{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:MZOEMO7WOT3MMIHMEMVMSNMMWF","short_pith_number":"pith:MZOEMO7W","canonical_record":{"source":{"id":"2404.07441","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-11T02:51:35Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"2fdbd6007e1814eb4b1d953279b8c31dd31328dffebe7f8340c5b14efb395330","abstract_canon_sha256":"d025f7dfeb908ae1f0bd76d51c82b331dc87ca292538849eba352c680a51ef78"},"schema_version":"1.0"},"canonical_sha256":"665c463bf674f6c620ec232ac9358cb14721287cc16e6fbd250c3d499e84f14d","source":{"kind":"arxiv","id":"2404.07441","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07441","created_at":"2026-05-17T23:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07441v4","created_at":"2026-05-17T23:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07441","created_at":"2026-05-17T23:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MZOEMO7WOT3M","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"MZOEMO7WOT3MMIHM","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"MZOEMO7W","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:MZOEMO7WOT3MMIHMEMVMSNMMWF","target":"record","payload":{"canonical_record":{"source":{"id":"2404.07441","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-11T02:51:35Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"2fdbd6007e1814eb4b1d953279b8c31dd31328dffebe7f8340c5b14efb395330","abstract_canon_sha256":"d025f7dfeb908ae1f0bd76d51c82b331dc87ca292538849eba352c680a51ef78"},"schema_version":"1.0"},"canonical_sha256":"665c463bf674f6c620ec232ac9358cb14721287cc16e6fbd250c3d499e84f14d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:18.451513Z","signature_b64":"hgPYxrvo16D2ZFJv/YZp64L61zBg1jdfMIQO6n3FVWsAXVTIY8ORqqRsVTgCHaqi+dSlrrmE4UkygLqUJNouBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"665c463bf674f6c620ec232ac9358cb14721287cc16e6fbd250c3d499e84f14d","last_reissued_at":"2026-05-17T23:39:18.450696Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:18.450696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.07441","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yv/GNkp/hA19XgJYVLdC8DRZpW6Z8JCt0dTaQ/vB7psOZiYa2I+kvkL2RzkO9Lj42OEqdOIvXd4OvFIar87WBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:37:36.184687Z"},"content_sha256":"27666d9a40016b54315ec684c4b8f6c624ff2750c284cc6245ea723562deb6f3","schema_version":"1.0","event_id":"sha256:27666d9a40016b54315ec684c4b8f6c624ff2750c284cc6245ea723562deb6f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:MZOEMO7WOT3MMIHMEMVMSNMMWF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Near Optimal Alphabet-Soundness Tradeoff PCPs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Dor Minzer, Kai Zhe Zheng","submitted_at":"2024-04-11T02:51:35Z","abstract_excerpt":"We show that for all $\\varepsilon>0$, for sufficiently large $q\\in\\mathbb{N}$ power of $2$, for all $\\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least $1-\\delta$, or value at most $1/q^{1-\\varepsilon}$. This establishes a nearly optimal alphabet-to-soundness tradeoff for $2$-query PCPs with alphabet size $q$, improving upon a result of [Chan, Journal of the ACM 2016]. Our result has the following implications:\n  1) Near optimal hardness for Quadratic Programming: it is NP-hard to approximate the value of a giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07441","kind":"arxiv","version":4},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkUTuJ1Qi8wqky0C9DznJFfazt0aGQDiquH4X/1tILAbxo4TgjZbyMOSh/0dyHApKeB8swF4/na3jpNIpVKzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:37:36.185245Z"},"content_sha256":"e3c11dac948ec620d8eeb435c2aef785c03072fd4e274e9f2c9c70616dfca102","schema_version":"1.0","event_id":"sha256:e3c11dac948ec620d8eeb435c2aef785c03072fd4e274e9f2c9c70616dfca102"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZOEMO7WOT3MMIHMEMVMSNMMWF/bundle.json","state_url":"https://pith.science/pith/MZOEMO7WOT3MMIHMEMVMSNMMWF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZOEMO7WOT3MMIHMEMVMSNMMWF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T13:37:36Z","links":{"resolver":"https://pith.science/pith/MZOEMO7WOT3MMIHMEMVMSNMMWF","bundle":"https://pith.science/pith/MZOEMO7WOT3MMIHMEMVMSNMMWF/bundle.json","state":"https://pith.science/pith/MZOEMO7WOT3MMIHMEMVMSNMMWF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZOEMO7WOT3MMIHMEMVMSNMMWF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MZOEMO7WOT3MMIHMEMVMSNMMWF","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":"d025f7dfeb908ae1f0bd76d51c82b331dc87ca292538849eba352c680a51ef78","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-11T02:51:35Z","title_canon_sha256":"2fdbd6007e1814eb4b1d953279b8c31dd31328dffebe7f8340c5b14efb395330"},"schema_version":"1.0","source":{"id":"2404.07441","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07441","created_at":"2026-05-17T23:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07441v4","created_at":"2026-05-17T23:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07441","created_at":"2026-05-17T23:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MZOEMO7WOT3M","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"MZOEMO7WOT3MMIHM","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"MZOEMO7W","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:e3c11dac948ec620d8eeb435c2aef785c03072fd4e274e9f2c9c70616dfca102","target":"graph","created_at":"2026-05-17T23:39:18Z","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":"We show that for all $\\varepsilon>0$, for sufficiently large $q\\in\\mathbb{N}$ power of $2$, for all $\\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least $1-\\delta$, or value at most $1/q^{1-\\varepsilon}$. This establishes a nearly optimal alphabet-to-soundness tradeoff for $2$-query PCPs with alphabet size $q$, improving upon a result of [Chan, Journal of the ACM 2016]. Our result has the following implications:\n  1) Near optimal hardness for Quadratic Programming: it is NP-hard to approximate the value of a giv","authors_text":"Dor Minzer, Kai Zhe Zheng","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-11T02:51:35Z","title":"Near Optimal Alphabet-Soundness Tradeoff PCPs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07441","kind":"arxiv","version":4},"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":"sha256:27666d9a40016b54315ec684c4b8f6c624ff2750c284cc6245ea723562deb6f3","target":"record","created_at":"2026-05-17T23:39:18Z","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":"d025f7dfeb908ae1f0bd76d51c82b331dc87ca292538849eba352c680a51ef78","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-11T02:51:35Z","title_canon_sha256":"2fdbd6007e1814eb4b1d953279b8c31dd31328dffebe7f8340c5b14efb395330"},"schema_version":"1.0","source":{"id":"2404.07441","kind":"arxiv","version":4}},"canonical_sha256":"665c463bf674f6c620ec232ac9358cb14721287cc16e6fbd250c3d499e84f14d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"665c463bf674f6c620ec232ac9358cb14721287cc16e6fbd250c3d499e84f14d","first_computed_at":"2026-05-17T23:39:18.450696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:18.450696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hgPYxrvo16D2ZFJv/YZp64L61zBg1jdfMIQO6n3FVWsAXVTIY8ORqqRsVTgCHaqi+dSlrrmE4UkygLqUJNouBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:18.451513Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.07441","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27666d9a40016b54315ec684c4b8f6c624ff2750c284cc6245ea723562deb6f3","sha256:e3c11dac948ec620d8eeb435c2aef785c03072fd4e274e9f2c9c70616dfca102"],"state_sha256":"39ea58310e905b28977feee3118bab379f63e9e316be664108d1b9a8919630bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+FeFYBL7Sa0bqFW0FdXLv9UvShHao+bMQ6JecbK2pW0XlWDjD6Uhcs/wD/dzm7uBH5F0I/AzAp5hBfixBPorDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:37:36.187093Z","bundle_sha256":"746a14ce6b9916cdcece357788fda5816ef7eef65e12f80bf294d5ed410b72b0"}}