{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FTWMC67L7DJYKIU2VFSB53ZO2T","short_pith_number":"pith:FTWMC67L","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"},"canonical_sha256":"2cecc17bebf8d385229aa9641eef2ed4e71d29988c992548a2f8262538385489","source":{"kind":"arxiv","id":"2411.15856","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15856","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15856v2","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15856","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"FTWMC67L7DJY","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"pith_short_16","alias_value":"FTWMC67L7DJYKIU2","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"pith_short_8","alias_value":"FTWMC67L","created_at":"2026-07-01T01:17:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FTWMC67L7DJYKIU2VFSB53ZO2T","target":"record","payload":{"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"},"canonical_sha256":"2cecc17bebf8d385229aa9641eef2ed4e71d29988c992548a2f8262538385489","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"},"source_kind":"arxiv","source_id":"2411.15856","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-01T01:17:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l5fqJXSf5xoljZvY+8WHRFeQl3hWXyvstMAAot+N8n9J84wYVNTP9AAFIux+JVB685GWM9Dp8ydHmJhoNF3xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:18:37.950447Z"},"content_sha256":"6bd34c53b5da549619b7c894e18500f2212cdea7cbf91874145dd328c3296827","schema_version":"1.0","event_id":"sha256:6bd34c53b5da549619b7c894e18500f2212cdea7cbf91874145dd328c3296827"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FTWMC67L7DJYKIU2VFSB53ZO2T","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-01T01:17:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MxgymetDkJkqcTsWvhDeXvH9uTpYzfMNnZwJuHvkelTE4yWccqhzk0lXxrU4UbiCC/M80KhbkZkrqqNVqkWzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:18:37.950993Z"},"content_sha256":"7d2ff305df49615ca4f6f15d4b1826b7d1b93052488d8f2713b979a31b55742b","schema_version":"1.0","event_id":"sha256:7d2ff305df49615ca4f6f15d4b1826b7d1b93052488d8f2713b979a31b55742b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/bundle.json","state_url":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T14:18:37Z","links":{"resolver":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T","bundle":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/bundle.json","state":"https://pith.science/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FTWMC67L7DJYKIU2VFSB53ZO2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FTWMC67L7DJYKIU2VFSB53ZO2T","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":"4857a0661ccc05faf826a9c5321917fbc66d70220ee94c8c1cd83565d90e46a5","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-11-24T14:20:56Z","title_canon_sha256":"5eeb45512efb16ed0097db2fdb797fbd15fa2c9b38fa5b4a19b3a5eaf897ba57"},"schema_version":"1.0","source":{"id":"2411.15856","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15856","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15856v2","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15856","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"pith_short_12","alias_value":"FTWMC67L7DJY","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"pith_short_16","alias_value":"FTWMC67L7DJYKIU2","created_at":"2026-07-01T01:17:38Z"},{"alias_kind":"pith_short_8","alias_value":"FTWMC67L","created_at":"2026-07-01T01:17:38Z"}],"graph_snapshots":[{"event_id":"sha256:7d2ff305df49615ca4f6f15d4b1826b7d1b93052488d8f2713b979a31b55742b","target":"graph","created_at":"2026-07-01T01:17:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.15856/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Chris Lambie-Hanson, Matteo Casarosa","cross_cats":["math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-11-24T14:20:56Z","title":"Simultaneously nonvanishing higher derived limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15856","kind":"arxiv","version":2},"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":"sha256:6bd34c53b5da549619b7c894e18500f2212cdea7cbf91874145dd328c3296827","target":"record","created_at":"2026-07-01T01:17:38Z","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":"4857a0661ccc05faf826a9c5321917fbc66d70220ee94c8c1cd83565d90e46a5","cross_cats_sorted":["math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-11-24T14:20:56Z","title_canon_sha256":"5eeb45512efb16ed0097db2fdb797fbd15fa2c9b38fa5b4a19b3a5eaf897ba57"},"schema_version":"1.0","source":{"id":"2411.15856","kind":"arxiv","version":2}},"canonical_sha256":"2cecc17bebf8d385229aa9641eef2ed4e71d29988c992548a2f8262538385489","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cecc17bebf8d385229aa9641eef2ed4e71d29988c992548a2f8262538385489","first_computed_at":"2026-07-01T01:17:38.492901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:38.492901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ufG/MbauggXTXp6E64NCMacsUYU/AMicxVJqZ6wxJ4+dew0ZEa1AX9Bf8ZfXQa7m0Y/N9ShJ0uh5XZSwTJPHAw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:38.493418Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15856","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bd34c53b5da549619b7c894e18500f2212cdea7cbf91874145dd328c3296827","sha256:7d2ff305df49615ca4f6f15d4b1826b7d1b93052488d8f2713b979a31b55742b"],"state_sha256":"edb355cca7ae180980b72f3f681e5812e130622389b59403cf2e620d0ace2fc7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S6PqYGonzhTDG457FSOxdD838mNS1VicH1W+IUHr0bFssOxIZfHhIk8leWMrdCZMUL6xmwl3CjycvzUMpjFDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:18:37.956019Z","bundle_sha256":"21b3b0eba6aa78eee37a6618e5fde8a89b59032776796da5de065645935a8c02"}}