{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:UV3LUJ5P3W4URTZZP74Y5PMGIL","short_pith_number":"pith:UV3LUJ5P","schema_version":"1.0","canonical_sha256":"a576ba27afddb948cf397ff98ebd8642ec83eccd34a0118d1c3baed8134ea6c1","source":{"kind":"arxiv","id":"1112.0344","version":1},"attestation_state":"computed","paper":{"title":"Analytic equivalence relations and bi-embedability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Luca Motto Ros, Sy-David Friedman","submitted_at":"2011-12-01T22:20:57Z","abstract_excerpt":"Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs (or on any class of countable structures consisting of the models of a sentence of L_{\\omega_1 \\omega}) is far from complete (see [5, 2]). In this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analyti"},"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":"1112.0344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-12-01T22:20:57Z","cross_cats_sorted":[],"title_canon_sha256":"a405ceb1c049b1a2a989b0c52ce3500858ac9c08b1d31e0097950cd85f3651bb","abstract_canon_sha256":"5a71b0d9c1e190f21d5068220f715e89ff758e53ed229c74b4ef038b212cb779"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:07.436508Z","signature_b64":"APrMsnmHuQwjvdNa3qU4mTXR7tzcimoe3ZH2zvpLh1n0vYc/tnsKthEdYi6uRvzj3CnywuJ2iyhF4kH+aOTgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a576ba27afddb948cf397ff98ebd8642ec83eccd34a0118d1c3baed8134ea6c1","last_reissued_at":"2026-05-18T04:07:07.435947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:07.435947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic equivalence relations and bi-embedability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Luca Motto Ros, Sy-David Friedman","submitted_at":"2011-12-01T22:20:57Z","abstract_excerpt":"Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This is in strong contrast to the case of the isomorphism relation, which as an equivalence relation on graphs (or on any class of countable structures consisting of the models of a sentence of L_{\\omega_1 \\omega}) is far from complete (see [5, 2]). In this article we strengthen the results of [5] by showing that not only does bi-embeddability give rise to analyti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0344","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":"1112.0344","created_at":"2026-05-18T04:07:07.436040+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0344v1","created_at":"2026-05-18T04:07:07.436040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0344","created_at":"2026-05-18T04:07:07.436040+00:00"},{"alias_kind":"pith_short_12","alias_value":"UV3LUJ5P3W4U","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"UV3LUJ5P3W4URTZZ","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"UV3LUJ5P","created_at":"2026-05-18T12:26:42.757692+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/UV3LUJ5P3W4URTZZP74Y5PMGIL","json":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL.json","graph_json":"https://pith.science/api/pith-number/UV3LUJ5P3W4URTZZP74Y5PMGIL/graph.json","events_json":"https://pith.science/api/pith-number/UV3LUJ5P3W4URTZZP74Y5PMGIL/events.json","paper":"https://pith.science/paper/UV3LUJ5P"},"agent_actions":{"view_html":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL","download_json":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL.json","view_paper":"https://pith.science/paper/UV3LUJ5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0344&json=true","fetch_graph":"https://pith.science/api/pith-number/UV3LUJ5P3W4URTZZP74Y5PMGIL/graph.json","fetch_events":"https://pith.science/api/pith-number/UV3LUJ5P3W4URTZZP74Y5PMGIL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL/action/storage_attestation","attest_author":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL/action/author_attestation","sign_citation":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL/action/citation_signature","submit_replication":"https://pith.science/pith/UV3LUJ5P3W4URTZZP74Y5PMGIL/action/replication_record"}},"created_at":"2026-05-18T04:07:07.436040+00:00","updated_at":"2026-05-18T04:07:07.436040+00:00"}