{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UQ3HHPQFGZOJ6NDRNHCGQLFFM3","short_pith_number":"pith:UQ3HHPQF","schema_version":"1.0","canonical_sha256":"a43673be05365c9f347169c4682ca566ece6f3b6526807a0f29ab7b4560b0316","source":{"kind":"arxiv","id":"1710.04405","version":1},"attestation_state":"computed","paper":{"title":"On Variations of statistical ward continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Huseyin Cakalli","submitted_at":"2017-10-12T08:20:01Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.04405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-12T08:20:01Z","cross_cats_sorted":[],"title_canon_sha256":"a5435ed20cc1e68341e74313bf5ee50e7dd68e5c9d27b31e990d5636018a6e8a","abstract_canon_sha256":"faeb80cd0024057821e42809ee60b6b1b3ead337af6f64534332bac5233860b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:01.173573Z","signature_b64":"dExo630BaAEnxzBpUoBHl0/LA4YNF8uyT7IKuErT9FCMbHCjzc0nJlOrCW4AaEas4oc1jwBYzeuw9pjOpQM+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a43673be05365c9f347169c4682ca566ece6f3b6526807a0f29ab7b4560b0316","last_reissued_at":"2026-05-18T00:33:01.172869Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:01.172869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Variations of statistical ward continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Huseyin Cakalli","submitted_at":"2017-10-12T08:20:01Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04405","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.04405","created_at":"2026-05-18T00:33:01.172983+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.04405v1","created_at":"2026-05-18T00:33:01.172983+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.04405","created_at":"2026-05-18T00:33:01.172983+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQ3HHPQFGZOJ","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQ3HHPQFGZOJ6NDR","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQ3HHPQF","created_at":"2026-05-18T12:31:46.661854+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3","json":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3.json","graph_json":"https://pith.science/api/pith-number/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/graph.json","events_json":"https://pith.science/api/pith-number/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/events.json","paper":"https://pith.science/paper/UQ3HHPQF"},"agent_actions":{"view_html":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3","download_json":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3.json","view_paper":"https://pith.science/paper/UQ3HHPQF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.04405&json=true","fetch_graph":"https://pith.science/api/pith-number/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/graph.json","fetch_events":"https://pith.science/api/pith-number/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/action/storage_attestation","attest_author":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/action/author_attestation","sign_citation":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/action/citation_signature","submit_replication":"https://pith.science/pith/UQ3HHPQFGZOJ6NDRNHCGQLFFM3/action/replication_record"}},"created_at":"2026-05-18T00:33:01.172983+00:00","updated_at":"2026-05-18T00:33:01.172983+00:00"}