{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WFETYJGFGE73WD6MUAYNVCFRTT","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":"6765160a95c535a000f754798b3dd762b84dafeadeb999e5743932f70d4c017c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-27T06:37:56Z","title_canon_sha256":"333028e90785eafb66212a098f39728cd141414eae131d5b8d9920c78a72f188"},"schema_version":"1.0","source":{"id":"1605.08516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08516","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08516v1","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08516","created_at":"2026-05-18T01:13:29Z"},{"alias_kind":"pith_short_12","alias_value":"WFETYJGFGE73","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WFETYJGFGE73WD6M","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WFETYJGF","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:7ae3edd21e9aa9e8df9f6ba310351cc3d5a5da79e9195fef8d52e62d4ab85134","target":"graph","created_at":"2026-05-18T01:13:29Z","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 classical theorem of Menshov states that every measurable function can redefined on a set of arbitrarily small Lebesgue measure, so that the resulting function has uniformly convergent Fourier series. We prove that the same is true if we replace Lebesgue measure with an arbitrary Borel measure.","authors_text":"Themis Mitsis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-27T06:37:56Z","title":"Menshov' \"adjustment theorem\" with respect to general measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08516","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":"sha256:47bfe87ea86e11ab7adeaa1d40fe618c27484a324d6140a06d152d7ccb16631d","target":"record","created_at":"2026-05-18T01:13:29Z","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":"6765160a95c535a000f754798b3dd762b84dafeadeb999e5743932f70d4c017c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-05-27T06:37:56Z","title_canon_sha256":"333028e90785eafb66212a098f39728cd141414eae131d5b8d9920c78a72f188"},"schema_version":"1.0","source":{"id":"1605.08516","kind":"arxiv","version":1}},"canonical_sha256":"b1493c24c5313fbb0fcca030da88b19ccef65016df2dc34db37b4880a6cdeb4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1493c24c5313fbb0fcca030da88b19ccef65016df2dc34db37b4880a6cdeb4f","first_computed_at":"2026-05-18T01:13:29.707345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:29.707345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/iuLMH3A6QTv3YHKE1X99L6OBH0YD9XVGbcr8RXooG6KAwoD9o6+OMgmn05Mq52TCzOLfDQKqoCiLkoGHAESDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:29.708000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47bfe87ea86e11ab7adeaa1d40fe618c27484a324d6140a06d152d7ccb16631d","sha256:7ae3edd21e9aa9e8df9f6ba310351cc3d5a5da79e9195fef8d52e62d4ab85134"],"state_sha256":"7bd5dcfc11378c0ead133bd46d20d4dadf7d83993f5855f94e180cdb5ee20f91"}