{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:TX5TWJTCGQAFUGEWASRYV2XIN4","short_pith_number":"pith:TX5TWJTC","canonical_record":{"source":{"id":"quant-ph/0408129","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-08-20T05:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"1c4d0304ec0bcd5d3c73cd3509dec33b34de5581bd5a472f2df04e0bfbf65fde","abstract_canon_sha256":"2b4ab7e04f297505116208c4e677908cd796bc1cb6486a887a5a9c8c0ad6ecac"},"schema_version":"1.0"},"canonical_sha256":"9dfb3b266234005a189604a38aeae86f2bf2136af78a543fdef1892ad303aaee","source":{"kind":"arxiv","id":"quant-ph/0408129","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0408129","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0408129v1","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0408129","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"TX5TWJTCGQAF","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"pith_short_16","alias_value":"TX5TWJTCGQAFUGEW","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"pith_short_8","alias_value":"TX5TWJTC","created_at":"2026-07-04T14:48:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:TX5TWJTCGQAFUGEWASRYV2XIN4","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0408129","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-08-20T05:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"1c4d0304ec0bcd5d3c73cd3509dec33b34de5581bd5a472f2df04e0bfbf65fde","abstract_canon_sha256":"2b4ab7e04f297505116208c4e677908cd796bc1cb6486a887a5a9c8c0ad6ecac"},"schema_version":"1.0"},"canonical_sha256":"9dfb3b266234005a189604a38aeae86f2bf2136af78a543fdef1892ad303aaee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:48:23.722575Z","signature_b64":"RcJz5kvnKUqAlULkJ2K2B7UTC/M35C0LFn6JAkiYVZL/dQ+4tt1rvWe3RZQCpc/id0AfiNwe3MOMLE9DaA08BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dfb3b266234005a189604a38aeae86f2bf2136af78a543fdef1892ad303aaee","last_reissued_at":"2026-07-04T14:48:23.722130Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:48:23.722130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0408129","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":"2026-07-04T14:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZS/bNjdXR7VeZCsAblTNq3Xw/3tphDIruNtt6YAgDq5xh1FojdltzDqVT4hI7qVnx2SsV4ulXLYUzne4uTueCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:04:00.099070Z"},"content_sha256":"e8b960d1e9206e659b1d1ee4e5e6efbf7b8ee2633b8cb9353c770647f54368d9","schema_version":"1.0","event_id":"sha256:e8b960d1e9206e659b1d1ee4e5e6efbf7b8ee2633b8cb9353c770647f54368d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:TX5TWJTCGQAFUGEWASRYV2XIN4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum computing and polynomial equations over the finite field Z_2","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Andrew P. Hines, Christopher M. Dawson, Duncan Mortimer, Henry L. Haselgrove, Michael A. Nielsen, Tobias J. Osborne","submitted_at":"2004-08-20T05:27:48Z","abstract_excerpt":"What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0408129","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/0408129/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":"2026-07-04T14:48:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ole5SrCINE8rYpkvgxJPs2ABb56o7qCIs32q6kTgdeULXNXvMZN42oBUswHxeJFDSu99X08DqLoEkq8GjfctAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:04:00.099563Z"},"content_sha256":"2a86a997c1e9396f2e57a80ca9fc83a3eb679e86b0e6bd1db9254e9e18e623b7","schema_version":"1.0","event_id":"sha256:2a86a997c1e9396f2e57a80ca9fc83a3eb679e86b0e6bd1db9254e9e18e623b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TX5TWJTCGQAFUGEWASRYV2XIN4/bundle.json","state_url":"https://pith.science/pith/TX5TWJTCGQAFUGEWASRYV2XIN4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TX5TWJTCGQAFUGEWASRYV2XIN4/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":"2026-08-03T21:04:00Z","links":{"resolver":"https://pith.science/pith/TX5TWJTCGQAFUGEWASRYV2XIN4","bundle":"https://pith.science/pith/TX5TWJTCGQAFUGEWASRYV2XIN4/bundle.json","state":"https://pith.science/pith/TX5TWJTCGQAFUGEWASRYV2XIN4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TX5TWJTCGQAFUGEWASRYV2XIN4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:TX5TWJTCGQAFUGEWASRYV2XIN4","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":"2b4ab7e04f297505116208c4e677908cd796bc1cb6486a887a5a9c8c0ad6ecac","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-08-20T05:27:48Z","title_canon_sha256":"1c4d0304ec0bcd5d3c73cd3509dec33b34de5581bd5a472f2df04e0bfbf65fde"},"schema_version":"1.0","source":{"id":"quant-ph/0408129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0408129","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0408129v1","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0408129","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"pith_short_12","alias_value":"TX5TWJTCGQAF","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"pith_short_16","alias_value":"TX5TWJTCGQAFUGEW","created_at":"2026-07-04T14:48:23Z"},{"alias_kind":"pith_short_8","alias_value":"TX5TWJTC","created_at":"2026-07-04T14:48:23Z"}],"graph_snapshots":[{"event_id":"sha256:2a86a997c1e9396f2e57a80ca9fc83a3eb679e86b0e6bd1db9254e9e18e623b7","target":"graph","created_at":"2026-07-04T14:48:23Z","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/0408129/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes.","authors_text":"Andrew P. Hines, Christopher M. Dawson, Duncan Mortimer, Henry L. Haselgrove, Michael A. Nielsen, Tobias J. Osborne","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-08-20T05:27:48Z","title":"Quantum computing and polynomial equations over the finite field Z_2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0408129","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:e8b960d1e9206e659b1d1ee4e5e6efbf7b8ee2633b8cb9353c770647f54368d9","target":"record","created_at":"2026-07-04T14:48:23Z","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":"2b4ab7e04f297505116208c4e677908cd796bc1cb6486a887a5a9c8c0ad6ecac","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-08-20T05:27:48Z","title_canon_sha256":"1c4d0304ec0bcd5d3c73cd3509dec33b34de5581bd5a472f2df04e0bfbf65fde"},"schema_version":"1.0","source":{"id":"quant-ph/0408129","kind":"arxiv","version":1}},"canonical_sha256":"9dfb3b266234005a189604a38aeae86f2bf2136af78a543fdef1892ad303aaee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dfb3b266234005a189604a38aeae86f2bf2136af78a543fdef1892ad303aaee","first_computed_at":"2026-07-04T14:48:23.722130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:48:23.722130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RcJz5kvnKUqAlULkJ2K2B7UTC/M35C0LFn6JAkiYVZL/dQ+4tt1rvWe3RZQCpc/id0AfiNwe3MOMLE9DaA08BQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:48:23.722575Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0408129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8b960d1e9206e659b1d1ee4e5e6efbf7b8ee2633b8cb9353c770647f54368d9","sha256:2a86a997c1e9396f2e57a80ca9fc83a3eb679e86b0e6bd1db9254e9e18e623b7"],"state_sha256":"7002bb45e21c33f0703cb71b8d02944a8a83bcfd9d6df8ecc908c8f73fa35161"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BxgrJBwBFLtaGZP60bnR7NTZEpIFB0Og8/Yc/kzPcXKT0bLHmPdl4EvJA28ZO468nv3VNa41o5B1iH+wcxaPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:04:00.103348Z","bundle_sha256":"5ead7c9564c61fb93581ae5121a76c1747b78d859edc5a9f00a5717d6b9ca3b9"}}