{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HPKN2ECLPAMG6CLXFGTSOONRF2","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":"46a11dbcd5cdc001f597bf724c88969af139d090a2d37ec0b06eb5906cc6f43a","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-02T17:12:25Z","title_canon_sha256":"6135c475a9378c80bd34c13ac1b1a353fb7bd849e2b0eb8a5727b22b442e4c49"},"schema_version":"1.0","source":{"id":"1304.0698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0698","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0698v2","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0698","created_at":"2026-05-18T01:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"HPKN2ECLPAMG","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HPKN2ECLPAMG6CLX","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HPKN2ECL","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:4814f6bfaad22b694896aa2ad4b4538c98935c76f2cdcce7133575e59cb83ad8","target":"graph","created_at":"2026-05-18T01:06:23Z","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":"Jayne and Rogers proved that every function from an analytic space into a separable metric space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each $F_\\sigma$ set under it is again $F_\\sigma$. Many researchers conjectured that the Jayne-Rogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-Slaman join theorem on the Turing degrees, we show the following variant of the Jayne-Rogers theorem at finite and transfinite levels of the hierarchy of Borel functions: For all countable ord","authors_text":"Takayuki Kihara","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-02T17:12:25Z","title":"Decomposing Borel functions using the Shore-Slaman join theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0698","kind":"arxiv","version":2},"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:fc2e1a01506d503453bdd9710e1e8efda6fcbdd45490e25b6f36b8169621faf5","target":"record","created_at":"2026-05-18T01:06:23Z","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":"46a11dbcd5cdc001f597bf724c88969af139d090a2d37ec0b06eb5906cc6f43a","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-02T17:12:25Z","title_canon_sha256":"6135c475a9378c80bd34c13ac1b1a353fb7bd849e2b0eb8a5727b22b442e4c49"},"schema_version":"1.0","source":{"id":"1304.0698","kind":"arxiv","version":2}},"canonical_sha256":"3bd4dd104b78186f097729a72739b12ea0730a9f402c4ce1fecc5fddebeae68a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bd4dd104b78186f097729a72739b12ea0730a9f402c4ce1fecc5fddebeae68a","first_computed_at":"2026-05-18T01:06:23.298010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:23.298010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/mNQn31tbTTrmA7hhvfm+RYPakzhm2eOUFQ35tD4VBNUOOAr3B/LRjDYke/5rJia1HGqs/ya4viZ2mC/GYAaBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:23.298454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc2e1a01506d503453bdd9710e1e8efda6fcbdd45490e25b6f36b8169621faf5","sha256:4814f6bfaad22b694896aa2ad4b4538c98935c76f2cdcce7133575e59cb83ad8"],"state_sha256":"6ad233cdff9a221e3a1f281a0772d8ea843ffe387efd6b3280b195188442dd31"}