{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KWKSH4XOKWNB43LXTI2XKSX72B","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":"32f7bcb87b1209d6ccb8e5d0132a763bb3315561f25e4c65614fe5cf60cca7d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-08-06T11:39:21Z","title_canon_sha256":"e46357e9e87fa9be856be31f3e3ffebd2ee702c26e07032a38b1c6b2e5425544"},"schema_version":"1.0","source":{"id":"1508.01366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01366","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01366v1","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01366","created_at":"2026-05-18T01:35:42Z"},{"alias_kind":"pith_short_12","alias_value":"KWKSH4XOKWNB","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KWKSH4XOKWNB43LX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KWKSH4XO","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:908df448b56037f069f94e76e211ff57d32b7bc7331a62d94effc8fe94212cea","target":"graph","created_at":"2026-05-18T01:35:42Z","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 investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\\to\\mathbb R$ which is not Baire measurable. We show that if $X$ is a product of normed spaces $X_n$, $a\\in X$ and $\\sigma(a)=\\{x\\in X:|\\{n\\in\\mathbb N: x_n\\ne a_n\\}|<\\aleph_0\\}$ is a subspace of $X$, equipped with the Tychonoff topology, then for any open set $G\\subseteq \\sigma(a)$ there is a strongly separately continuous function $f:\\sigma(a)\\to \\mathbb R$ such that the discontin","authors_text":"Olena Karlova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-08-06T11:39:21Z","title":"On Baire classification of strongly separately continuous functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01366","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":"sha256:8c452e14f7ab5f839192a47a891001e207f309bec213ab0395971af66d03f47e","target":"record","created_at":"2026-05-18T01:35:42Z","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":"32f7bcb87b1209d6ccb8e5d0132a763bb3315561f25e4c65614fe5cf60cca7d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-08-06T11:39:21Z","title_canon_sha256":"e46357e9e87fa9be856be31f3e3ffebd2ee702c26e07032a38b1c6b2e5425544"},"schema_version":"1.0","source":{"id":"1508.01366","kind":"arxiv","version":1}},"canonical_sha256":"559523f2ee559a1e6d779a35754affd05f569eef0ac790ec891f6d483207bdc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"559523f2ee559a1e6d779a35754affd05f569eef0ac790ec891f6d483207bdc4","first_computed_at":"2026-05-18T01:35:42.786988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:42.786988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/OE0fmlqa4mE8r4ar+xtf84g8CcDgk0W1htPTKcsCvGIsg3Qq9l9TEKJsFMf8Ok2npExj2m788poYps2f4VGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:42.787513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c452e14f7ab5f839192a47a891001e207f309bec213ab0395971af66d03f47e","sha256:908df448b56037f069f94e76e211ff57d32b7bc7331a62d94effc8fe94212cea"],"state_sha256":"ab206aa3d9c9408b6d1a4233eb89801c4f3283dee756f282aa6bdd861ffdf0ed"}