{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:56FRVO77CHYFUNHRMKDDMF6XJ7","short_pith_number":"pith:56FRVO77","schema_version":"1.0","canonical_sha256":"ef8b1abbff11f05a34f162863617d74fdf78ed1b7446209a99274d67eec6f8e5","source":{"kind":"arxiv","id":"2605.23517","version":1},"attestation_state":"computed","paper":{"title":"Probabilistically checkable proofs for the Existential Theory of the Reals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jack Stade","submitted_at":"2026-05-22T11:31:18Z","abstract_excerpt":"We prove a PCP theorem for the existential theory of the reals, showing that MAX-ETR-INV is $\\exists\\mathbb{R}$-hard to approximate to within some constant factor.\n  The existential theory of the reals (ETR) is a decision problem asking if there exists a set of real-valued variables satisfying some constraints involving polynomials and inequalities, and $\\exists\\mathbb{R}$ is the complexity class of problems polynomial-time reducible to ETR. Many important geometric problems are known to be $\\exists\\mathbb{R}$-complete.\n  $\\exists\\mathbb{R}$-hardness results frequently work by a reduction from"},"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":"2605.23517","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2026-05-22T11:31:18Z","cross_cats_sorted":[],"title_canon_sha256":"4b0494095b629c7a909e52b25cf86167c03806038dd8b1702883bc30bfc85ee1","abstract_canon_sha256":"cf9e23cc5febcdff837eef84cb06198cbde190b69cced2aca1dad8b48f542f4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:58.860799Z","signature_b64":"1Zdg+ckP75ncljKey+G48goZ+ZhjlMqz5frV/skJAvMLOIJA5f3q+YsD422KVBmjNZmX7/0YkJyd36LS7ryBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef8b1abbff11f05a34f162863617d74fdf78ed1b7446209a99274d67eec6f8e5","last_reissued_at":"2026-05-25T02:01:58.859978Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:58.859978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probabilistically checkable proofs for the Existential Theory of the Reals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Jack Stade","submitted_at":"2026-05-22T11:31:18Z","abstract_excerpt":"We prove a PCP theorem for the existential theory of the reals, showing that MAX-ETR-INV is $\\exists\\mathbb{R}$-hard to approximate to within some constant factor.\n  The existential theory of the reals (ETR) is a decision problem asking if there exists a set of real-valued variables satisfying some constraints involving polynomials and inequalities, and $\\exists\\mathbb{R}$ is the complexity class of problems polynomial-time reducible to ETR. Many important geometric problems are known to be $\\exists\\mathbb{R}$-complete.\n  $\\exists\\mathbb{R}$-hardness results frequently work by a reduction from"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23517","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23517/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":"2605.23517","created_at":"2026-05-25T02:01:58.860115+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.23517v1","created_at":"2026-05-25T02:01:58.860115+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23517","created_at":"2026-05-25T02:01:58.860115+00:00"},{"alias_kind":"pith_short_12","alias_value":"56FRVO77CHYF","created_at":"2026-05-25T02:01:58.860115+00:00"},{"alias_kind":"pith_short_16","alias_value":"56FRVO77CHYFUNHR","created_at":"2026-05-25T02:01:58.860115+00:00"},{"alias_kind":"pith_short_8","alias_value":"56FRVO77","created_at":"2026-05-25T02:01:58.860115+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/56FRVO77CHYFUNHRMKDDMF6XJ7","json":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7.json","graph_json":"https://pith.science/api/pith-number/56FRVO77CHYFUNHRMKDDMF6XJ7/graph.json","events_json":"https://pith.science/api/pith-number/56FRVO77CHYFUNHRMKDDMF6XJ7/events.json","paper":"https://pith.science/paper/56FRVO77"},"agent_actions":{"view_html":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7","download_json":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7.json","view_paper":"https://pith.science/paper/56FRVO77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.23517&json=true","fetch_graph":"https://pith.science/api/pith-number/56FRVO77CHYFUNHRMKDDMF6XJ7/graph.json","fetch_events":"https://pith.science/api/pith-number/56FRVO77CHYFUNHRMKDDMF6XJ7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7/action/storage_attestation","attest_author":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7/action/author_attestation","sign_citation":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7/action/citation_signature","submit_replication":"https://pith.science/pith/56FRVO77CHYFUNHRMKDDMF6XJ7/action/replication_record"}},"created_at":"2026-05-25T02:01:58.860115+00:00","updated_at":"2026-05-25T02:01:58.860115+00:00"}