{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NNQZO35LDSZNG45K6LFFUTMZZC","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":"f077fc295b2a876b94e20bf3a0cccc268f9a8938359f1dabc078ebe10367a8c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T05:26:03Z","title_canon_sha256":"435bcd2d0ee14c1a8c219e0883cf23622e0bd259e2f10edfd411245c52b34c9c"},"schema_version":"1.0","source":{"id":"1310.8028","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8028","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8028v2","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8028","created_at":"2026-05-18T02:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"NNQZO35LDSZN","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NNQZO35LDSZNG45K","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NNQZO35L","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:8dfad24b9b311129028df3f7a87a2fb51f637e8b8ee2a8e3028a0bfabb404cf5","target":"graph","created_at":"2026-05-18T02:42:28Z","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":"Let $E\\subseteq F$ and $E'\\subseteq F'$ be Borel equivalence relations on the standard Borel spaces $X$ and $Y$, respectively. The pair $(E,F)$ is simultaneously Borel reducible to the pair $(E',F')$ if there is a Borel function $f:X\\to Y$ that is both a reduction from $E$ to $E'$ and a reduction from $F$ to $F'$. Simultaneous Borel embeddings and isomorphisms are defined analogously. We classify all pairs $E\\subseteq F$ of smooth countable Borel equivalence relations up to simultaneous Borel bireducibility and biembeddability, and a significant portion of such pairs up to simultaneous Borel i","authors_text":"Scott Schneider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T05:26:03Z","title":"Simultaneous Reducibility of Pairs of Borel Equivalence Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8028","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:b8e794104b787b59db5ec7a1a903567aec4354251ed57cb7ef5a2eb134d550a2","target":"record","created_at":"2026-05-18T02:42:28Z","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":"f077fc295b2a876b94e20bf3a0cccc268f9a8938359f1dabc078ebe10367a8c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-30T05:26:03Z","title_canon_sha256":"435bcd2d0ee14c1a8c219e0883cf23622e0bd259e2f10edfd411245c52b34c9c"},"schema_version":"1.0","source":{"id":"1310.8028","kind":"arxiv","version":2}},"canonical_sha256":"6b61976fab1cb2d373aaf2ca5a4d99c88da0f21776d215ce901faa41ca1d183b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b61976fab1cb2d373aaf2ca5a4d99c88da0f21776d215ce901faa41ca1d183b","first_computed_at":"2026-05-18T02:42:28.641374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:28.641374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BvZw21Z1e+sj3lFpO8U9NvdSk3lKPch+VpzFqR3e5bl7iSNCupLcpDDmaiHwxbkKqUlG7v1qoaStWsmHI5KSDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:28.642295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8028","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8e794104b787b59db5ec7a1a903567aec4354251ed57cb7ef5a2eb134d550a2","sha256:8dfad24b9b311129028df3f7a87a2fb51f637e8b8ee2a8e3028a0bfabb404cf5"],"state_sha256":"f0d0beed07b2724611d804c5ce1a6dbfc5ffc2184754afbf974920bdc274e05d"}