{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XRCRHIZXOL7LCZSV7FYQXLSFZ7","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":"5a7289cec8a87527acffed2efd3969f07c0b59e1117006fd88d05da7d88685c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-05-14T14:19:04Z","title_canon_sha256":"88e8271580cb7f6f8b2c20c869179b74aa723c2a7dde5e1a560263ded3e5d8dd"},"schema_version":"1.0","source":{"id":"1205.3674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3674","created_at":"2026-05-18T03:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3674v1","created_at":"2026-05-18T03:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3674","created_at":"2026-05-18T03:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"XRCRHIZXOL7L","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XRCRHIZXOL7LCZSV","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XRCRHIZX","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:488de9a6b08fabb2fafb6ee89e6351be0df6ca760f57f04d836da61acc5c8441","target":"graph","created_at":"2026-05-18T03:55:34Z","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":"A real function $f$ is ward continuous if $f$ preserves quasi-Cauchyness, i.e. $(f(x_{n}))$ is a quasi-Cauchy sequence whenever $(x_{n})$ is quasi-Cauchy; and a subset $E$ of $\\textbf{R}$ is quasi-Cauchy compact if any sequence $\\textbf{x}=(x_{n})$ of points in $E$ has a quasi-Cauchy subsequence where $\\textbf{R}$ is the set of real numbers. These known results suggest to us introducing a concept of upward (respectively, downward) half quasi-Cauchy continuity in the sense that a function $f$ is upward (respectively, downward) half quasi-Cauchy continuous if it preserves upward (respectively, d","authors_text":"Huseyin Cakalli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-05-14T14:19:04Z","title":"Half quasi-Cauchy sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3674","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:f90d6bd6839edff31baee4d5ee4f9f41929efab4804348c252bc5364402bbefe","target":"record","created_at":"2026-05-18T03:55:34Z","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":"5a7289cec8a87527acffed2efd3969f07c0b59e1117006fd88d05da7d88685c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-05-14T14:19:04Z","title_canon_sha256":"88e8271580cb7f6f8b2c20c869179b74aa723c2a7dde5e1a560263ded3e5d8dd"},"schema_version":"1.0","source":{"id":"1205.3674","kind":"arxiv","version":1}},"canonical_sha256":"bc4513a33772feb16655f9710bae45cfdedd72a6e966dee04897d03fbf76e3d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc4513a33772feb16655f9710bae45cfdedd72a6e966dee04897d03fbf76e3d1","first_computed_at":"2026-05-18T03:55:34.458189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:34.458189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zffP+2FI8fKe5f2dph8I/XZv2wa7kHNwnkcJyfxb5aVjZMWZlsspH/CwKuqbS/RfkiLr6UcO1C8QDG2hHIPrDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:34.459024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f90d6bd6839edff31baee4d5ee4f9f41929efab4804348c252bc5364402bbefe","sha256:488de9a6b08fabb2fafb6ee89e6351be0df6ca760f57f04d836da61acc5c8441"],"state_sha256":"56250da0d220e3b1594f52a6f34fb39bafb3e59e13872f7c9f5a6b4e6671773e"}