{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6PGGRNDHOJU7FFVLC7RUEFHUWA","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":"0ebcc6d5332c42f2d07e447a0395deefb6552bb5411a5bbd79f2ffc90da7efea","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-09-23T23:04:53Z","title_canon_sha256":"0bd82a92e940f723caecb9e594571cdac9826d41b1163fd5fb2492dff36457b8"},"schema_version":"1.0","source":{"id":"1409.6770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6770","created_at":"2026-05-18T02:42:00Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6770v1","created_at":"2026-05-18T02:42:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6770","created_at":"2026-05-18T02:42:00Z"},{"alias_kind":"pith_short_12","alias_value":"6PGGRNDHOJU7","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6PGGRNDHOJU7FFVL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6PGGRNDH","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:0e23af8138251b0fa99847881444b4466cd0fe0a6fdb7d68e4dac65ca0f62c71","target":"graph","created_at":"2026-05-18T02:42:00Z","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":"We show that for any bounded function $f:[a,b]\\rightarrow{\\mathbb R}$ and $\\epsilon>0$ there is a partition $P$ of $[a,b]$ with respect to which the Riemann sum of $f$ using right endpoints is within $\\epsilon$ of the upper Darboux sum of $f$. This leads to an elementary proof of the theorem of Gillespie \\cite{G} showing that Cauchy's and Riemann's definitions of integrability coincide.","authors_text":"Scott Schneider","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-09-23T23:04:53Z","title":"A note on Cauchy integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6770","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":"sha256:5bb39a5a7e785afd443aefcce1c9e5ece83146b3fc124ac7d500ffcd6e75caa3","target":"record","created_at":"2026-05-18T02:42:00Z","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":"0ebcc6d5332c42f2d07e447a0395deefb6552bb5411a5bbd79f2ffc90da7efea","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2014-09-23T23:04:53Z","title_canon_sha256":"0bd82a92e940f723caecb9e594571cdac9826d41b1163fd5fb2492dff36457b8"},"schema_version":"1.0","source":{"id":"1409.6770","kind":"arxiv","version":1}},"canonical_sha256":"f3cc68b4677269f296ab17e34214f4b03f7c75a9b84b14d3879780fc5655bc4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3cc68b4677269f296ab17e34214f4b03f7c75a9b84b14d3879780fc5655bc4a","first_computed_at":"2026-05-18T02:42:00.453534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:00.453534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"altq62eVRByfqPMKA2a2T9T98u3zclE4guTI+bOs4SWGpfI3/NOvxS8nscSXxq5JKdzRaswu+0zupLjo2AE6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:00.453897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bb39a5a7e785afd443aefcce1c9e5ece83146b3fc124ac7d500ffcd6e75caa3","sha256:0e23af8138251b0fa99847881444b4466cd0fe0a6fdb7d68e4dac65ca0f62c71"],"state_sha256":"b04f088158239e66d5fe22294638b6777eb8ce8452bb22d7e01c2d996f92455c"}