{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:525IIALQDZQQOFSSHNH2WMO6YG","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":"0b3322c444c7a22103fbbc5b68189921cf5cc0317b8d33fe33bf607bd954e470","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-10T02:05:28Z","title_canon_sha256":"4e18b73eaf173ae90dda3fc15cf014e98dbbe9067f8a8aa5145d789f4fbbbb63"},"schema_version":"1.0","source":{"id":"1903.03902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.03902","created_at":"2026-05-17T23:51:40Z"},{"alias_kind":"arxiv_version","alias_value":"1903.03902v1","created_at":"2026-05-17T23:51:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03902","created_at":"2026-05-17T23:51:40Z"},{"alias_kind":"pith_short_12","alias_value":"525IIALQDZQQ","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"525IIALQDZQQOFSS","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"525IIALQ","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:2a4b278923df4f4fae7eaa3f80a251f7a72bc303fd6ff903f2998690923e98c0","target":"graph","created_at":"2026-05-17T23:51:40Z","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":"Assume $\\mathsf{ZF + AD^+ + V = L(\\mathscr{P}(\\mathbb{R}))}$. Let $\\approx$ denote the relation of being in bijection. Let $\\kappa \\in \\mathrm{ON}$ and $\\langle E_\\alpha : \\alpha < \\kappa\\rangle$ be a sequence of equivalence relations on $\\mathbb{R}$ with all classes countable and for all $\\alpha < \\kappa$, $\\mathbb{R} / E_\\alpha \\approx \\mathbb{R}$. Then the disjoint union $\\bigsqcup_{\\alpha < \\kappa} \\mathbb{R} / E_\\alpha$ is in bijection with $\\mathbb{R} \\times \\kappa$ and $\\bigsqcup_{\\alpha < \\kappa} \\mathbb{R} / E_\\alpha$ has the J\\'onsson property.\n  Assume $\\mathsf{ZF + AD^+ + V = L(\\ma","authors_text":"Stephen Jackson, William Chan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-10T02:05:28Z","title":"Cardinality of Wellordered Disjoint Unions of Quotients of Smooth Equivalence Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03902","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:ae44fa7e4411a158e9ae1b6f0c77f60114d7a8209c47b3f4aed7e9d1672ba045","target":"record","created_at":"2026-05-17T23:51:40Z","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":"0b3322c444c7a22103fbbc5b68189921cf5cc0317b8d33fe33bf607bd954e470","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-10T02:05:28Z","title_canon_sha256":"4e18b73eaf173ae90dda3fc15cf014e98dbbe9067f8a8aa5145d789f4fbbbb63"},"schema_version":"1.0","source":{"id":"1903.03902","kind":"arxiv","version":1}},"canonical_sha256":"eeba8401701e610716523b4fab31dec1ad3f414e32caa74f3dc27c34898b7111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eeba8401701e610716523b4fab31dec1ad3f414e32caa74f3dc27c34898b7111","first_computed_at":"2026-05-17T23:51:40.656944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:40.656944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g1axQGUHiQZpQmvTbdrAIdzrMmJvjYzRghrZgYWJ/XSIh7N0siD9D66hD5n+7JapqIFGpt2PUdlIMSf/hop8AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:40.657476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.03902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae44fa7e4411a158e9ae1b6f0c77f60114d7a8209c47b3f4aed7e9d1672ba045","sha256:2a4b278923df4f4fae7eaa3f80a251f7a72bc303fd6ff903f2998690923e98c0"],"state_sha256":"572bc1d464131fb9c28655e3e5f1c55b2c651699af5cd77bb5e4109f5d8f6ca8"}