{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2FXXZKYFCIWBOIH4DQGGJ4QBGF","short_pith_number":"pith:2FXXZKYF","schema_version":"1.0","canonical_sha256":"d16f7cab05122c1720fc1c0c64f20131435a803aa8320bbb7a6ff8177bae7414","source":{"kind":"arxiv","id":"1407.5745","version":1},"attestation_state":"computed","paper":{"title":"Diagonals of separately continuous functions and their analogs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Oleksandr Sobchuk, Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2014-07-22T06:12:19Z","abstract_excerpt":"We prove that for a topological space $X$, an equiconnected space $Z$ and a Baire-one mapping $g:X\\to Z$ there exists a separately continuous mapping $f:X^2\\to Z$ with the diagonal $g$, i.e. $g(x)=f(x,x)$ for every $x\\in X$. Under a mild assumptions on $X$ and $Z$ we obtain that diagonals of separately continuous mappings $f:X^2\\to Z$ are exactly Baire-one functions, and diagonals of mappings $f:X^2\\to Z$ which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.5745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2014-07-22T06:12:19Z","cross_cats_sorted":[],"title_canon_sha256":"86bcdff24430b837772555401ea272be298c5dfb418cc3120c3a1826cae0cebc","abstract_canon_sha256":"d421cabf58ea6ed941c6e698427a03d590932077f11ee9945afb5b5328eb6e5b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:06.714240Z","signature_b64":"MeLMuLPy61mse+a6u2Wof0JgCXY5Ah7FQMKIALgRlG8SQwwij/erjRC6ARZcoUS6VrHm5SeEdsQJOph/rw5fCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d16f7cab05122c1720fc1c0c64f20131435a803aa8320bbb7a6ff8177bae7414","last_reissued_at":"2026-05-18T02:47:06.713833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:06.713833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Diagonals of separately continuous functions and their analogs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Oleksandr Sobchuk, Olena Karlova, Volodymyr Mykhaylyuk","submitted_at":"2014-07-22T06:12:19Z","abstract_excerpt":"We prove that for a topological space $X$, an equiconnected space $Z$ and a Baire-one mapping $g:X\\to Z$ there exists a separately continuous mapping $f:X^2\\to Z$ with the diagonal $g$, i.e. $g(x)=f(x,x)$ for every $x\\in X$. Under a mild assumptions on $X$ and $Z$ we obtain that diagonals of separately continuous mappings $f:X^2\\to Z$ are exactly Baire-one functions, and diagonals of mappings $f:X^2\\to Z$ which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5745","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.5745","created_at":"2026-05-18T02:47:06.713900+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.5745v1","created_at":"2026-05-18T02:47:06.713900+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5745","created_at":"2026-05-18T02:47:06.713900+00:00"},{"alias_kind":"pith_short_12","alias_value":"2FXXZKYFCIWB","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2FXXZKYFCIWBOIH4","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2FXXZKYF","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF","json":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF.json","graph_json":"https://pith.science/api/pith-number/2FXXZKYFCIWBOIH4DQGGJ4QBGF/graph.json","events_json":"https://pith.science/api/pith-number/2FXXZKYFCIWBOIH4DQGGJ4QBGF/events.json","paper":"https://pith.science/paper/2FXXZKYF"},"agent_actions":{"view_html":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF","download_json":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF.json","view_paper":"https://pith.science/paper/2FXXZKYF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.5745&json=true","fetch_graph":"https://pith.science/api/pith-number/2FXXZKYFCIWBOIH4DQGGJ4QBGF/graph.json","fetch_events":"https://pith.science/api/pith-number/2FXXZKYFCIWBOIH4DQGGJ4QBGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF/action/storage_attestation","attest_author":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF/action/author_attestation","sign_citation":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF/action/citation_signature","submit_replication":"https://pith.science/pith/2FXXZKYFCIWBOIH4DQGGJ4QBGF/action/replication_record"}},"created_at":"2026-05-18T02:47:06.713900+00:00","updated_at":"2026-05-18T02:47:06.713900+00:00"}