{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:E4LGKWFPW36AWUW4X2C5CLGZRB","short_pith_number":"pith:E4LGKWFP","canonical_record":{"source":{"id":"quant-ph/9911082","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1999-11-18T08:39:50Z","cross_cats_sorted":[],"title_canon_sha256":"5a5dc96ca7743057c5477ea991268c8da5e2af21957eaedd1b95b7f7b174d54a","abstract_canon_sha256":"234c3510c879303bf09055a9c5edfd1b2948f38550c4496cef537b132844aba4"},"schema_version":"1.0"},"canonical_sha256":"27166558afb6fc0b52dcbe85d12cd9885727a5ba73c165ce69ae6343adeb07ac","source":{"kind":"arxiv","id":"quant-ph/9911082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9911082","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9911082v1","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9911082","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"E4LGKWFPW36A","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"pith_short_16","alias_value":"E4LGKWFPW36AWUW4","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"pith_short_8","alias_value":"E4LGKWFP","created_at":"2026-07-04T14:47:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:E4LGKWFPW36AWUW4X2C5CLGZRB","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9911082","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1999-11-18T08:39:50Z","cross_cats_sorted":[],"title_canon_sha256":"5a5dc96ca7743057c5477ea991268c8da5e2af21957eaedd1b95b7f7b174d54a","abstract_canon_sha256":"234c3510c879303bf09055a9c5edfd1b2948f38550c4496cef537b132844aba4"},"schema_version":"1.0"},"canonical_sha256":"27166558afb6fc0b52dcbe85d12cd9885727a5ba73c165ce69ae6343adeb07ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:47:29.907333Z","signature_b64":"WJYJycTLCiiX+fXnSRirs2DtnO1O6dzogV/nKbIOuewFiWAcnD4oMRcxqy62WyAneZbMpHGB9BCwFc2DnIKmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27166558afb6fc0b52dcbe85d12cd9885727a5ba73c165ce69ae6343adeb07ac","last_reissued_at":"2026-07-04T14:47:29.906935Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:47:29.906935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9911082","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":"2026-07-04T14:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W5JrF8l2jvKp7t0bClEmnvIFa30olt/EAJjy9qyPTqxeJKmmJFjrEIxdRaQyVIWG9inc/E+wZYiCeTriWOBxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T17:09:35.909967Z"},"content_sha256":"4c69d31afcc31b8b1d3673130dff5d2dcd5fb9026afdd89c7604dfc470d30ce7","schema_version":"1.0","event_id":"sha256:4c69d31afcc31b8b1d3673130dff5d2dcd5fb9026afdd89c7604dfc470d30ce7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:E4LGKWFPW36AWUW4X2C5CLGZRB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Quantum Algorithm for finding the Maximum","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Ashish Ahuja, Sanjiv Kapoor","submitted_at":"1999-11-18T08:39:50Z","abstract_excerpt":"This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by exploiting the property of quantum states to exist in a superposition of states and hence performing an operation on a number of elements in one go. A tight upper bound of 6.8(sqrt(N)) for the number of steps needed using this algorithm was found. These steps are the number of queries made to the oracle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9911082","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/9911082/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":"2026-07-04T14:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/x/ZpLNRXG7njAFjCs2rEFQVg+/QBPssA1QhYm12ge6dpgSDQK23zgNp5B87m4eyJWlvBOguOmSofHvUK7UsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T17:09:35.910356Z"},"content_sha256":"603c712c974a44c8388f184f73cfaad1dad8827cc2a981da5bc95c1a9e1fc120","schema_version":"1.0","event_id":"sha256:603c712c974a44c8388f184f73cfaad1dad8827cc2a981da5bc95c1a9e1fc120"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4LGKWFPW36AWUW4X2C5CLGZRB/bundle.json","state_url":"https://pith.science/pith/E4LGKWFPW36AWUW4X2C5CLGZRB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4