{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:FTWMC67L7DJYKIU2VFSB53ZO2T","short_pith_number":"pith:FTWMC67L","schema_version":"1.0","canonical_sha256":"2cecc17bebf8d385229aa9641eef2ed4e71d29988c992548a2f8262538385489","source":{"kind":"arxiv","id":"2411.15856","version":2},"attestation_state":"computed","paper":{"title":"Simultaneously nonvanishing higher derived limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson, Matteo Casarosa","submitted_at":"2024-11-24T14:20:56Z","abstract_excerpt":"The derived functors $\\lim^n$ of the inverse limit find many applications in algebra and topology. In particular, the vanishing of certain derived limits $\\lim^n \\mathbf{A}[H]$, parametrized by an abelian group $H$, has implications for strong homology and condensed mathematics. In this paper, we prove that if $\\mathfrak{d}=\\omega_n$, then $\\lim^n \\mathbf{A}[H] \\neq 0$ holds for $H=\\mathbb{Z}^{(\\omega_n)}$ (i.e. the direct sum of $\\omega_n$-many copies of $\\mathbb{Z}$). The same holds for $H=\\mathbb{Z}$ under the assumption that $\\mathrm{w}\\diamondsuit(S^{k+1}_k)$ holds for all $k < n$. In par"},"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":"2411.15856","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-11-24T14:20:56Z","cross_cats_sorted":["math.AT","math.CT"],"title_canon_sha256":"5eeb45512efb16ed0097db2fdb797fbd15fa2c9b38fa5b4a19b3a5eaf897ba57","abstract_canon_sha256":"4857a0661ccc05faf826a9c5321917fbc66d70220ee94c8c1cd83565d90e46a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:17:38.493418Z","signature_b64":"ufG/MbauggXTXp6E64NCMacsUYU/AMicxVJqZ6wxJ4+dew0ZEa1AX9Bf8ZfXQa7m0Y/N9ShJ0uh5XZSwTJPHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cecc17bebf8d385229aa9641eef2ed4e71d29988c992548a2f8262538385489","last_reissued_at":"2026-07-01T01:17:38.492901Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:17:38.492901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simultaneously nonvanishing higher derived limits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CT"],"primary_cat":"math.LO","authors_text":"Chris Lambie-Hanson, Matteo Casarosa","submitted_at":"2024-11-24T14:20:56Z","abstract_excerpt":"The derived functors $\\lim^n$ of the inverse limit find many applications in algebra and topology. In particular, the vanishing of certain derived limits $\\lim^n \\mathbf{A}[H]$, parametrized by an abelian group $H$, has implications for strong homology and condensed mathematics. In this paper, we prove that if $\\mathfrak{d}=\\omega_n$, then $\\lim^n \\mathbf{A}[H] \\neq 0$ holds for $H=\\mathbb{Z}^{(\\omega_n)}$ (i.e. the direct sum of $\\omega_n$-many copies of $\\mathbb{Z}$). The same holds for $H=\\mathbb{Z}$ under the assumption that $\\mathrm{w}\\diamondsuit(S^{k+1}_k)$ holds for all $k < n$. In par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15856","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/2411.15856/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":"2411.15856","created_at":"2026-07-01T01:17:38.492962+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.15856v2","created_at":"2026-07-01T01:17:38.492962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15856","created_at":"2026-07-01T01:17:38.492962+00:00"},{"alias_kind":"pith_short_12","alias_value":"FTWMC67L7DJY","created_at":"2026-07-01T01:17:38.492962+00:00"},{"alias_kind":"pith_short_16","alias_value":"FTWMC67L7DJYKIU2","created_at":"2026-07-01T01:17:38.492962+00:00"},{"alias_kind":"pith_short_8","alias_value":"FTWMC67L","created_at":"2026-07-01T01:17:38.492962+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.05471","citing_title":"Higher limits of wider systems","ref_index":11,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T","json":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T.json","graph_json":"https://pith.science/api/pith-number/FTWMC67L7DJYKIU2VFSB53ZO2T/graph.json","events_json":"https://pith.science/api/pith-number/FTWMC67L7DJYKIU2VFSB53ZO2T/events.json","paper":"https://pith.science/paper/FTWMC67L"},"agent_actions":{"view_html":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T","download_json":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T.json","view_paper":"https://pith.science/paper/FTWMC67L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.15856&json=true","fetch_graph":"https://pith.science/api/pith-number/FTWMC67L7DJYKIU2VFSB53ZO2T/graph.json","fetch_events":"https://pith.science/api/pith-number/FTWMC67L7DJYKIU2VFSB53ZO2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/action/storage_attestation","attest_author":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/action/author_attestation","sign_citation":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/action/citation_signature","submit_replication":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/action/replication_record"}},"created_at":"2026-07-01T01:17:38.492962+00:00","updated_at":"2026-07-01T01:17:38.492962+00:00"}