{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DOATB5SLBSFTRPX5EU2JUPOUFU","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":"48432fa731d27e7d1b010ee6fa5dc3d635ef1c2e6cd774f47396230a158c3f3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-01-22T20:50:30Z","title_canon_sha256":"41b99716bfea42c41b960a29e9f26c087ad39c8fd568d8d4e8707b608ac3d7bf"},"schema_version":"1.0","source":{"id":"1801.07317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07317","created_at":"2026-05-18T00:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07317v1","created_at":"2026-05-18T00:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07317","created_at":"2026-05-18T00:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"DOATB5SLBSFT","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DOATB5SLBSFTRPX5","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DOATB5SL","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:6685b41d5ac1d0fe4fc18e1823702bf1250f797f90983cb8dec759183d392eb0","target":"graph","created_at":"2026-05-18T00:25:13Z","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":"Bennett and Gill (1981) showed that P^A != NP^A != coNP^A for a random oracle A, with probability 1. We investigate whether this result extends to individual polynomial-time random oracles. We consider two notions of random oracles: p-random oracles in the sense of martingales and resource-bounded measure (Lutz, 1992; Ambos-Spies et al., 1997), and p-betting-game random oracles using the betting games generalization of resource-bounded measure (Buhrman et al., 2000). Every p-betting-game random oracle is also p-random; whether the two notions are equivalent is an open problem.\n  (1) We first s","authors_text":"Adewale Sekoni, Hadi Shafei, John M. Hitchcock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-01-22T20:50:30Z","title":"Polynomial-Time Random Oracles and Separating Complexity Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07317","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":"sha256:0b5f9311ab10c7d01a23aeaf1a229bbdc406ff5f670729ec5a7912e778aff3e8","target":"record","created_at":"2026-05-18T00:25:13Z","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":"48432fa731d27e7d1b010ee6fa5dc3d635ef1c2e6cd774f47396230a158c3f3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2018-01-22T20:50:30Z","title_canon_sha256":"41b99716bfea42c41b960a29e9f26c087ad39c8fd568d8d4e8707b608ac3d7bf"},"schema_version":"1.0","source":{"id":"1801.07317","kind":"arxiv","version":1}},"canonical_sha256":"1b8130f64b0c8b38befd25349a3dd42d2a9238f7ba8f4d494e6fd0f568939aa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b8130f64b0c8b38befd25349a3dd42d2a9238f7ba8f4d494e6fd0f568939aa6","first_computed_at":"2026-05-18T00:25:13.132596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:13.132596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"stRy4Y5Iw0h22WWgiML6Oc83zJ/VtTm08muu4tw8iPj41FLZvPFnkVKqsdEhkn5VsQQU8Z+zkgOHwwXNxlLJDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:13.133163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b5f9311ab10c7d01a23aeaf1a229bbdc406ff5f670729ec5a7912e778aff3e8","sha256:6685b41d5ac1d0fe4fc18e1823702bf1250f797f90983cb8dec759183d392eb0"],"state_sha256":"abd2c6db591f9fe50e918c3aabefe51c06c003f8aa84018938c0fff5312d1edc"}