{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YSKBDQ3M7XC7TZYA24CROXCIRO","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":"f1d281d728050a17b56d54ca166428deefafa858ee82334d4b19786771a21761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-17T20:22:41Z","title_canon_sha256":"8514410f15d1887d9cbed607f7f1268d249530d26cf9038a60ffc434bb4cffc8"},"schema_version":"1.0","source":{"id":"1011.4697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4697","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4697v1","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4697","created_at":"2026-05-18T04:03:57Z"},{"alias_kind":"pith_short_12","alias_value":"YSKBDQ3M7XC7","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YSKBDQ3M7XC7TZYA","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YSKBDQ3M","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:ccfb9ddbc32fba840d000a419c6d715b4bc6170e95b1f8eba72c8efcf72717e5","target":"graph","created_at":"2026-05-18T04:03:57Z","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"},"paper":{"abstract_excerpt":"Cauchy's condensation test allows to determine the convergence of a monotone series by looking at a weighted subseries that only involves terms of the original series indexed by the powers of two. It is natural to ask whether the converse is also true: Is it possible to determine the convergence of an arbitrary subseries of a monotone series by looking at a suitably weighted version of the original series? In this note we show that the answer is affirmative and introduce a new convergence test particularly designed for this purpose.","authors_text":"Lasse Leskel\\\"a, Mikko Stenlund","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-17T20:22:41Z","title":"A Dilution Test for the Convergence of Subseries of a Monotone Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4697","kind":"arxiv","version":1},"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":"sha256:4ae21fa4e3b6243d48a1ce26e74999d0efe8a66874d9714ade3b26f4df82fa9d","target":"record","created_at":"2026-05-18T04:03:57Z","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":"f1d281d728050a17b56d54ca166428deefafa858ee82334d4b19786771a21761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-11-17T20:22:41Z","title_canon_sha256":"8514410f15d1887d9cbed607f7f1268d249530d26cf9038a60ffc434bb4cffc8"},"schema_version":"1.0","source":{"id":"1011.4697","kind":"arxiv","version":1}},"canonical_sha256":"c49411c36cfdc5f9e700d705175c488b801bc5ecdc54c68c831d76163c0f09f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c49411c36cfdc5f9e700d705175c488b801bc5ecdc54c68c831d76163c0f09f3","first_computed_at":"2026-05-18T04:03:57.019508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:57.019508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pifANbzWNFs/pNbDZhO56VXm0Q6ce0e2WItNSq5nC5iQ99C78NCUUYKoEOimG//BYFA9SF+OTYZoatbljv0DCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:57.020001Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4697","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ae21fa4e3b6243d48a1ce26e74999d0efe8a66874d9714ade3b26f4df82fa9d","sha256:ccfb9ddbc32fba840d000a419c6d715b4bc6170e95b1f8eba72c8efcf72717e5"],"state_sha256":"599d1a0bcf36d092ae4a888c29a8bdc6f552be300eb0daec9c2684b0a9428ec7"}