{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N5SDQDF7TUQ6DUUWM2CHBKHZ52","short_pith_number":"pith:N5SDQDF7","canonical_record":{"source":{"id":"1406.0373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-06-02T14:01:18Z","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"title_canon_sha256":"2085c0ed41355eaccb062878e85947ff8d1cc55c63ab90c00756c7d5b0ee11d2","abstract_canon_sha256":"25f7a99d173e32bf44d48fde0b5a8f9c09cc27f6f531e26e0ab80f089e54a0ea"},"schema_version":"1.0"},"canonical_sha256":"6f64380cbf9d21e1d296668470a8f9eea37167f7ce96eff69a5af8945c03a248","source":{"kind":"arxiv","id":"1406.0373","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0373","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0373v1","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0373","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"N5SDQDF7TUQ6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N5SDQDF7TUQ6DUUW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N5SDQDF7","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N5SDQDF7TUQ6DUUWM2CHBKHZ52","target":"record","payload":{"canonical_record":{"source":{"id":"1406.0373","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-06-02T14:01:18Z","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"title_canon_sha256":"2085c0ed41355eaccb062878e85947ff8d1cc55c63ab90c00756c7d5b0ee11d2","abstract_canon_sha256":"25f7a99d173e32bf44d48fde0b5a8f9c09cc27f6f531e26e0ab80f089e54a0ea"},"schema_version":"1.0"},"canonical_sha256":"6f64380cbf9d21e1d296668470a8f9eea37167f7ce96eff69a5af8945c03a248","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.082511Z","signature_b64":"QEf7O/mj4trZ2foJOU3wUDe4XdhGVhPbYIKS6HjlN6ipo8dKvchoWW2xFwDbb/wbEyIJmV25lI+CMNWmpg+uDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f64380cbf9d21e1d296668470a8f9eea37167f7ce96eff69a5af8945c03a248","last_reissued_at":"2026-05-18T02:50:41.081908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.081908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.0373","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hxEEc7qaWAqarg9qrzVbde4EHXP/gxzrTeN23UvWgobptbwJ8EZlRu/XdS6EyfgAVG1Xtl+K57n+CTo7FbKOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:39:57.086904Z"},"content_sha256":"80025e94e51654af0bf6cd030ededa3c13d0a4e7123f7eb26aba585825951844","schema_version":"1.0","event_id":"sha256:80025e94e51654af0bf6cd030ededa3c13d0a4e7123f7eb26aba585825951844"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N5SDQDF7TUQ6DUUWM2CHBKHZ52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","math.IT"],"primary_cat":"cs.CR","authors_text":"Masaki Yamamoto, Osamu Watanabe, Ryuhei Mori, Takeshi Koshiba","submitted_at":"2014-06-02T14:01:18Z","abstract_excerpt":"Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0373","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":""},"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":"2026-05-18T02:50:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3BtWMz96+S9Pbu6GYIl3MLaPUvJNjML2rRf5RU4etOVuV4tjIWoNBYmU1Sq2aU0ewNXJUlX/ghZTjKbCeIzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:39:57.087629Z"},"content_sha256":"7059aca64402f929706261bb04431318703213e8e57a985a1a057c36c0eaef2b","schema_version":"1.0","event_id":"sha256:7059aca64402f929706261bb04431318703213e8e57a985a1a057c36c0eaef2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5SDQDF7TUQ6DUUWM2CHBKHZ52/bundle.json","state_url":"https://pith.science/pith/N5SDQDF7TUQ6DUUWM2CHBKHZ52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5SDQDF7TUQ6DUUWM2CHBKHZ52/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":"2026-05-26T14:39:57Z","links":{"resolver":"https://pith.science/pith/N5SDQDF7TUQ6DUUWM2CHBKHZ52","bundle":"https://pith.science/pith/N5SDQDF7TUQ6DUUWM2CHBKHZ52/bundle.json","state":"https://pith.science/pith/N5SDQDF7TUQ6DUUWM2CHBKHZ52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5SDQDF7TUQ6DUUWM2CHBKHZ52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N5SDQDF7TUQ6DUUWM2CHBKHZ52","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":"25f7a99d173e32bf44d48fde0b5a8f9c09cc27f6f531e26e0ab80f089e54a0ea","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-06-02T14:01:18Z","title_canon_sha256":"2085c0ed41355eaccb062878e85947ff8d1cc55c63ab90c00756c7d5b0ee11d2"},"schema_version":"1.0","source":{"id":"1406.0373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0373","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0373v1","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0373","created_at":"2026-05-18T02:50:41Z"},{"alias_kind":"pith_short_12","alias_value":"N5SDQDF7TUQ6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N5SDQDF7TUQ6DUUW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N5SDQDF7","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:7059aca64402f929706261bb04431318703213e8e57a985a1a057c36c0eaef2b","target":"graph","created_at":"2026-05-18T02:50:41Z","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":"Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear","authors_text":"Masaki Yamamoto, Osamu Watanabe, Ryuhei Mori, Takeshi Koshiba","cross_cats":["cs.CC","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-06-02T14:01:18Z","title":"Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0373","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":"sha256:80025e94e51654af0bf6cd030ededa3c13d0a4e7123f7eb26aba585825951844","target":"record","created_at":"2026-05-18T02:50:41Z","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":"25f7a99d173e32bf44d48fde0b5a8f9c09cc27f6f531e26e0ab80f089e54a0ea","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2014-06-02T14:01:18Z","title_canon_sha256":"2085c0ed41355eaccb062878e85947ff8d1cc55c63ab90c00756c7d5b0ee11d2"},"schema_version":"1.0","source":{"id":"1406.0373","kind":"arxiv","version":1}},"canonical_sha256":"6f64380cbf9d21e1d296668470a8f9eea37167f7ce96eff69a5af8945c03a248","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f64380cbf9d21e1d296668470a8f9eea37167f7ce96eff69a5af8945c03a248","first_computed_at":"2026-05-18T02:50:41.081908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:41.081908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QEf7O/mj4trZ2foJOU3wUDe4XdhGVhPbYIKS6HjlN6ipo8dKvchoWW2xFwDbb/wbEyIJmV25lI+CMNWmpg+uDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:41.082511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80025e94e51654af0bf6cd030ededa3c13d0a4e7123f7eb26aba585825951844","sha256:7059aca64402f929706261bb04431318703213e8e57a985a1a057c36c0eaef2b"],"state_sha256":"88f7b9bfab27fd68e62f47e015f52548537a9f720f8cee9c55a74cbadf504c6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TsYijrrexWU4zBnzTd97mUhX7n8Ctk+PH8i4KNzLkIILwhrFbRkCYepPKtuMYQPBGRSn01dWUcLH9fU+iiyGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:39:57.091456Z","bundle_sha256":"89ebc67aa2f4affd07536d04b23ce6365192410dd3b957c16067ac5d17072cb3"}}