{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:T7WZ7QDHKEFQ3HLTU2HZTOYQUX","short_pith_number":"pith:T7WZ7QDH","canonical_record":{"source":{"id":"quant-ph/9805082","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-05-27T22:35:27Z","cross_cats_sorted":[],"title_canon_sha256":"0f8763b2f7d16001c725ed47c00a3bafbaa8bd60adf4f562311bcef490818325","abstract_canon_sha256":"383db99c15ffea77428b2b11a1975cc372475909c8411aab6767f5b2e6582364"},"schema_version":"1.0"},"canonical_sha256":"9fed9fc067510b0d9d73a68f99bb10a5e67ce85ec0ec8c53f8a881a8f76dcdf2","source":{"kind":"arxiv","id":"quant-ph/9805082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9805082","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9805082v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9805082","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"T7WZ7QDHKEFQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"T7WZ7QDHKEFQ3HLT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"T7WZ7QDH","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:T7WZ7QDHKEFQ3HLTU2HZTOYQUX","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9805082","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-05-27T22:35:27Z","cross_cats_sorted":[],"title_canon_sha256":"0f8763b2f7d16001c725ed47c00a3bafbaa8bd60adf4f562311bcef490818325","abstract_canon_sha256":"383db99c15ffea77428b2b11a1975cc372475909c8411aab6767f5b2e6582364"},"schema_version":"1.0"},"canonical_sha256":"9fed9fc067510b0d9d73a68f99bb10a5e67ce85ec0ec8c53f8a881a8f76dcdf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:35.437594Z","signature_b64":"28K6H0ppRznMMa9oLB8aBInwJmBnQwXtDIEnmaAI7Al1uNKrV42UAQniIVRdcrGr9xiA9NZsxF/Fjp0Tw7FvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fed9fc067510b0d9d73a68f99bb10a5e67ce85ec0ec8c53f8a881a8f76dcdf2","last_reissued_at":"2026-05-18T00:53:35.437186Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:35.437186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9805082","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":"2026-05-18T00:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KaK9tH4OrJnoRtXpdp+8ISdLJ1vnnvWxsBRWjO93SaIt+0neNGTPhN6yAOZzhXU94Z6IYP9AwGbIsQMDqlfBAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:05:40.937154Z"},"content_sha256":"c94625e6a313b58b2cb1a5ddb984b347f96534995a93ea8fe840d914688fe8a0","schema_version":"1.0","event_id":"sha256:c94625e6a313b58b2cb1a5ddb984b347f96534995a93ea8fe840d914688fe8a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:T7WZ7QDHKEFQ3HLTU2HZTOYQUX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Counting","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"(2) Odense University), Alain Tapp (1) ((1) Universite de Montreal, Gilles Brassard (1), Peter Hoyer (2)","submitted_at":"1998-05-27T22:35:27Z","abstract_excerpt":"We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover's and Shor's quantum algorithms to perform approximate counting, which can be seen as an amplitude estimation process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9805082","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":""},"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":"2026-05-18T00:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8tUVgBnG+J/q3T/aP4gLt37Ar9Ghq84vsKp9je80AcWgaW7L0/I9aoVHrp7HY0usVbDDyBgsxxhhkZgF7oZeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:05:40.937506Z"},"content_sha256":"b50d834ad64c5498654cb3dd2fe512d515d30b983a1ce48a9c8459497401495c","schema_version":"1.0","event_id":"sha256:b50d834ad64c5498654cb3dd2fe512d515d30b983a1ce48a9c8459497401495c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7WZ7QDHKEFQ3HLTU2HZTOYQUX/bundle.json","state_url":"https://pith.science/pith/T7WZ7QDHKEFQ3HLTU2HZTOYQUX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7WZ7QDHKEFQ3HLTU2HZTOYQUX/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":"2026-06-01T07:05:40Z","links":{"resolver":"https://pith.science/pith/T7WZ7QDHKEFQ3HLTU2HZTOYQUX","bundle":"https://pith.science/pith/T7WZ7QDHKEFQ3HLTU2HZTOYQUX/bundle.json","state":"https://pith.science/pith/T7WZ7QDHKEFQ3HLTU2HZTOYQUX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7WZ7QDHKEFQ3HLTU2HZTOYQUX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:T7WZ7QDHKEFQ3HLTU2HZTOYQUX","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":"383db99c15ffea77428b2b11a1975cc372475909c8411aab6767f5b2e6582364","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1998-05-27T22:35:27Z","title_canon_sha256":"0f8763b2f7d16001c725ed47c00a3bafbaa8bd60adf4f562311bcef490818325"},"schema_version":"1.0","source":{"id":"quant-ph/9805082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9805082","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9805082v1","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9805082","created_at":"2026-05-18T00:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"T7WZ7QDHKEFQ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"T7WZ7QDHKEFQ3HLT","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"T7WZ7QDH","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:b50d834ad64c5498654cb3dd2fe512d515d30b983a1ce48a9c8459497401495c","target":"graph","created_at":"2026-05-18T00:53:35Z","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"},"paper":{"abstract_excerpt":"We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover's and Shor's quantum algorithms to perform approximate counting, which can be seen as an amplitude estimation process.","authors_text":"(2) Odense University), Alain Tapp (1) ((1) Universite de Montreal, Gilles Brassard (1), Peter Hoyer (2)","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1998-05-27T22:35:27Z","title":"Quantum Counting"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9805082","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:c94625e6a313b58b2cb1a5ddb984b347f96534995a93ea8fe840d914688fe8a0","target":"record","created_at":"2026-05-18T00:53:35Z","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":"383db99c15ffea77428b2b11a1975cc372475909c8411aab6767f5b2e6582364","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1998-05-27T22:35:27Z","title_canon_sha256":"0f8763b2f7d16001c725ed47c00a3bafbaa8bd60adf4f562311bcef490818325"},"schema_version":"1.0","source":{"id":"quant-ph/9805082","kind":"arxiv","version":1}},"canonical_sha256":"9fed9fc067510b0d9d73a68f99bb10a5e67ce85ec0ec8c53f8a881a8f76dcdf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fed9fc067510b0d9d73a68f99bb10a5e67ce85ec0ec8c53f8a881a8f76dcdf2","first_computed_at":"2026-05-18T00:53:35.437186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:35.437186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28K6H0ppRznMMa9oLB8aBInwJmBnQwXtDIEnmaAI7Al1uNKrV42UAQniIVRdcrGr9xiA9NZsxF/Fjp0Tw7FvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:35.437594Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9805082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c94625e6a313b58b2cb1a5ddb984b347f96534995a93ea8fe840d914688fe8a0","sha256:b50d834ad64c5498654cb3dd2fe512d515d30b983a1ce48a9c8459497401495c"],"state_sha256":"b1b63e4d47437fa702a8c4c4c5f8b306ce083bc042b608a00c4ef276a834f95d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IlAYfuyvg8rAEiUrBVmaDavh2TVwLwBLDBAo4mW+XB54+wsmAWbNGZpeBxyWxAdFJoDQQqbyaRlvmb1S4x0wDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:05:40.939369Z","bundle_sha256":"fe7d0f386996a1493b7187b9d62750eb676cef728b750b378396116fbb5f9586"}}