{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:25FVA4TYTQEMFNMERECQG2EXLO","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":"1dc7cb4568c5c528498438b5c526b2766d4bd24f66a7542a7558ac864471511d","cross_cats_sorted":["math.CA","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-26T20:11:02Z","title_canon_sha256":"426de3bc1f895ee023b1e558c8446856bb6ddbce8ce4c3281f9ad0947615c3f4"},"schema_version":"1.0","source":{"id":"1005.4940","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4940","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4940v3","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4940","created_at":"2026-05-18T04:40:30Z"},{"alias_kind":"pith_short_12","alias_value":"25FVA4TYTQEM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"25FVA4TYTQEMFNME","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"25FVA4TY","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:fc48853d76c086ef9a56afc8c59de4fbbe719384abdc37de5c08dbb80313c995","target":"graph","created_at":"2026-05-18T04:40:30Z","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":"Recently, a concept of forward continuity and a concept of forward compactness are introduced in the senses that a function $f$ is forward continuous if $\\lim_{n\\to\\infty} \\Delta f(x_{n})=0$ whenever $\\lim_{n\\to\\infty} \\Delta x_{n}=0$,\\; and a subset $E$ of $\\textbf{R}$ is forward compact if any sequence $\\textbf{x}=(x_{n})$ of points in $E$ has a subsequence $\\textbf{z}=(z_{k})=(x_{n_{k}})$ of the sequence $\\textbf{x}$ such that $\\lim_{k\\to \\infty} \\Delta z_{k}=0$ where $\\Delta z_{k}=z_{k+1}-z_{k}$. These concepts suggest us to introduce a concept of second forward continuity in the sense tha","authors_text":"Huseyin Cakalli","cross_cats":["math.CA","math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-26T20:11:02Z","title":"$delta$-Quasi Cauchy Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4940","kind":"arxiv","version":3},"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":"sha256:693e36edf8e0e1536dffcf912dca11fd7f9734748ca88503e0e1f3eb65f00317","target":"record","created_at":"2026-05-18T04:40:30Z","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":"1dc7cb4568c5c528498438b5c526b2766d4bd24f66a7542a7558ac864471511d","cross_cats_sorted":["math.CA","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-05-26T20:11:02Z","title_canon_sha256":"426de3bc1f895ee023b1e558c8446856bb6ddbce8ce4c3281f9ad0947615c3f4"},"schema_version":"1.0","source":{"id":"1005.4940","kind":"arxiv","version":3}},"canonical_sha256":"d74b5072789c08c2b58489050368975b8ad0d679c38799ebd58a99236a84f30a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d74b5072789c08c2b58489050368975b8ad0d679c38799ebd58a99236a84f30a","first_computed_at":"2026-05-18T04:40:30.627687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:30.627687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WZ1vQ+Ao7epeJJdjNLWHV9WsMlOdhv+k8SU2thdsnzgm/89UJiGbdDZG1LWUVMxEEDSl0JF2zP7cxJ5b06ITBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:30.628252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4940","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:693e36edf8e0e1536dffcf912dca11fd7f9734748ca88503e0e1f3eb65f00317","sha256:fc48853d76c086ef9a56afc8c59de4fbbe719384abdc37de5c08dbb80313c995"],"state_sha256":"470eea7e64129a45c757cdbcceb1d17cc5e194beb4e56415870fdf768b5d2494"}