{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:JSQ5WXMD2I5AVEZZVM542HUUQZ","short_pith_number":"pith:JSQ5WXMD","schema_version":"1.0","canonical_sha256":"4ca1db5d83d23a0a9339ab3bcd1e94867506fda23140183917a1c84d4744b078","source":{"kind":"arxiv","id":"2606.22472","version":1},"attestation_state":"computed","paper":{"title":"Quantum Codes with Transversal $CCZ$ Gates and Sublinear $Z$-Stabilizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Itzhak Tamo, Ohad Elishco","submitted_at":"2026-06-21T12:32:50Z","abstract_excerpt":"We construct quantum CSS codes with transversal \\(CCZ\\) gates whose \\(Z\\)-stabilizers admit sublinear-weight generating sets. We build on the algebraic puncturing framework of Guruswami and Golowich \\cite{GG24}, which turns classical codes with the required Schur-product and distance conditions into CSS codes with transversal \\(CCZ\\). However, applying the framework directly to the algebraic expander codes of \\cite{KT26} runs into their small dual distance, and therefore produces only sublinear quantum dimension. Our main technical step is a refined puncturing theorem in which the global dual-"},"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":"2606.22472","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2026-06-21T12:32:50Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3b70dc76a26a06b845ede345dfc58f981a567e2c56773e854e2c3c1cea80e862","abstract_canon_sha256":"c5aaff05e6c72d789807e152859b42582b4cda7b9323bbe3443e235dc170b476"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:39.266863Z","signature_b64":"1VIluXEMUJZFjAvIq1cw4aRrZKVi+Hg4ynny+EDT+fXPGBvxp1h4tUIfuFYzNqxKH7ipH6t/vWr7PRpOeVuUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ca1db5d83d23a0a9339ab3bcd1e94867506fda23140183917a1c84d4744b078","last_reissued_at":"2026-06-23T02:13:39.266470Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:39.266470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Codes with Transversal $CCZ$ Gates and Sublinear $Z$-Stabilizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Itzhak Tamo, Ohad Elishco","submitted_at":"2026-06-21T12:32:50Z","abstract_excerpt":"We construct quantum CSS codes with transversal \\(CCZ\\) gates whose \\(Z\\)-stabilizers admit sublinear-weight generating sets. We build on the algebraic puncturing framework of Guruswami and Golowich \\cite{GG24}, which turns classical codes with the required Schur-product and distance conditions into CSS codes with transversal \\(CCZ\\). However, applying the framework directly to the algebraic expander codes of \\cite{KT26} runs into their small dual distance, and therefore produces only sublinear quantum dimension. Our main technical step is a refined puncturing theorem in which the global dual-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22472","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/2606.22472/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":"2606.22472","created_at":"2026-06-23T02:13:39.266533+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22472v1","created_at":"2026-06-23T02:13:39.266533+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22472","created_at":"2026-06-23T02:13:39.266533+00:00"},{"alias_kind":"pith_short_12","alias_value":"JSQ5WXMD2I5A","created_at":"2026-06-23T02:13:39.266533+00:00"},{"alias_kind":"pith_short_16","alias_value":"JSQ5WXMD2I5AVEZZ","created_at":"2026-06-23T02:13:39.266533+00:00"},{"alias_kind":"pith_short_8","alias_value":"JSQ5WXMD","created_at":"2026-06-23T02:13:39.266533+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/JSQ5WXMD2I5AVEZZVM542HUUQZ","json":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ.json","graph_json":"https://pith.science/api/pith-number/JSQ5WXMD2I5AVEZZVM542HUUQZ/graph.json","events_json":"https://pith.science/api/pith-number/JSQ5WXMD2I5AVEZZVM542HUUQZ/events.json","paper":"https://pith.science/paper/JSQ5WXMD"},"agent_actions":{"view_html":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ","download_json":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ.json","view_paper":"https://pith.science/paper/JSQ5WXMD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22472&json=true","fetch_graph":"https://pith.science/api/pith-number/JSQ5WXMD2I5AVEZZVM542HUUQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JSQ5WXMD2I5AVEZZVM542HUUQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ/action/storage_attestation","attest_author":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ/action/author_attestation","sign_citation":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ/action/citation_signature","submit_replication":"https://pith.science/pith/JSQ5WXMD2I5AVEZZVM542HUUQZ/action/replication_record"}},"created_at":"2026-06-23T02:13:39.266533+00:00","updated_at":"2026-06-23T02:13:39.266533+00:00"}