{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SJD7FXVOTJZV5NUOJCCX6J3XFB","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":"4130d74446d99e16fd4512da304d0e17bebdd0fd5bf2856b5c6a14d241834823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-09T07:12:25Z","title_canon_sha256":"134c539c83b62574360acb20e5e872be8685fbecfe0609f36579ba3117d599f7"},"schema_version":"1.0","source":{"id":"1203.2003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2003","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2003v1","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2003","created_at":"2026-05-18T04:00:27Z"},{"alias_kind":"pith_short_12","alias_value":"SJD7FXVOTJZV","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SJD7FXVOTJZV5NUO","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SJD7FXVO","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:f627931d14b6b28c1b3b3bab8d3193432b728118d2a1326d3b921d8517354109","target":"graph","created_at":"2026-05-18T04:00:27Z","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":"An ideal $I$ is a family of subsets of positive integers $\\textbf{N}$ which is closed under taking finite unions and subsets of its elements. A sequence $(x_n)$ of real numbers is said to be $I$-convergent to a real number $L$, if for each \\;$ \\varepsilon> 0$ the set $\\{n:|x_{n}-L|\\geq \\varepsilon\\}$ belongs to $I$. We introduce $I$-ward compactness of a subset of $\\textbf{R}$, the set of real numbers, and $I$-ward continuity of a real function in the senses that a subset $E$ of $\\textbf{R}$ is $I$-ward compact if any sequence $(x_{n})$ of points in $E$ has an $I$-quasi-Cauchy subsequence, and","authors_text":"Bipan Hazarika, Huseyin Cakalli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-09T07:12:25Z","title":"Ideal-quasi-Cauchy sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2003","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":"sha256:37d87fdd7daafb6e4e51fb7ab4a8d2a11365599c9fe665b56f3346110f65bc05","target":"record","created_at":"2026-05-18T04:00:27Z","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":"4130d74446d99e16fd4512da304d0e17bebdd0fd5bf2856b5c6a14d241834823","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-09T07:12:25Z","title_canon_sha256":"134c539c83b62574360acb20e5e872be8685fbecfe0609f36579ba3117d599f7"},"schema_version":"1.0","source":{"id":"1203.2003","kind":"arxiv","version":1}},"canonical_sha256":"9247f2deae9a735eb68e48857f2777284d587046b804d79d8b3801e088e7da74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9247f2deae9a735eb68e48857f2777284d587046b804d79d8b3801e088e7da74","first_computed_at":"2026-05-18T04:00:27.755712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:27.755712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iz74KhqFTQojBWNIvzCECfp81UGauORdfdsj3pF5DXnKqzgtjgl4DoDqsH0/e18bPbLZXQSKUpwHTZxlci3NDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:27.756364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37d87fdd7daafb6e4e51fb7ab4a8d2a11365599c9fe665b56f3346110f65bc05","sha256:f627931d14b6b28c1b3b3bab8d3193432b728118d2a1326d3b921d8517354109"],"state_sha256":"e1d1e639507df66ebe2c4eb36c5e0d47e8df5bbdafa76acc0d2723009955c9a3"}