{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UUMS6LXSXNAAPZRDOZ3UU2JECS","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":"4fc537ba9a0ba43b60d9b61aa482078db21e704759e228f9896b0566d21418ea","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-06-02T16:21:30Z","title_canon_sha256":"420eb70de916d54259e1f10821db8edb744d6abb445ab04a4e0cdd9d5d1470a8"},"schema_version":"1.0","source":{"id":"2506.01832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01832","created_at":"2026-07-05T11:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01832v2","created_at":"2026-07-05T11:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01832","created_at":"2026-07-05T11:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"UUMS6LXSXNAA","created_at":"2026-07-05T11:15:47Z"},{"alias_kind":"pith_short_16","alias_value":"UUMS6LXSXNAAPZRD","created_at":"2026-07-05T11:15:47Z"},{"alias_kind":"pith_short_8","alias_value":"UUMS6LXS","created_at":"2026-07-05T11:15:47Z"}],"graph_snapshots":[{"event_id":"sha256:c24ab14650562c36a09b8957bd0a45b21078b0f55a5adb464771608854b69baf","target":"graph","created_at":"2026-07-05T11:15:47Z","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/2506.01832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain new explicit pseudorandom generators for several computational models involving groups. Our main results are as follows:\n  1. We consider read-once group-products over a finite group $G$, i.e., tests of the form $\\prod_{i=1}^n g_i^{x_i}$ where $g_i\\in G$, a special case of read-once permutation branching programs. We give generators with optimal seed length $c_G \\log(n/\\varepsilon)$ over any $p$-group. The proof uses the small-bias plus noise paradigm, but derandomizes the noise to avoid the recursion in previous work. Our generator works when the bits are read in any order. Previous","authors_text":"Chin Ho Lee, Emanuele Viola","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-06-02T16:21:30Z","title":"Pseudorandom bits for non-commutative programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01832","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":"sha256:85869f6427e833810da7001d66eb7d7e13756fd77ffd1948a95f97aa7722e07d","target":"record","created_at":"2026-07-05T11:15:47Z","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":"4fc537ba9a0ba43b60d9b61aa482078db21e704759e228f9896b0566d21418ea","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2025-06-02T16:21:30Z","title_canon_sha256":"420eb70de916d54259e1f10821db8edb744d6abb445ab04a4e0cdd9d5d1470a8"},"schema_version":"1.0","source":{"id":"2506.01832","kind":"arxiv","version":2}},"canonical_sha256":"a5192f2ef2bb4007e62376774a692414a8858edcb7b2bf57c2f6f35fbd0ff663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5192f2ef2bb4007e62376774a692414a8858edcb7b2bf57c2f6f35fbd0ff663","first_computed_at":"2026-07-05T11:15:47.620435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:15:47.620435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhRfrOT6osSKq+NhwVDwmQ3XnO7Op5EZr2U84TTsm2CRuaCjA9vXL8SUB++8zw20Y4OqkjR7heplHEO4UGseDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:15:47.620940Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85869f6427e833810da7001d66eb7d7e13756fd77ffd1948a95f97aa7722e07d","sha256:c24ab14650562c36a09b8957bd0a45b21078b0f55a5adb464771608854b69baf"],"state_sha256":"9bfc6ec75036e0e205658d5ed999ba6921e098300ec30909b9cfe283207992cc"}