{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:A6DSFXXR23OP6RTOD5Q2ER4GIA","short_pith_number":"pith:A6DSFXXR","schema_version":"1.0","canonical_sha256":"078722def1d6dcff466e1f61a24786403c45c67bf1a8aaf9df961c5174a17f91","source":{"kind":"arxiv","id":"2606.22334","version":1},"attestation_state":"computed","paper":{"title":"Lattice-quantile estimation of {\\pi} and convex-region integrals from coined two-dimensional quantum walks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chih-Yu Chen, En-Jui Kuo, Jen-Yu Chang, Tsung-Wei Huang","submitted_at":"2026-06-21T04:52:59Z","abstract_excerpt":"Monte Carlo integration is fundamentally limited by the M^(-1/2) rate that the Cramer-Rao bound imposes on any sample-mean estimator of an expectation value, regardless of how the samples are drawn. Coined discrete-time quantum walks (DTQWs) are known to spread ballistically - their position variance scales as T^2 against the diffusive T of classical random walks - yet this faster spreading has not been exploited for numerical integration. We show that coupling the ballistic scaling of a 2D DTQW to the Hardy-Huxley asymptotic for Gauss circle lattice counts produces estimators whose dominant e"},"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":"2606.22334","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-21T04:52:59Z","cross_cats_sorted":[],"title_canon_sha256":"77bad3c35cf383eff575c2bbc7ac1c8a46886e794be1eeb46c053f5586b4890f","abstract_canon_sha256":"a277ce02ebd3908bbcb6336156966f435cbf2c6d8967ebee7e1c781f2f480f87"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:35.116045Z","signature_b64":"FBxJHsi82ijUEWc9ZvppmbJ8TsmLik/baPl9wWYWtT4UHCK3XsmORfn5AiVOEchltMgVgqUsMXErrNEDBtsMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"078722def1d6dcff466e1f61a24786403c45c67bf1a8aaf9df961c5174a17f91","last_reissued_at":"2026-06-23T02:13:35.115651Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:35.115651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice-quantile estimation of {\\pi} and convex-region integrals from coined two-dimensional quantum walks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chih-Yu Chen, En-Jui Kuo, Jen-Yu Chang, Tsung-Wei Huang","submitted_at":"2026-06-21T04:52:59Z","abstract_excerpt":"Monte Carlo integration is fundamentally limited by the M^(-1/2) rate that the Cramer-Rao bound imposes on any sample-mean estimator of an expectation value, regardless of how the samples are drawn. Coined discrete-time quantum walks (DTQWs) are known to spread ballistically - their position variance scales as T^2 against the diffusive T of classical random walks - yet this faster spreading has not been exploited for numerical integration. We show that coupling the ballistic scaling of a 2D DTQW to the Hardy-Huxley asymptotic for Gauss circle lattice counts produces estimators whose dominant e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22334","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/2606.22334/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.22334","created_at":"2026-06-23T02:13:35.115719+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22334v1","created_at":"2026-06-23T02:13:35.115719+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22334","created_at":"2026-06-23T02:13:35.115719+00:00"},{"alias_kind":"pith_short_12","alias_value":"A6DSFXXR23OP","created_at":"2026-06-23T02:13:35.115719+00:00"},{"alias_kind":"pith_short_16","alias_value":"A6DSFXXR23OP6RTO","created_at":"2026-06-23T02:13:35.115719+00:00"},{"alias_kind":"pith_short_8","alias_value":"A6DSFXXR","created_at":"2026-06-23T02:13:35.115719+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/A6DSFXXR23OP6RTOD5Q2ER4GIA","json":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA.json","graph_json":"https://pith.science/api/pith-number/A6DSFXXR23OP6RTOD5Q2ER4GIA/graph.json","events_json":"https://pith.science/api/pith-number/A6DSFXXR23OP6RTOD5Q2ER4GIA/events.json","paper":"https://pith.science/paper/A6DSFXXR"},"agent_actions":{"view_html":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA","download_json":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA.json","view_paper":"https://pith.science/paper/A6DSFXXR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22334&json=true","fetch_graph":"https://pith.science/api/pith-number/A6DSFXXR23OP6RTOD5Q2ER4GIA/graph.json","fetch_events":"https://pith.science/api/pith-number/A6DSFXXR23OP6RTOD5Q2ER4GIA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA/action/storage_attestation","attest_author":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA/action/author_attestation","sign_citation":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA/action/citation_signature","submit_replication":"https://pith.science/pith/A6DSFXXR23OP6RTOD5Q2ER4GIA/action/replication_record"}},"created_at":"2026-06-23T02:13:35.115719+00:00","updated_at":"2026-06-23T02:13:35.115719+00:00"}