{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2TL5FDGGBWUDVCCMVVASOOQZGC","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":"8d246b5a6b9250f13da23f781cf4d53afd339f8de4c6dcbf91b7b3531f4e59ed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-03-21T12:58:38Z","title_canon_sha256":"c3aeb6f05ed3ddd4dad466d9c0bc008abc0c01a9633992b1734cc575267cc9a0"},"schema_version":"1.0","source":{"id":"2503.17114","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.17114","created_at":"2026-07-05T11:36:29Z"},{"alias_kind":"arxiv_version","alias_value":"2503.17114v2","created_at":"2026-07-05T11:36:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.17114","created_at":"2026-07-05T11:36:29Z"},{"alias_kind":"pith_short_12","alias_value":"2TL5FDGGBWUD","created_at":"2026-07-05T11:36:29Z"},{"alias_kind":"pith_short_16","alias_value":"2TL5FDGGBWUDVCCM","created_at":"2026-07-05T11:36:29Z"},{"alias_kind":"pith_short_8","alias_value":"2TL5FDGG","created_at":"2026-07-05T11:36:29Z"}],"graph_snapshots":[{"event_id":"sha256:3801ba426b623ce8755cfbd07d61409a49cee6e0498a659a57855f6a5ad328b8","target":"graph","created_at":"2026-07-05T11:36:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2503.17114/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a circuit $C : \\{0,1\\}^n \\to \\{0,1\\}^m$ from a circuit class $F$, with $m > n$, finding a $y \\in \\{0,1\\}^m$ such that $\\forall x \\in \\{0,1\\}^n$, $C(x) \\ne y$, is the range avoidance problem (denoted by $F$-$avoid$). Deterministic polynomial time algorithms (even with access to $NP$ oracles) solving this problem is known to imply explicit constructions of various pseudorandom objects like hard Boolean functions, linear codes, PRGs etc. Deterministic polynomial time algorithms are known for $NC^0_2$-$avoid$ when $m > n$, and for $NC^0_3$-$avoid$ when $m \\ge \\frac{n^2}{\\log n}$, where $NC^0","authors_text":"Jayalal Sarma, Neha Kuntewar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-03-21T12:58:38Z","title":"Range Avoidance in Boolean Circuits via Turan-type Bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.17114","kind":"arxiv","version":2},"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:c21d44d83d66cc67b8afa8e5859db90b8953711507ae1c570026d0b798d38ab8","target":"record","created_at":"2026-07-05T11:36:29Z","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":"8d246b5a6b9250f13da23f781cf4d53afd339f8de4c6dcbf91b7b3531f4e59ed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-03-21T12:58:38Z","title_canon_sha256":"c3aeb6f05ed3ddd4dad466d9c0bc008abc0c01a9633992b1734cc575267cc9a0"},"schema_version":"1.0","source":{"id":"2503.17114","kind":"arxiv","version":2}},"canonical_sha256":"d4d7d28cc60da83a884cad41273a1930ae17b803c64f6cd243dc5592b37de2d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4d7d28cc60da83a884cad41273a1930ae17b803c64f6cd243dc5592b37de2d8","first_computed_at":"2026-07-05T11:36:29.771507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:29.771507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RiAMn149FtlsC1h807xzsjPGlaJHVAz9jSvyCmJfYzI4ER5A+7U22df51zYO7Kfz0XbetJ5Qxtnabd6Wz8nyAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:29.771959Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.17114","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c21d44d83d66cc67b8afa8e5859db90b8953711507ae1c570026d0b798d38ab8","sha256:3801ba426b623ce8755cfbd07d61409a49cee6e0498a659a57855f6a5ad328b8"],"state_sha256":"842f8baef610a324e4f49e28f1e8ca71c44e0ec17118a3295f21ace78868b3aa"}