{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:JXD2KSXV27HUDDASJWN5ZUS3SZ","short_pith_number":"pith:JXD2KSXV","schema_version":"1.0","canonical_sha256":"4dc7a54af5d7cf418c124d9bdcd25b966b24bbe6c6703839d8572ba0f7ff9719","source":{"kind":"arxiv","id":"1705.09710","version":1},"attestation_state":"computed","paper":{"title":"A Block-Sensitivity Lower Bound for Quantum Testing Hamming Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Marcos Villagra","submitted_at":"2017-05-26T20:41:40Z","abstract_excerpt":"The Gap-Hamming distance problem is the promise problem of deciding if the Hamming distance $h$ between two strings of length $n$ is greater than $a$ or less than $b$, where the gap $g=|a-b|\\geq 1$ and $a$ and $b$ could depend on $n$. In this short note, we give a lower bound of $\\Omega( \\sqrt{n/g})$ on the quantum query complexity of computing the Gap-Hamming distance between two given strings of lenght $n$. The proof is a combinatorial argument based on block sensitivity and a reduction from a threshold function."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.09710","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-05-26T20:41:40Z","cross_cats_sorted":[],"title_canon_sha256":"3e9ba685a0742538de3185aab064f49a6982bee5df5b505753176d1b574d6f91","abstract_canon_sha256":"e4526ee64af8471ed0d3a1bb7e056805ceddb525aa11ac1027a95e9773236ade"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:34.660837Z","signature_b64":"Xvvng6nbkUb2jslZ0Rsd5/xwx7/enpuJd/6/LIjQ/VIO358YZ9NhRFdOMhxLsfBe0oUfV8vAprpMRvNeLvE9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dc7a54af5d7cf418c124d9bdcd25b966b24bbe6c6703839d8572ba0f7ff9719","last_reissued_at":"2026-05-18T00:43:34.660246Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:34.660246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Block-Sensitivity Lower Bound for Quantum Testing Hamming Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Marcos Villagra","submitted_at":"2017-05-26T20:41:40Z","abstract_excerpt":"The Gap-Hamming distance problem is the promise problem of deciding if the Hamming distance $h$ between two strings of length $n$ is greater than $a$ or less than $b$, where the gap $g=|a-b|\\geq 1$ and $a$ and $b$ could depend on $n$. In this short note, we give a lower bound of $\\Omega( \\sqrt{n/g})$ on the quantum query complexity of computing the Gap-Hamming distance between two given strings of lenght $n$. The proof is a combinatorial argument based on block sensitivity and a reduction from a threshold function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09710","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.09710","created_at":"2026-05-18T00:43:34.660354+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.09710v1","created_at":"2026-05-18T00:43:34.660354+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09710","created_at":"2026-05-18T00:43:34.660354+00:00"},{"alias_kind":"pith_short_12","alias_value":"JXD2KSXV27HU","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"JXD2KSXV27HUDDAS","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"JXD2KSXV","created_at":"2026-05-18T12:31:24.725408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ","json":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ.json","graph_json":"https://pith.science/api/pith-number/JXD2KSXV27HUDDASJWN5ZUS3SZ/graph.json","events_json":"https://pith.science/api/pith-number/JXD2KSXV27HUDDASJWN5ZUS3SZ/events.json","paper":"https://pith.science/paper/JXD2KSXV"},"agent_actions":{"view_html":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ","download_json":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ.json","view_paper":"https://pith.science/paper/JXD2KSXV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.09710&json=true","fetch_graph":"https://pith.science/api/pith-number/JXD2KSXV27HUDDASJWN5ZUS3SZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JXD2KSXV27HUDDASJWN5ZUS3SZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ/action/storage_attestation","attest_author":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ/action/author_attestation","sign_citation":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ/action/citation_signature","submit_replication":"https://pith.science/pith/JXD2KSXV27HUDDASJWN5ZUS3SZ/action/replication_record"}},"created_at":"2026-05-18T00:43:34.660354+00:00","updated_at":"2026-05-18T00:43:34.660354+00:00"}