"view_html":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC","download_json":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC.json","view_paper":"https://pith.science/paper/CZZTZPNO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.11110&json=true","fetch_graph":"https://pith.science/api/pith-number/CZZTZPNOG6SP2BFPD7GVU4BYBC/graph.json","fetch_events":"https://pith.science/api/pith-number/CZZTZPNOG6SP2BFPD7GVU4BYBC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC/action/storage_attestation","attest_author":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC/action/author_attestation","sign_citation":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC/action/citation_signature","submit_replication":"https://pith.science/pith/CZZTZPNOG6SP2BFPD7GVU4BYBC/action/replication_record"}},"created_at":"2026-07-05T06:07:09.401680+00:00","updated_at":"2026-07-05T06:07:09.401680+00:00"}