{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:L6XG52VNI7J32S6DFFTFJS7SEF","short_pith_number":"pith:L6XG52VN","schema_version":"1.0","canonical_sha256":"5fae6eeaad47d3bd4bc3296654cbf2215100a1c169abe98e312ef30d408901ef","source":{"kind":"arxiv","id":"1908.09164","version":3},"attestation_state":"computed","paper":{"title":"A homological approach to chromatic complexity of algebraic K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Gabriel Angelini-Knoll, J.D. Quigley","submitted_at":"2019-08-24T16:34:10Z","abstract_excerpt":"The family of Thom spectra $y(n)$ interpolates between the sphere spectrum and the mod two Eilenberg--MacLane spectrum. Computations of Mahowald, Ravenel, Shick, and the authors show that the associative ring spectrum $y(n)$ has type $n$. Using trace methods, we give evidence that algebraic K-theory preserves this chromatic complexity. Our approach sheds light on the chromatic complexity of topological negative cyclic homology and topological periodic cyclic homology, which approximate algebraic K-theory and are of independent interest. Our main contribution is a homological approach that can "},"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":"1908.09164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-08-24T16:34:10Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"c2bf1e253b5a3a2a1bb41b89210a31710b6f209250e52180895995c8efbcba0c","abstract_canon_sha256":"6db1eab19282b5ebdd71b60da3b638f426252987d35388ee0208cf0073f89ba7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:44.391481Z","signature_b64":"uGvQ5zt7F19v8G1NRzTOyL7PGW/oOhW4JbUPe4koPmK1vyCIZeadiQORuLs9s7djIGqcwQhqGZ32nrnNh/F0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fae6eeaad47d3bd4bc3296654cbf2215100a1c169abe98e312ef30d408901ef","last_reissued_at":"2026-07-05T11:14:44.391044Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:44.391044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A homological approach to chromatic complexity of algebraic K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Gabriel Angelini-Knoll, J.D. Quigley","submitted_at":"2019-08-24T16:34:10Z","abstract_excerpt":"The family of Thom spectra $y(n)$ interpolates between the sphere spectrum and the mod two Eilenberg--MacLane spectrum. Computations of Mahowald, Ravenel, Shick, and the authors show that the associative ring spectrum $y(n)$ has type $n$. Using trace methods, we give evidence that algebraic K-theory preserves this chromatic complexity. Our approach sheds light on the chromatic complexity of topological negative cyclic homology and topological periodic cyclic homology, which approximate algebraic K-theory and are of independent interest. Our main contribution is a homological approach that can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09164","kind":"arxiv","version":3},"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/1908.09164/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":"1908.09164","created_at":"2026-07-05T11:14:44.391092+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.09164v3","created_at":"2026-07-05T11:14:44.391092+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.09164","created_at":"2026-07-05T11:14:44.391092+00:00"},{"alias_kind":"pith_short_12","alias_value":"L6XG52VNI7J3","created_at":"2026-07-05T11:14:44.391092+00:00"},{"alias_kind":"pith_short_16","alias_value":"L6XG52VNI7J32S6D","created_at":"2026-07-05T11:14:44.391092+00:00"},{"alias_kind":"pith_short_8","alias_value":"L6XG52VN","created_at":"2026-07-05T11:14:44.391092+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF","json":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF.json","graph_json":"https://pith.science/api/pith-number/L6XG52VNI7J32S6DFFTFJS7SEF/graph.json","events_json":"https://pith.science/api/pith-number/L6XG52VNI7J32S6DFFTFJS7SEF/events.json","paper":"https://pith.science/paper/L6XG52VN"},"agent_actions":{"view_html":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF","download_json":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF.json","view_paper":"https://pith.science/paper/L6XG52VN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.09164&json=true","fetch_graph":"https://pith.science/api/pith-number/L6XG52VNI7J32S6DFFTFJS7SEF/graph.json","fetch_events":"https://pith.science/api/pith-number/L6XG52VNI7J32S6DFFTFJS7SEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF/action/storage_attestation","attest_author":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF/action/author_attestation","sign_citation":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF/action/citation_signature","submit_replication":"https://pith.science/pith/L6XG52VNI7J32S6DFFTFJS7SEF/action/replication_record"}},"created_at":"2026-07-05T11:14:44.391092+00:00","updated_at":"2026-07-05T11:14:44.391092+00:00"}