{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:VYP7Z5RQTD3H5MG4RIOVZUA2WQ","short_pith_number":"pith:VYP7Z5RQ","canonical_record":{"source":{"id":"quant-ph/0511200","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-11-21T10:56:29Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"e08ffeafadbb8cb307fe9c05c713e60f7c0d526892be4bacba415da9611804b0","abstract_canon_sha256":"6c3db521fb299ce7cb21c79775fdf8fcad8c9d16a1b6f2adcd66f62556d981de"},"schema_version":"1.0"},"canonical_sha256":"ae1ffcf63098f67eb0dc8a1d5cd01ab426f8d8d809d33ccb38d54d2112155fce","source":{"kind":"arxiv","id":"quant-ph/0511200","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0511200","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0511200v2","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0511200","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"pith_short_12","alias_value":"VYP7Z5RQTD3H","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"pith_short_16","alias_value":"VYP7Z5RQTD3H5MG4","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"pith_short_8","alias_value":"VYP7Z5RQ","created_at":"2026-07-04T14:51:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:VYP7Z5RQTD3H5MG4RIOVZUA2WQ","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0511200","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-11-21T10:56:29Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"e08ffeafadbb8cb307fe9c05c713e60f7c0d526892be4bacba415da9611804b0","abstract_canon_sha256":"6c3db521fb299ce7cb21c79775fdf8fcad8c9d16a1b6f2adcd66f62556d981de"},"schema_version":"1.0"},"canonical_sha256":"ae1ffcf63098f67eb0dc8a1d5cd01ab426f8d8d809d33ccb38d54d2112155fce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:51:52.065997Z","signature_b64":"KofY4sE8IX+mUM9L8Z9V2I8Q1u2h/XY6X3QrVygThALBfN+WcPkPCfN5SuAUkxFuhZO4PvR8ofFRRB0bLCu3CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae1ffcf63098f67eb0dc8a1d5cd01ab426f8d8d809d33ccb38d54d2112155fce","last_reissued_at":"2026-07-04T14:51:52.065567Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:51:52.065567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0511200","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:51:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ntkHL/sI971z2rLF2/09MI2o3toWGg3aqcNIViWLPE3f+Z+jsi8L78yNqDb6mhULcfV8gPOITj2NoX1Ustg7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:36:00.913937Z"},"content_sha256":"28ef953a7c6c353dfb5ff0fbe92fc4014b7a10ac6936eae531440a81c5a9142c","schema_version":"1.0","event_id":"sha256:28ef953a7c6c353dfb5ff0fbe92fc4014b7a10ac6936eae531440a81c5a9142c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:VYP7Z5RQTD3H5MG4RIOVZUA2WQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Quantum Lower Bound Method, with Applications to Direct Product Theorems and Time-Space Tradeoffs","license":"","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Andris Ambainis (U Waterloo), Robert Spalek (CWI), Ronald de Wolf (CWI)","submitted_at":"2005-11-21T10:56:29Z","abstract_excerpt":"We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct product theorem for 2-sided error quantum algorithms computing k independent instances of a symmetric Boolean function: if the algorithm uses significantly less than k times the number of queries needed for one instance of the function, then its success probability is exponentially small in k. We also use the polynomial method to prove a direct product theorem "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0511200","kind":"arxiv","version":2},"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/0511200/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":"2026-07-04T14:51:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uk9XQtxOrlMnaiphoCathCrPySN8BtCLhhW6jc+ChiKw6oAC13zFezhZqHJEvIen+TOm0e/zWF3Oj2VyiLjNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:36:00.914602Z"},"content_sha256":"876ec4958ff9a19558e76ed5cd9f5cac452a0a4dba5f932e06c308d3fd78aae7","schema_version":"1.0","event_id":"sha256:876ec4958ff9a19558e76ed5cd9f5cac452a0a4dba5f932e06c308d3fd78aae7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYP7Z5RQTD3H5MG4RIOVZUA2WQ/bundle.json","state_url":"https://