{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PGJGOY4K4JLSMD2PIJ26BHC5EY","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":"2b06885c887cf7eba130c264c75523be823612f328d874a372824ae01575b292","cross_cats_sorted":["cs.CR","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-28T20:03:46Z","title_canon_sha256":"a8d91939f73ff63d239f55abbcedaf63d276aa12a33dab2a23fb3950c4402b86"},"schema_version":"1.0","source":{"id":"1903.12243","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12243","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12243v1","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12243","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"pith_short_12","alias_value":"PGJGOY4K4JLS","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PGJGOY4K4JLSMD2P","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PGJGOY4K","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:0283bf59bf1a4b9e3395c705f2e8f624ca112de344cf72768183aa6810c2c533","target":"graph","created_at":"2026-05-17T23:49:54Z","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":"Motivated by the quest for scalable and succinct zero knowledge arguments, we revisit worst-case-to-average-case reductions for linear spaces, raised by [Rothblum, Vadhan, Wigderson, STOC 2013]. We first show a sharp quantitative form of a theorem which says that if an affine space $U$ is $\\delta$-far in relative Hamming distance from a linear code $V$ - this is the worst-case assumption - then most elements of $U$ are almost $\\delta$-far from $V$ - this is the average case. This leads to an optimal analysis of the soundness of the FRI protocol of [Ben-Sasson, et.al., eprint 2018] for proving ","authors_text":"Eli Ben-Sasson, Lior Goldberg, Shubhangi Saraf, Swastik Kopparty","cross_cats":["cs.CR","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-28T20:03:46Z","title":"DEEP-FRI: Sampling outside the box improves soundness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12243","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":"sha256:58c8e38d9d241c54ad1127ecc7ff3e89a7c480d198acd4d504f7f8ffafe6fa87","target":"record","created_at":"2026-05-17T23:49:54Z","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":"2b06885c887cf7eba130c264c75523be823612f328d874a372824ae01575b292","cross_cats_sorted":["cs.CR","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2019-03-28T20:03:46Z","title_canon_sha256":"a8d91939f73ff63d239f55abbcedaf63d276aa12a33dab2a23fb3950c4402b86"},"schema_version":"1.0","source":{"id":"1903.12243","kind":"arxiv","version":1}},"canonical_sha256":"799267638ae257260f4f4275e09c5d260a259230411a999f9c598b6febbfe31f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"799267638ae257260f4f4275e09c5d260a259230411a999f9c598b6febbfe31f","first_computed_at":"2026-05-17T23:49:54.492933Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:54.492933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvpwpnFPv1e5nCYoQ9mpoYgFKeNpACC/+0CCuxGvQZ/qoDAfDd0/OXeCoH6m6P9rxYsVYSXSmvpZZbypnIONBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:54.493521Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.12243","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58c8e38d9d241c54ad1127ecc7ff3e89a7c480d198acd4d504f7f8ffafe6fa87","sha256:0283bf59bf1a4b9e3395c705f2e8f624ca112de344cf72768183aa6810c2c533"],"state_sha256":"fecd81a472a851dfa306ca30a8973c2554e7c66a9e6adcc934c38b79f67829e5"}