{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HSXDUBYM5YS7OH3OQKVTLDYRJX","short_pith_number":"pith:HSXDUBYM","schema_version":"1.0","canonical_sha256":"3cae3a070cee25f71f6e82ab358f114dcb2fdfd5fca426281ffeac062ce59282","source":{"kind":"arxiv","id":"2407.20874","version":1},"attestation_state":"computed","paper":{"title":"On the MacWilliams Theorem over Codes and Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Fengxia Liu, Kun Tian, Zhiyong Zheng","submitted_at":"2024-07-30T14:54:02Z","abstract_excerpt":"Analogies between codes and lattices have been extensively studied for the last decades, in this dictionary, the MacWilliams identity is the finite analog of the Jacobi-Poisson formula of the Theta function. Motivated by the random theory of lattices, the statistical significance of MacWilliams theorem is considered, indeed, MacWilliams distribution provides a finite analog of the classical Gauss distribution. In particular, the MacWilliams distribution over quotient space of a code is statistical close to the uniform distribution. In the respect of lattices, the analogy of MacWilliams identit"},"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":"2407.20874","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2024-07-30T14:54:02Z","cross_cats_sorted":[],"title_canon_sha256":"2fd891755e5aa5f513400da789b921a9658919a006cdd6d95c5d7d59c1141ce5","abstract_canon_sha256":"37fdbd6e928068309242c0a122e6e64617c8cd1ac7c6b586594a5bbdd309fe34"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:50:19.867575Z","signature_b64":"ETf5NtcT3rL/KyS4Iu/7XWPIQBh7C6vkG25cU5aGHbQMu+E+9Y2kzWaFb4bkJzdLGalmR1UoKB+CJqnqW5AzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cae3a070cee25f71f6e82ab358f114dcb2fdfd5fca426281ffeac062ce59282","last_reissued_at":"2026-07-05T08:50:19.867106Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:50:19.867106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the MacWilliams Theorem over Codes and Lattices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Fengxia Liu, Kun Tian, Zhiyong Zheng","submitted_at":"2024-07-30T14:54:02Z","abstract_excerpt":"Analogies between codes and lattices have been extensively studied for the last decades, in this dictionary, the MacWilliams identity is the finite analog of the Jacobi-Poisson formula of the Theta function. Motivated by the random theory of lattices, the statistical significance of MacWilliams theorem is considered, indeed, MacWilliams distribution provides a finite analog of the classical Gauss distribution. In particular, the MacWilliams distribution over quotient space of a code is statistical close to the uniform distribution. In the respect of lattices, the analogy of MacWilliams identit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20874","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/2407.20874/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":"2407.20874","created_at":"2026-07-05T08:50:19.867162+00:00"},{"alias_kind":"arxiv_version","alias_value":"2407.20874v1","created_at":"2026-07-05T08:50:19.867162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20874","created_at":"2026-07-05T08:50:19.867162+00:00"},{"alias_kind":"pith_short_12","alias_value":"HSXDUBYM5YS7","created_at":"2026-07-05T08:50:19.867162+00:00"},{"alias_kind":"pith_short_16","alias_value":"HSXDUBYM5YS7OH3O","created_at":"2026-07-05T08:50:19.867162+00:00"},{"alias_kind":"pith_short_8","alias_value":"HSXDUBYM","created_at":"2026-07-05T08:50:19.867162+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/HSXDUBYM5YS7OH3OQKVTLDYRJX","json":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX.json","graph_json":"https://pith.science/api/pith-number/HSXDUBYM5YS7OH3OQKVTLDYRJX/graph.json","events_json":"https://pith.science/api/pith-number/HSXDUBYM5YS7OH3OQKVTLDYRJX/events.json","paper":"https://pith.science/paper/HSXDUBYM"},"agent_actions":{"view_html":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX","download_json":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX.json","view_paper":"https://pith.science/paper/HSXDUBYM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2407.20874&json=true","fetch_graph":"https://pith.science/api/pith-number/HSXDUBYM5YS7OH3OQKVTLDYRJX/graph.json","fetch_events":"https://pith.science/api/pith-number/HSXDUBYM5YS7OH3OQKVTLDYRJX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX/action/storage_attestation","attest_author":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX/action/author_attestation","sign_citation":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX/action/citation_signature","submit_replication":"https://pith.science/pith/HSXDUBYM5YS7OH3OQKVTLDYRJX/action/replication_record"}},"created_at":"2026-07-05T08:50:19.867162+00:00","updated_at":"2026-07-05T08:50:19.867162+00:00"}