{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VEKWOYN77UJD537SHR2LFOQQ3W","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":"8070ea904e96323a9d81a908f5275982017530a1dbe8b0b7901b1d0202afafc9","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-31T19:38:41Z","title_canon_sha256":"15374a6ac01775de0b643681a053c702bcf3d19cd1e3331ce3e63080edbd27bd"},"schema_version":"1.0","source":{"id":"1801.00343","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00343","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00343v2","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00343","created_at":"2026-05-17T23:43:33Z"},{"alias_kind":"pith_short_12","alias_value":"VEKWOYN77UJD","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VEKWOYN77UJD537S","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VEKWOYN7","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:5e275fcc0dc139f597e0fe296bab67a6d733e2de559207212c4cfc5e2ad6f881","target":"graph","created_at":"2026-05-17T23:43:33Z","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":"Let $x$ be a sequence taking values in a separable metric space and $\\mathcal{I}$ be a generalized density ideal or an $F_\\sigma$-ideal on the positive integers (in particular, $\\mathcal{I}$ can be any Erd{\\H o}s--Ulam ideal or any summable ideal). It is shown that the collection of subsequences of $x$ which preserve the set of $\\mathcal{I}$-cluster points of $x$ [respectively, $\\mathcal{I}$-limit points] is of second category if and only if the set of $\\mathcal{I}$-cluster points of $x$ [resp., $\\mathcal{I}$-limit points] coincides with the set of ordinary limit points of $x$; moreover, in th","authors_text":"Paolo Leonetti","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-31T19:38:41Z","title":"Limit points of subsequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00343","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:b1fde1a0b95769f1db35aa4d586de74096428138998249e5dc305e3a946a72be","target":"record","created_at":"2026-05-17T23:43:33Z","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":"8070ea904e96323a9d81a908f5275982017530a1dbe8b0b7901b1d0202afafc9","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-31T19:38:41Z","title_canon_sha256":"15374a6ac01775de0b643681a053c702bcf3d19cd1e3331ce3e63080edbd27bd"},"schema_version":"1.0","source":{"id":"1801.00343","kind":"arxiv","version":2}},"canonical_sha256":"a9156761bffd123eeff23c74b2ba10dda5647d8e737f790b1fd8ce46287b66f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9156761bffd123eeff23c74b2ba10dda5647d8e737f790b1fd8ce46287b66f9","first_computed_at":"2026-05-17T23:43:33.409280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:33.409280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28U58FRqVVb0LhYPCcmt62vigxYmRQF4g9Exh/83IINirlVdOuyYuZuGtYj6POBWSHd/0DIaGelNzW4+SEPRBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:33.409650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00343","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1fde1a0b95769f1db35aa4d586de74096428138998249e5dc305e3a946a72be","sha256:5e275fcc0dc139f597e0fe296bab67a6d733e2de559207212c4cfc5e2ad6f881"],"state_sha256":"67a7a1b00a60deb8f13b8b1b64cf5eba1999b3d0457e66921129964fabe8a9bf"}