{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SIOIY6PY6AJDHHAQKRQKSPA73G","short_pith_number":"pith:SIOIY6PY","schema_version":"1.0","canonical_sha256":"921c8c79f8f012339c105460a93c1fd990c6da92e7bd7ea36d9dceee02ab6351","source":{"kind":"arxiv","id":"2502.09514","version":2},"attestation_state":"computed","paper":{"title":"Continuous-Variable Quantum MacWilliams Identities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"quant-ph","authors_text":"Ansgar G. Burchards","submitted_at":"2025-02-13T17:30:22Z","abstract_excerpt":"We derive bounds on general quantum error correcting codes against the displacement noise channel. The bounds limit the distances attainable by codes and also apply in an approximate setting. Our main result is a quantum analogue of the classical Cohn-Elkies bound on sphere packing densities attainable in Euclidean space. We further derive a quantum version of Levenshtein's sphere packing bound and argue that Gottesman--Kitaev--Preskill (GKP) codes based on the $E_8$ and Leech lattices achieve optimal distances. The main technical tool is a continuous-variable version of the quantum MacWilliam"},"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":"2502.09514","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-02-13T17:30:22Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"95faf47c0d4ed53bf26e8600827328abad36b9daf9a7e1fb869dcc929d7b26c8","abstract_canon_sha256":"f991ece405336465f773b9a96a85266d0a627e9e1773d950592dc72959bf474e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:16.952392Z","signature_b64":"jA1yJ3oRaMSBHIM07FtMd/A3Szpirzcd44ZKVuFKv2Y+yJKjj/I6+z08X5jZkS5b9P98RJjHKbnkMru5MZ+gDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"921c8c79f8f012339c105460a93c1fd990c6da92e7bd7ea36d9dceee02ab6351","last_reissued_at":"2026-07-05T10:40:16.951910Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:16.951910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuous-Variable Quantum MacWilliams Identities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"quant-ph","authors_text":"Ansgar G. Burchards","submitted_at":"2025-02-13T17:30:22Z","abstract_excerpt":"We derive bounds on general quantum error correcting codes against the displacement noise channel. The bounds limit the distances attainable by codes and also apply in an approximate setting. Our main result is a quantum analogue of the classical Cohn-Elkies bound on sphere packing densities attainable in Euclidean space. We further derive a quantum version of Levenshtein's sphere packing bound and argue that Gottesman--Kitaev--Preskill (GKP) codes based on the $E_8$ and Leech lattices achieve optimal distances. The main technical tool is a continuous-variable version of the quantum MacWilliam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.09514","kind":"arxiv","version":2},"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/2502.09514/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":"2502.09514","created_at":"2026-07-05T10:40:16.951967+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.09514v2","created_at":"2026-07-05T10:40:16.951967+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.09514","created_at":"2026-07-05T10:40:16.951967+00:00"},{"alias_kind":"pith_short_12","alias_value":"SIOIY6PY6AJD","created_at":"2026-07-05T10:40:16.951967+00:00"},{"alias_kind":"pith_short_16","alias_value":"SIOIY6PY6AJDHHAQ","created_at":"2026-07-05T10:40:16.951967+00:00"},{"alias_kind":"pith_short_8","alias_value":"SIOIY6PY","created_at":"2026-07-05T10:40:16.951967+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/SIOIY6PY6AJDHHAQKRQKSPA73G","json":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G.json","graph_json":"https://pith.science/api/pith-number/SIOIY6PY6AJDHHAQKRQKSPA73G/graph.json","events_json":"https://pith.science/api/pith-number/SIOIY6PY6AJDHHAQKRQKSPA73G/events.json","paper":"https://pith.science/paper/SIOIY6PY"},"agent_actions":{"view_html":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G","download_json":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G.json","view_paper":"https://pith.science/paper/SIOIY6PY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.09514&json=true","fetch_graph":"https://pith.science/api/pith-number/SIOIY6PY6AJDHHAQKRQKSPA73G/graph.json","fetch_events":"https://pith.science/api/pith-number/SIOIY6PY6AJDHHAQKRQKSPA73G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G/action/storage_attestation","attest_author":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G/action/author_attestation","sign_citation":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G/action/citation_signature","submit_replication":"https://pith.science/pith/SIOIY6PY6AJDHHAQKRQKSPA73G/action/replication_record"}},"created_at":"2026-07-05T10:40:16.951967+00:00","updated_at":"2026-07-05T10:40:16.951967+00:00"}