{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:PBBACDXB4NBNZ2HYPHRCMSOM7V","short_pith_number":"pith:PBBACDXB","canonical_record":{"source":{"id":"quant-ph/0308125","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-08-23T20:39:56Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"429c622e99d11757d4eb81dd4aefaaba98aaa0c1f8a2969405ccf69b5123e2e9","abstract_canon_sha256":"bf8193d2c50bebd8cfcab0d428066057b7451b7536ba853fbc00384501c27d03"},"schema_version":"1.0"},"canonical_sha256":"7842010ee1e342dce8f879e22649ccfd74e351b998987a66d0777ee65a61d61a","source":{"kind":"arxiv","id":"quant-ph/0308125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0308125","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0308125v1","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0308125","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"PBBACDXB4NBN","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"pith_short_16","alias_value":"PBBACDXB4NBNZ2HY","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"pith_short_8","alias_value":"PBBACDXB","created_at":"2026-07-04T14:46:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:PBBACDXB4NBNZ2HYPHRCMSOM7V","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0308125","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-08-23T20:39:56Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"429c622e99d11757d4eb81dd4aefaaba98aaa0c1f8a2969405ccf69b5123e2e9","abstract_canon_sha256":"bf8193d2c50bebd8cfcab0d428066057b7451b7536ba853fbc00384501c27d03"},"schema_version":"1.0"},"canonical_sha256":"7842010ee1e342dce8f879e22649ccfd74e351b998987a66d0777ee65a61d61a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:46:23.520708Z","signature_b64":"caqY60pZdzmiJqr6PC0KbGNYAhK3Gdutf0mvFjN/sC7/+tHnmCeiopChTX9rfNt4pt8M8FHpYIcAyonKHiCqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7842010ee1e342dce8f879e22649ccfd74e351b998987a66d0777ee65a61d61a","last_reissued_at":"2026-07-04T14:46:23.520299Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:46:23.520299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0308125","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":"2026-07-04T14:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eRpm6B6a7WAY3oqB79KhpqwoijHmlyeqhK8NX75aZbpOYBbSUvj4/YpdfkV90NVsutda0VGqwXAp5raUzqldBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T19:31:57.287936Z"},"content_sha256":"749ee119018f09a6dae50bff8b17efe71040d822e1e546c4bbc8037158add26d","schema_version":"1.0","event_id":"sha256:749ee119018f09a6dae50bff8b17efe71040d822e1e546c4bbc8037158add26d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:PBBACDXB4NBNZ2HYPHRCMSOM7V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum NP and a Quantum Hierarchy","license":"","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Tomoyuki Yamakami","submitted_at":"2003-08-23T20:39:56Z","abstract_excerpt":"The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define \"Quantum NP,\" the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill, Kitaev, and Watrous. From an operator point of view, NP can be viewed as the result of the exists-operator applied to P. Recently, Green, Homer, Moore, and Pollett proposed its quantum version, called the N-operator, which is an abstraction of NQP. This paper introduces the exists^{Q}-operator, which is an abstraction of QMA, and its complement, the forall^{Q}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0308125","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0308125/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:46:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YH7o+7vaOsZ5MtKA11SxY50yNK1jVIduzMzNX34o3WiwjeI0PMd5pWQsCnl5Qi+DMakruY81kqLGTTXSCUAMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T19:31:57.288291Z"},"content_sha256":"b3ef77161f9a9d7d9751fde4d1a8c3e86f3b494eeb5d2eaa3b7fd392341b4a85","schema_version":"1.0","event_id":"sha256:b3ef77161f9a9d7d9751fde4d1a8c3e86f3b494eeb5d2eaa3b7fd392341b4a85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBBACDXB4NBNZ2HYPHRCMSOM7V/bundle.json","state_url":"https://pith.science/pith