{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SVLMHOA4M2VKUYMGOM3EDKVXOV","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":"332f231cf505939d8efaa07d131eb84b8833fbc3aa5228dab98d0208308b5232","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2023-08-18T13:28:02Z","title_canon_sha256":"88cbea36166cf581cc0aa0d4dd25ffbc3d52bd7c5d965876f01ccf8d97fb5e43"},"schema_version":"1.0","source":{"id":"2308.09549","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.09549","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"2308.09549v7","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.09549","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"SVLMHOA4M2VK","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"pith_short_16","alias_value":"SVLMHOA4M2VKUYMG","created_at":"2026-05-20T00:02:45Z"},{"alias_kind":"pith_short_8","alias_value":"SVLMHOA4","created_at":"2026-05-20T00:02:45Z"}],"graph_snapshots":[{"event_id":"sha256:1ab4e5e99bf1db36f6c1562299ba4b586dee84792b454ea1930cea5779936664","target":"graph","created_at":"2026-05-20T00:02:45Z","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/2308.09549/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we extend the techniques used in our previous work to show that there exists a probabilistic Turing machine running within time $O(n^k)$ for all $k\\in\\mathbb{N}_1$ accepting a language $L_d$ that is different from any language in $\\mathcal{P}$, and then further to prove that $L_d\\in\\mathcal{BPP}$, thus separating the complexity class $\\mathcal{BPP}$ from the class $\\mathcal{P}$ (i.e., $\\mathcal{P}\\subsetneqq\\mathcal{BPP}$).\n  Since the complexity class $\\mathcal{BQP}$ of {\\em bounded error quantum polynomial-time} contains the complexity class $\\mathcal{BPP}$ (i.e., $\\mathcal{BP","authors_text":"Tianrong Lin","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2023-08-18T13:28:02Z","title":"Probabilistic Computers (So Quantum Computers) Are More Rigorously Powerful Than Traditional Computers, and Derandomization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.09549","kind":"arxiv","version":7},"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:f576c867fe7fa42a52142ee13f79a3d029413277a7b3ef1c875a691c9cc05ea9","target":"record","created_at":"2026-05-20T00:02:45Z","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":"332f231cf505939d8efaa07d131eb84b8833fbc3aa5228dab98d0208308b5232","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2023-08-18T13:28:02Z","title_canon_sha256":"88cbea36166cf581cc0aa0d4dd25ffbc3d52bd7c5d965876f01ccf8d97fb5e43"},"schema_version":"1.0","source":{"id":"2308.09549","kind":"arxiv","version":7}},"canonical_sha256":"9556c3b81c66aaaa6186733641aab775691aea3b7caad0a5b3418c3da19bd482","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9556c3b81c66aaaa6186733641aab775691aea3b7caad0a5b3418c3da19bd482","first_computed_at":"2026-05-20T00:02:45.147908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:45.147908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ybmgRKzXZgirye4U1kZ7tfHWuMWeo6IMJ6cjsMU+WHCDQrmV+wXuKVLKXXxXBILlCcF+nncOXxD6VJ+Q52xkBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:45.148444Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.09549","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f576c867fe7fa42a52142ee13f79a3d029413277a7b3ef1c875a691c9cc05ea9","sha256:1ab4e5e99bf1db36f6c1562299ba4b586dee84792b454ea1930cea5779936664"],"state_sha256":"c1c6bc8f5a97848183df2eaa331334ef17aa5e3b56bad6d6c01daa353827f80b"}