{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:NRG4ZS24EOEJN5D4BUMDILOMK7","short_pith_number":"pith:NRG4ZS24","schema_version":"1.0","canonical_sha256":"6c4dcccb5c238896f47c0d18342dcc57dbb1bf6a42cbc037e1c977d02e06d384","source":{"kind":"arxiv","id":"2001.04383","version":3},"attestation_state":"computed","paper":{"title":"MIP*=RE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.OA"],"primary_cat":"quant-ph","authors_text":"Anand Natarajan, Henry Yuen, John Wright, Thomas Vidick, Zhengfeng Ji","submitted_at":"2020-01-13T16:32:40Z","abstract_excerpt":"We show that the class MIP* of languages that can be decided by a classical verifier interacting with multiple all-powerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages. Our proof builds upon the quantum low-degree test of (Natarajan and Vidick, FOCS 2018) and the classical low-individual degree test of (Ji, et al., 2020) by integrating recent developments from (Natarajan and Wright, FOCS 2019) and combining them with the recursive compression framework of (Fitzsimons et al., STOC 2019).\n  An immediate byproduct of our result is that there i"},"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":"2001.04383","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2020-01-13T16:32:40Z","cross_cats_sorted":["cs.CC","math.OA"],"title_canon_sha256":"16fc50fbbd3d5aec78abeaae64f67287f2faf3e61931f2c643728e43252dec34","abstract_canon_sha256":"04e44f6379f8db6b308ac74632b73b8ae0532d08f35d0f16fe31aca975306cec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:13:03.140012Z","signature_b64":"s15FlQQhgO0z2O5BIgFYUmoFOmbd6swf3Tw2wMziPJJ7Z/hE+8fkbM7o3nqld3XkSjFn6pIqYAwKZv6pqGTxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c4dcccb5c238896f47c0d18342dcc57dbb1bf6a42cbc037e1c977d02e06d384","last_reissued_at":"2026-07-05T05:13:03.139594Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:13:03.139594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"MIP*=RE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.OA"],"primary_cat":"quant-ph","authors_text":"Anand Natarajan, Henry Yuen, John Wright, Thomas Vidick, Zhengfeng Ji","submitted_at":"2020-01-13T16:32:40Z","abstract_excerpt":"We show that the class MIP* of languages that can be decided by a classical verifier interacting with multiple all-powerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages. Our proof builds upon the quantum low-degree test of (Natarajan and Vidick, FOCS 2018) and the classical low-individual degree test of (Ji, et al., 2020) by integrating recent developments from (Natarajan and Wright, FOCS 2019) and combining them with the recursive compression framework of (Fitzsimons et al., STOC 2019).\n  An immediate byproduct of our result is that there i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.04383","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.04383/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2001.04383","created_at":"2026-07-05T05:13:03.139651+00:00"},{"alias_kind":"arxiv_version","alias_value":"2001.04383v3","created_at":"2026-07-05T05:13:03.139651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.04383","created_at":"2026-07-05T05:13:03.139651+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRG4ZS24EOEJ","created_at":"2026-07-05T05:13:03.139651+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRG4ZS24EOEJN5D4","created_at":"2026-07-05T05:13:03.139651+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRG4ZS24","created_at":"2026-07-05T05:13:03.139651+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":16,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06876","citing_title":"XOR Games at Full Tilt: The Hardness of Binary Nonlocal Games","ref_index":15,"is_internal_anchor":true},{"citing_arxiv_id":"2606.23372","citing_title":"Bounding Classical and Quantum Correlations in Bayesian Networks with Quasiprobabilities","ref_index":48,"is_internal_anchor":false},{"citing_arxiv_id":"2606.21664","citing_title":"No-signaling values of quantum games--an operator algebra perspective","ref_index":20,"is_internal_anchor":false},{"citing_arxiv_id":"2606.20399","citing_title":"Linked Fates: How Small of an Ambiguity Increase Can Make the Difference Between Equaling and Separating from P?","ref_index":32,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30853","citing_title":"Rethinking quantum information in gravity and fields","ref_index":167,"is_internal_anchor":false},{"citing_arxiv_id":"2606.18369","citing_title":"Amenable traces and the joint numerical radius","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2306.14344","citing_title":"On steering in the C*-algebraic framework","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2305.12122","citing_title":"RFD property for groupoid C*-algebras of amenable groupoids and for crossed products by amenable actions","ref_index":7,"is_internal_anchor":false},{"citing_arxiv_id":"2310.12662","citing_title":"A mathematical foundation for self-testing: Lifting common assumptions","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09872","citing_title":"Multi-Prover Interactive Proof Systems with Leakage","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16669","citing_title":"On ultraproduct approximations and property (T) factors","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2506.10902","citing_title":"Nuclear C*-algebras: 99 problems","ref_index":228,"is_internal_anchor":false},{"citing_arxiv_id":"2509.20350","citing_title":"Nonlocal Games in the High-Noise Regime: Optimal Quantum Values and Rigidity","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2512.07160","citing_title":"Beyond real: Investigating the role of complex numbers in self-testing","ref_index":16,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09872","citing_title":"Multi-Prover Interactive Proof Systems with Leakage","ref_index":15,"is_internal_anchor":false},{"citing_arxiv_id":"2604.12212","citing_title":"Free information geometry and the model theory of noncommutative stochastic processes","ref_index":51,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7","json":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7.json","graph_json":"https://pith.science/api/pith-number/NRG4ZS24EOEJN5D4BUMDILOMK7/graph.json","events_json":"https://pith.science/api/pith-number/NRG4ZS24EOEJN5D4BUMDILOMK7/events.json","paper":"https://pith.science/paper/NRG4ZS24"},"agent_actions":{"view_html":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7","download_json":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7.json","view_paper":"https://pith.science/paper/NRG4ZS24","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2001.04383&json=true","fetch_graph":"https://pith.science/api/pith-number/NRG4ZS24EOEJN5D4BUMDILOMK7/graph.json","fetch_events":"https://pith.science/api/pith-number/NRG4ZS24EOEJN5D4BUMDILOMK7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7/action/storage_attestation","attest_author":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7/action/author_attestation","sign_citation":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7/action/citation_signature","submit_replication":"https://pith.science/pith/NRG4ZS24EOEJN5D4BUMDILOMK7/action/replication_record"}},"created_at":"2026-07-05T05:13:03.139651+00:00","updated_at":"2026-07-05T05:13:03.139651+00:00"}