{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ADTAJ6LF2YM463JEIL7VU7OJWI","short_pith_number":"pith:ADTAJ6LF","schema_version":"1.0","canonical_sha256":"00e604f965d619cf6d2442ff5a7dc9b23370f8792669516271e7144aefdc827e","source":{"kind":"arxiv","id":"2410.07048","version":2},"attestation_state":"computed","paper":{"title":"Syntomic cohomology of Morava K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"Dylan Wilson, Gabriel Angelini-Knoll, Jeremy Hahn","submitted_at":"2024-10-09T16:39:45Z","abstract_excerpt":"We compute the MU-based syntomic cohomologies, mod $(p,v_1,\\cdots,v_{n+1})$, of all $\\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope conjecture, and redshift conjecture for the algebraic K-theories of all $\\mathbb{E}_{1}$-$\\mathbb{S}$-algebra forms of $(2p^n-2)$-periodic Morava K-theory. Notably, the motivic spectral sequence computing $\\pi_*TC(k(n))_p$ is concentrated on at most three lines, independently of $n$."},"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":"2410.07048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-10-09T16:39:45Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"4f58e36c5666bd32e84206f3c872368ce76777e6e17658ee931847faa63e47f1","abstract_canon_sha256":"97f15a84c1c10bbe0f678d405fa3a34e4fdcdc9393a03fb3be3375949cce833c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:47:31.675519Z","signature_b64":"L8hVWsHdZkf3jX1hrU5Quu6nNB2G8f4xYm+eFshhgWud3/Q5DcvxHDaxxsPxRc7nvh2e8rthg57Y2S/BNOYLBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00e604f965d619cf6d2442ff5a7dc9b23370f8792669516271e7144aefdc827e","last_reissued_at":"2026-07-05T10:47:31.675006Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:47:31.675006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Syntomic cohomology of Morava K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.KT","authors_text":"Dylan Wilson, Gabriel Angelini-Knoll, Jeremy Hahn","submitted_at":"2024-10-09T16:39:45Z","abstract_excerpt":"We compute the MU-based syntomic cohomologies, mod $(p,v_1,\\cdots,v_{n+1})$, of all $\\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope conjecture, and redshift conjecture for the algebraic K-theories of all $\\mathbb{E}_{1}$-$\\mathbb{S}$-algebra forms of $(2p^n-2)$-periodic Morava K-theory. Notably, the motivic spectral sequence computing $\\pi_*TC(k(n))_p$ is concentrated on at most three lines, independently of $n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07048","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/2410.07048/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":"2410.07048","created_at":"2026-07-05T10:47:31.675074+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.07048v2","created_at":"2026-07-05T10:47:31.675074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.07048","created_at":"2026-07-05T10:47:31.675074+00:00"},{"alias_kind":"pith_short_12","alias_value":"ADTAJ6LF2YM4","created_at":"2026-07-05T10:47:31.675074+00:00"},{"alias_kind":"pith_short_16","alias_value":"ADTAJ6LF2YM463JE","created_at":"2026-07-05T10:47:31.675074+00:00"},{"alias_kind":"pith_short_8","alias_value":"ADTAJ6LF","created_at":"2026-07-05T10:47:31.675074+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/ADTAJ6LF2YM463JEIL7VU7OJWI","json":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI.json","graph_json":"https://pith.science/api/pith-number/ADTAJ6LF2YM463JEIL7VU7OJWI/graph.json","events_json":"https://pith.science/api/pith-number/ADTAJ6LF2YM463JEIL7VU7OJWI/events.json","paper":"https://pith.science/paper/ADTAJ6LF"},"agent_actions":{"view_html":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI","download_json":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI.json","view_paper":"https://pith.science/paper/ADTAJ6LF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.07048&json=true","fetch_graph":"https://pith.science/api/pith-number/ADTAJ6LF2YM463JEIL7VU7OJWI/graph.json","fetch_events":"https://pith.science/api/pith-number/ADTAJ6LF2YM463JEIL7VU7OJWI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI/action/storage_attestation","attest_author":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI/action/author_attestation","sign_citation":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI/action/citation_signature","submit_replication":"https://pith.science/pith/ADTAJ6LF2YM463JEIL7VU7OJWI/action/replication_record"}},"created_at":"2026-07-05T10:47:31.675074+00:00","updated_at":"2026-07-05T10:47:31.675074+00:00"}