{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UQ3HHPQFGZOJ6NDRNHCGQLFFM3","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":"faeb80cd0024057821e42809ee60b6b1b3ead337af6f64534332bac5233860b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-12T08:20:01Z","title_canon_sha256":"a5435ed20cc1e68341e74313bf5ee50e7dd68e5c9d27b31e990d5636018a6e8a"},"schema_version":"1.0","source":{"id":"1710.04405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.04405","created_at":"2026-05-18T00:33:01Z"},{"alias_kind":"arxiv_version","alias_value":"1710.04405v1","created_at":"2026-05-18T00:33:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04405","created_at":"2026-05-18T00:33:01Z"},{"alias_kind":"pith_short_12","alias_value":"UQ3HHPQFGZOJ","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"UQ3HHPQFGZOJ6NDR","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"UQ3HHPQF","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:15d03008005348cda0307595d2df33cce30f0d47c0faecd04d3b7172ccdb4ae2","target":"graph","created_at":"2026-05-18T00:33:01Z","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":"In this paper, we introduce a concept of statistically $p$-quasi-Cauchyness of a real sequence in the sense that a sequence $(\\alpha_{k})$ is statistically $p$-quasi-Cauchy if $\\lim_{n\\rightarrow\\infty}\\frac{1}{n}|\\{k\\leq n: |\\alpha_{k+p}-\\alpha_{k}|\\geq{\\varepsilon}\\}|=0$ for each $\\varepsilon>0$. A function $f$ is called statistically $p$-ward continuous on a subset $A$ of the set of real umbers $\\mathbb{R}$ if it preserves statistically $p$-quasi-Cauchy sequences, i.e. the sequence $f(\\textbf{x})=(f(\\alpha_{n}))$ is statistically $p$-quasi-Cauchy whenever $\\boldsymbol\\alpha=(\\alpha_{n})$ is","authors_text":"Huseyin Cakalli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-12T08:20:01Z","title":"On Variations of statistical ward continuity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04405","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":"sha256:048cb3f607433890446aa20bc3dfa3ee2c369b04e209b3b2fe69e28c319fcb49","target":"record","created_at":"2026-05-18T00:33:01Z","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":"faeb80cd0024057821e42809ee60b6b1b3ead337af6f64534332bac5233860b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-12T08:20:01Z","title_canon_sha256":"a5435ed20cc1e68341e74313bf5ee50e7dd68e5c9d27b31e990d5636018a6e8a"},"schema_version":"1.0","source":{"id":"1710.04405","kind":"arxiv","version":1}},"canonical_sha256":"a43673be05365c9f347169c4682ca566ece6f3b6526807a0f29ab7b4560b0316","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a43673be05365c9f347169c4682ca566ece6f3b6526807a0f29ab7b4560b0316","first_computed_at":"2026-05-18T00:33:01.172869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:01.172869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dExo630BaAEnxzBpUoBHl0/LA4YNF8uyT7IKuErT9FCMbHCjzc0nJlOrCW4AaEas4oc1jwBYzeuw9pjOpQM+Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:01.173573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.04405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:048cb3f607433890446aa20bc3dfa3ee2c369b04e209b3b2fe69e28c319fcb49","sha256:15d03008005348cda0307595d2df33cce30f0d47c0faecd04d3b7172ccdb4ae2"],"state_sha256":"4e95fb675140e5e87d869841012685bb92dd777baa09a5ae1046bea1024aafef"}