/PBBACDXB4NBNZ2HYPHRCMSOM7V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBBACDXB4NBNZ2HYPHRCMSOM7V/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":"2026-08-18T19:31:57Z","links":{"resolver":"https://pith.science/pith/PBBACDXB4NBNZ2HYPHRCMSOM7V","bundle":"https://pith.science/pith/PBBACDXB4NBNZ2HYPHRCMSOM7V/bundle.json","state":"https://pith.science/pith/PBBACDXB4NBNZ2HYPHRCMSOM7V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBBACDXB4NBNZ2HYPHRCMSOM7V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:PBBACDXB4NBNZ2HYPHRCMSOM7V","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":"bf8193d2c50bebd8cfcab0d428066057b7451b7536ba853fbc00384501c27d03","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"2003-08-23T20:39:56Z","title_canon_sha256":"429c622e99d11757d4eb81dd4aefaaba98aaa0c1f8a2969405ccf69b5123e2e9"},"schema_version":"1.0","source":{"id":"quant-ph/0308125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0308125","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0308125v1","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0308125","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"pith_short_12","alias_value":"PBBACDXB4NBN","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"pith_short_16","alias_value":"PBBACDXB4NBNZ2HY","created_at":"2026-07-04T14:46:23Z"},{"alias_kind":"pith_short_8","alias_value":"PBBACDXB","created_at":"2026-07-04T14:46:23Z"}],"graph_snapshots":[{"event_id":"sha256:b3ef77161f9a9d7d9751fde4d1a8c3e86f3b494eeb5d2eaa3b7fd392341b4a85","target":"graph","created_at":"2026-07-04T14:46:23Z","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/quant-ph/0308125/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define \"Quantum NP,\" the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill, Kitaev, and Watrous. From an operator point of view, NP can be viewed as the result of the exists-operator applied to P. Recently, Green, Homer, Moore, and Pollett proposed its quantum version, called the N-operator, which is an abstraction of NQP. This paper introduces the exists^{Q}-operator, which is an abstraction of QMA, and its complement, the forall^{Q}","authors_text":"Tomoyuki Yamakami","cross_cats":["cs.CC"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2003-08-23T20:39:56Z","title":"Quantum NP and a Quantum Hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0308125","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":"sha256:749ee119018f09a6dae50bff8b17efe71040d822e1e546c4bbc8037158add26d","target":"record","created_at":"2026-07-04T14:46:23Z","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":"bf8193d2c50bebd8cfcab0d428066057b7451b7536ba853fbc00384501c27d03","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"2003-08-23T20:39:56Z","title_canon_sha256":"429c622e99d11757d4eb81dd4aefaaba98aaa0c1f8a2969405ccf69b5123e2e9"},"schema_version":"1.0","source":{"id":"quant-ph/0308125","kind":"arxiv","version":1}},"canonical_sha256":"7842010ee1e342dce8f879e22649ccfd74e351b998987a66d0777ee65a61d61a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7842010ee1e342dce8f879e22649ccfd74e351b998987a66d0777ee65a61d61a","first_computed_at":"2026-07-04T14:46:23.520299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:46:23.520299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"caqY60pZdzmiJqr6PC0KbGNYAhK3Gdutf0mvFjN/sC7/+tHnmCeiopChTX9rfNt4pt8M8FHpYIcAyonKHiCqDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:46:23.520708Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0308125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:749ee119018f09a6dae50bff8b17efe71040d822e1e546c4bbc8037158add26d","sha256:b3ef77161f9a9d7d9751fde4d1a8c3e86f3b494eeb5d2eaa3b7fd392341b4a85"],"state_sha256":"7c780f06355facb1bd8751fefe8448b4f25d0c97d735adb9d5ca42a4645073dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oiG7oCquaBoSHjnd/tETTjN6TbUbj6SYVWKQx5elUaRtGgW3rpN9UZSzjDIogqnRV4LZ1Fix/u2wObiYDVHzBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T19:31:57.292213Z","bundle_sha256":"a1f49d9f2dc47effeb044c6468ac8f411956fa20b48595f5562747ac68ad3ab9"}}