pith.science/pith/VYP7Z5RQTD3H5MG4RIOVZUA2WQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYP7Z5RQTD3H5MG4RIOVZUA2WQ/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":"2026-08-05T14:36:00Z","links":{"resolver":"https://pith.science/pith/VYP7Z5RQTD3H5MG4RIOVZUA2WQ","bundle":"https://pith.science/pith/VYP7Z5RQTD3H5MG4RIOVZUA2WQ/bundle.json","state":"https://pith.science/pith/VYP7Z5RQTD3H5MG4RIOVZUA2WQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYP7Z5RQTD3H5MG4RIOVZUA2WQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:VYP7Z5RQTD3H5MG4RIOVZUA2WQ","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":"6c3db521fb299ce7cb21c79775fdf8fcad8c9d16a1b6f2adcd66f62556d981de","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"2005-11-21T10:56:29Z","title_canon_sha256":"e08ffeafadbb8cb307fe9c05c713e60f7c0d526892be4bacba415da9611804b0"},"schema_version":"1.0","source":{"id":"quant-ph/0511200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0511200","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0511200v2","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0511200","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"pith_short_12","alias_value":"VYP7Z5RQTD3H","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"pith_short_16","alias_value":"VYP7Z5RQTD3H5MG4","created_at":"2026-07-04T14:51:52Z"},{"alias_kind":"pith_short_8","alias_value":"VYP7Z5RQ","created_at":"2026-07-04T14:51:52Z"}],"graph_snapshots":[{"event_id":"sha256:876ec4958ff9a19558e76ed5cd9f5cac452a0a4dba5f932e06c308d3fd78aae7","target":"graph","created_at":"2026-07-04T14:51:52Z","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/0511200/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct product theorem for 2-sided error quantum algorithms computing k independent instances of a symmetric Boolean function: if the algorithm uses significantly less than k times the number of queries needed for one instance of the function, then its success probability is exponentially small in k. We also use the polynomial method to prove a direct product theorem ","authors_text":"Andris Ambainis (U Waterloo), Robert Spalek (CWI), Ronald de Wolf (CWI)","cross_cats":["cs.CC"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2005-11-21T10:56:29Z","title":"A New Quantum Lower Bound Method, with Applications to Direct Product Theorems and Time-Space Tradeoffs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0511200","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":"sha256:28ef953a7c6c353dfb5ff0fbe92fc4014b7a10ac6936eae531440a81c5a9142c","target":"record","created_at":"2026-07-04T14:51:52Z","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":"6c3db521fb299ce7cb21c79775fdf8fcad8c9d16a1b6f2adcd66f62556d981de","cross_cats_sorted":["cs.CC"],"license":"","primary_cat":"quant-ph","submitted_at":"2005-11-21T10:56:29Z","title_canon_sha256":"e08ffeafadbb8cb307fe9c05c713e60f7c0d526892be4bacba415da9611804b0"},"schema_version":"1.0","source":{"id":"quant-ph/0511200","kind":"arxiv","version":2}},"canonical_sha256":"ae1ffcf63098f67eb0dc8a1d5cd01ab426f8d8d809d33ccb38d54d2112155fce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae1ffcf63098f67eb0dc8a1d5cd01ab426f8d8d809d33ccb38d54d2112155fce","first_computed_at":"2026-07-04T14:51:52.065567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:51:52.065567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KofY4sE8IX+mUM9L8Z9V2I8Q1u2h/XY6X3QrVygThALBfN+WcPkPCfN5SuAUkxFuhZO4PvR8ofFRRB0bLCu3CQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:51:52.065997Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0511200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28ef953a7c6c353dfb5ff0fbe92fc4014b7a10ac6936eae531440a81c5a9142c","sha256:876ec4958ff9a19558e76ed5cd9f5cac452a0a4dba5f932e06c308d3fd78aae7"],"state_sha256":"337ff050713b2c3fe93f50091f26f2dfad87151b54a4192eaf5880aa91175d3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQ0smf9V0NTYbEbpI3U5jncJwwJWkTVwJGu+1RNx3WvnD5BiF81u0YSXxcGs7Go+9kA3lEQO2TYKrmh+hrBxCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:36:00.919660Z","bundle_sha256":"c8ef870e0154c099c7da65d38963430eac6e29711ac6b46aefb71015a829bc20"}}