LGKWFPW36AWUW4X2C5CLGZRB/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":"2026-07-22T17:09:35Z","links":{"resolver":"https://pith.science/pith/E4LGKWFPW36AWUW4X2C5CLGZRB","bundle":"https://pith.science/pith/E4LGKWFPW36AWUW4X2C5CLGZRB/bundle.json","state":"https://pith.science/pith/E4LGKWFPW36AWUW4X2C5CLGZRB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4LGKWFPW36AWUW4X2C5CLGZRB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:E4LGKWFPW36AWUW4X2C5CLGZRB","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":"234c3510c879303bf09055a9c5edfd1b2948f38550c4496cef537b132844aba4","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-11-18T08:39:50Z","title_canon_sha256":"5a5dc96ca7743057c5477ea991268c8da5e2af21957eaedd1b95b7f7b174d54a"},"schema_version":"1.0","source":{"id":"quant-ph/9911082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9911082","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9911082v1","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9911082","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"E4LGKWFPW36A","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"pith_short_16","alias_value":"E4LGKWFPW36AWUW4","created_at":"2026-07-04T14:47:29Z"},{"alias_kind":"pith_short_8","alias_value":"E4LGKWFP","created_at":"2026-07-04T14:47:29Z"}],"graph_snapshots":[{"event_id":"sha256:603c712c974a44c8388f184f73cfaad1dad8827cc2a981da5bc95c1a9e1fc120","target":"graph","created_at":"2026-07-04T14:47:29Z","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/9911082/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper describes a quantum algorithm for finding the maximum among N items. The classical method for the same problem takes O(N) steps because we need to compare two numbers in one step. This algorithm takes O(sqrt(N)) steps by exploiting the property of quantum states to exist in a superposition of states and hence performing an operation on a number of elements in one go. A tight upper bound of 6.8(sqrt(N)) for the number of steps needed using this algorithm was found. These steps are the number of queries made to the oracle.","authors_text":"Ashish Ahuja, Sanjiv Kapoor","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1999-11-18T08:39:50Z","title":"A Quantum Algorithm for finding the Maximum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9911082","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":"sha256:4c69d31afcc31b8b1d3673130dff5d2dcd5fb9026afdd89c7604dfc470d30ce7","target":"record","created_at":"2026-07-04T14:47:29Z","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":"234c3510c879303bf09055a9c5edfd1b2948f38550c4496cef537b132844aba4","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1999-11-18T08:39:50Z","title_canon_sha256":"5a5dc96ca7743057c5477ea991268c8da5e2af21957eaedd1b95b7f7b174d54a"},"schema_version":"1.0","source":{"id":"quant-ph/9911082","kind":"arxiv","version":1}},"canonical_sha256":"27166558afb6fc0b52dcbe85d12cd9885727a5ba73c165ce69ae6343adeb07ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27166558afb6fc0b52dcbe85d12cd9885727a5ba73c165ce69ae6343adeb07ac","first_computed_at":"2026-07-04T14:47:29.906935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:47:29.906935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WJYJycTLCiiX+fXnSRirs2DtnO1O6dzogV/nKbIOuewFiWAcnD4oMRcxqy62WyAneZbMpHGB9BCwFc2DnIKmCw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:47:29.907333Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9911082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c69d31afcc31b8b1d3673130dff5d2dcd5fb9026afdd89c7604dfc470d30ce7","sha256:603c712c974a44c8388f184f73cfaad1dad8827cc2a981da5bc95c1a9e1fc120"],"state_sha256":"3387bcbc508c3e0ed71870b9388387e0f02f6a32d1ed9b0e48b85bef759534ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UgCFS2WzdrLlaUlKr+OM8+qwxOqAdQDPXOnpra4U7WfOB4d87BU8AMb++PKx53qqhnXyFIlssSRHXoiifHnVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T17:09:35.913905Z","bundle_sha256":"1bc1dcef866238213097ab93805d6a7048cd5b4f7fdb8aef10b4b8112498e4f0"}}