{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:IRPTC7EQT7HODSGJ4G2JDB4TGD","short_pith_number":"pith:IRPTC7EQ","schema_version":"1.0","canonical_sha256":"445f317c909fcee1c8c9e1b491879330d21b8a099a926ceccbf011cc49f2e1cb","source":{"kind":"arxiv","id":"2607.19874","version":1},"attestation_state":"computed","paper":{"title":"Removing Online Exponential Net Search from Solovay-Kitaev","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Cl\\'ement Maria (DATASHAPE), COATI), Henrique Ennes (DATASHAPE, UniCA","submitted_at":"2026-07-22T08:01:43Z","abstract_excerpt":"The Solovay-Kitaev algorithm describes how to approximate, to arbitrary precision, a matrix in the special unitary group SU(d) using any fixed universal gate set. Although the algorithm scales as O(poly(log(1/$\\epsilon$))), where $\\epsilon$ is the maximum targeted approximation error, its running time depends exponentially on the qudit dimension d. This bad dependence can be traced to its explicit use of an $\\epsilon$_0-net of size 2 $\\Omega$(d^2) , which is queried O(poly(log(1/$\\epsilon$))) times throughout the execution. For this reason, the standard Solovay-Kitaev theorem is usually stated"},"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":"2607.19874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2026-07-22T08:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"f7609be50e19913dc81be6e0f6d9bc8ac30787c8ed96be653dad0ac2b17fb15a","abstract_canon_sha256":"58f603385134b4a3089ed879ca78037e596f9fde86d444ad7f98d997a6439773"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-23T01:24:05.072176Z","signature_b64":"o0ZhHbYf7ugbC6atJgIAkpmKr/rWT3sFCLmG67dMU6ZA6CyETWQhmBcGAAcTE4Tr8ClEZ1yQYvF6i4eUVTv2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"445f317c909fcee1c8c9e1b491879330d21b8a099a926ceccbf011cc49f2e1cb","last_reissued_at":"2026-07-23T01:24:05.071378Z","signature_status":"signed_v1","first_computed_at":"2026-07-23T01:24:05.071378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Removing Online Exponential Net Search from Solovay-Kitaev","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Cl\\'ement Maria (DATASHAPE), COATI), Henrique Ennes (DATASHAPE, UniCA","submitted_at":"2026-07-22T08:01:43Z","abstract_excerpt":"The Solovay-Kitaev algorithm describes how to approximate, to arbitrary precision, a matrix in the special unitary group SU(d) using any fixed universal gate set. Although the algorithm scales as O(poly(log(1/$\\epsilon$))), where $\\epsilon$ is the maximum targeted approximation error, its running time depends exponentially on the qudit dimension d. This bad dependence can be traced to its explicit use of an $\\epsilon$_0-net of size 2 $\\Omega$(d^2) , which is queried O(poly(log(1/$\\epsilon$))) times throughout the execution. For this reason, the standard Solovay-Kitaev theorem is usually stated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19874","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/2607.19874/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":"2607.19874","created_at":"2026-07-23T01:24:05.071817+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.19874v1","created_at":"2026-07-23T01:24:05.071817+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19874","created_at":"2026-07-23T01:24:05.071817+00:00"},{"alias_kind":"pith_short_12","alias_value":"IRPTC7EQT7HO","created_at":"2026-07-23T01:24:05.071817+00:00"},{"alias_kind":"pith_short_16","alias_value":"IRPTC7EQT7HODSGJ","created_at":"2026-07-23T01:24:05.071817+00:00"},{"alias_kind":"pith_short_8","alias_value":"IRPTC7EQ","created_at":"2026-07-23T01:24:05.071817+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/IRPTC7EQT7HODSGJ4G2JDB4TGD","json":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD.json","graph_json":"https://pith.science/api/pith-number/IRPTC7EQT7HODSGJ4G2JDB4TGD/graph.json","events_json":"https://pith.science/api/pith-number/IRPTC7EQT7HODSGJ4G2JDB4TGD/events.json","paper":"https://pith.science/paper/IRPTC7EQ"},"agent_actions":{"view_html":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD","download_json":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD.json","view_paper":"https://pith.science/paper/IRPTC7EQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.19874&json=true","fetch_graph":"https://pith.science/api/pith-number/IRPTC7EQT7HODSGJ4G2JDB4TGD/graph.json","fetch_events":"https://pith.science/api/pith-number/IRPTC7EQT7HODSGJ4G2JDB4TGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD/action/storage_attestation","attest_author":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD/action/author_attestation","sign_citation":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD/action/citation_signature","submit_replication":"https://pith.science/pith/IRPTC7EQT7HODSGJ4G2JDB4TGD/action/replication_record"}},"created_at":"2026-07-23T01:24:05.071817+00:00","updated_at":"2026-07-23T01:24:05.071817+00:00"}