{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:O2VTE3GBGKRFIFDCEUG5HTC2PW","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":"5cb9ec8320b1db9e223f83aa21ab82af64311baec2a6d83477bdf923a5fc0ae8","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1994-11-07T00:00:00Z","title_canon_sha256":"a4122cd392cd8bb3367d744cdc3c5281770356de93ad51c1b2920840bae04a43"},"schema_version":"1.0","source":{"id":"math/9411206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9411206","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9411206v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9411206","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"O2VTE3GBGKRF","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"O2VTE3GBGKRFIFDC","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"O2VTE3GB","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:a2c85ade961dfb45dec9fcc77be32a00889cf331656ed591daac38fdeceeb85b","target":"graph","created_at":"2026-05-18T01:05:50Z","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 function f:R -> R is approximately continuous iff it is continuous in the density topology, i.e., for any ordinary open set U the set E=f^{-1}(U) is measurable and has Lebesgue density one at each of its points. Denjoy proved that approximately continuous functions are Baire 1., i.e., pointwise For any f:R^2 -> R define f_x(y) = f^y(x) = f(x,y). A function f:R^2 -> R is separately continuous if f_x and f^y are continuous for every x,y in R. Lebesgue in his first paper proved that any separately continuous function is Baire 1. Sierpinski showed that there exists a nonmeasurable f:R^2 -> R whi","authors_text":"Arnold W. Miller, M. Laczkovich","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1994-11-07T00:00:00Z","title":"Measurability of functions with approximately continuous vertical sections and measurable horizontal sections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9411206","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":"sha256:0fc81be5949f659bb0ca0fa0f69e32133f17c2b913b67c54afaa1cf895212038","target":"record","created_at":"2026-05-18T01:05:50Z","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":"5cb9ec8320b1db9e223f83aa21ab82af64311baec2a6d83477bdf923a5fc0ae8","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1994-11-07T00:00:00Z","title_canon_sha256":"a4122cd392cd8bb3367d744cdc3c5281770356de93ad51c1b2920840bae04a43"},"schema_version":"1.0","source":{"id":"math/9411206","kind":"arxiv","version":1}},"canonical_sha256":"76ab326cc132a2541462250dd3cc5a7dbb6de2668b42aa762ec5f907b9f1cf7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76ab326cc132a2541462250dd3cc5a7dbb6de2668b42aa762ec5f907b9f1cf7b","first_computed_at":"2026-05-18T01:05:50.902193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.902193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"29AyuogENFShjHWQ1lt2RhfsDnw++o1gYbGOFlN8k8bMAs87uoFuugQcqYBSrx4G7VXTOjW6ls1F5EHSHt9pBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.902614Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9411206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fc81be5949f659bb0ca0fa0f69e32133f17c2b913b67c54afaa1cf895212038","sha256:a2c85ade961dfb45dec9fcc77be32a00889cf331656ed591daac38fdeceeb85b"],"state_sha256":"7f147464a2c961f579b006d995e1c16773bcdd3d9c85fbbfa9ff758c29fbcda7"}