{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:INOG4GEJBBP335EVH6WIDJRPPJ","short_pith_number":"pith:INOG4GEJ","schema_version":"1.0","canonical_sha256":"435c6e1889085fbdf4953fac81a62f7a65861d1be4404f6acdd8f60f1f28d4c9","source":{"kind":"arxiv","id":"2501.01549","version":1},"attestation_state":"computed","paper":{"title":"Quantum Error Correction with Goppa Codes from Maximal Curves: Design, Simulation, and Performance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.AG","authors_text":"Vahid Nourozi","submitted_at":"2025-01-02T21:43:59Z","abstract_excerpt":"This paper characterizes Goppa codes of certain maximal curves over finite fields defined by equations of the form $y^n = x^m + x$. We investigate Algebraic Geometric and quantum stabilizer codes associated with these maximal curves and propose modifications to improve their parameters. The theoretical analysis is complemented by extensive simulation results, which validate the performance of these codes under various error rates. We provide concrete examples of the constructed codes, comparing them with known results to highlight their strengths and trade-offs. The simulation data, presented "},"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":"2501.01549","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2025-01-02T21:43:59Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"0afe07f3577777f3a6d409d11027dc6d62636a8f4eca9655a127bde3eb122b34","abstract_canon_sha256":"32ac37268afeed802faa433936eb4e8e0cde7f2ff9f62760691533c434b28413"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:29.563495Z","signature_b64":"zNOvfa99KM5nPE5CNHLGVaCJsMDz4ogRoZgyJy+NnUL2p6hVZx9TPAXxC3ka6QwW4o5kE+rHkL2w6/6fQOZ9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"435c6e1889085fbdf4953fac81a62f7a65861d1be4404f6acdd8f60f1f28d4c9","last_reissued_at":"2026-07-05T10:10:29.562995Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:29.562995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum Error Correction with Goppa Codes from Maximal Curves: Design, Simulation, and Performance","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.AG","authors_text":"Vahid Nourozi","submitted_at":"2025-01-02T21:43:59Z","abstract_excerpt":"This paper characterizes Goppa codes of certain maximal curves over finite fields defined by equations of the form $y^n = x^m + x$. We investigate Algebraic Geometric and quantum stabilizer codes associated with these maximal curves and propose modifications to improve their parameters. The theoretical analysis is complemented by extensive simulation results, which validate the performance of these codes under various error rates. We provide concrete examples of the constructed codes, comparing them with known results to highlight their strengths and trade-offs. The simulation data, presented "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01549","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/2501.01549/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":"2501.01549","created_at":"2026-07-05T10:10:29.563043+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.01549v1","created_at":"2026-07-05T10:10:29.563043+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01549","created_at":"2026-07-05T10:10:29.563043+00:00"},{"alias_kind":"pith_short_12","alias_value":"INOG4GEJBBP3","created_at":"2026-07-05T10:10:29.563043+00:00"},{"alias_kind":"pith_short_16","alias_value":"INOG4GEJBBP335EV","created_at":"2026-07-05T10:10:29.563043+00:00"},{"alias_kind":"pith_short_8","alias_value":"INOG4GEJ","created_at":"2026-07-05T10:10:29.563043+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/INOG4GEJBBP335EVH6WIDJRPPJ","json":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ.json","graph_json":"https://pith.science/api/pith-number/INOG4GEJBBP335EVH6WIDJRPPJ/graph.json","events_json":"https://pith.science/api/pith-number/INOG4GEJBBP335EVH6WIDJRPPJ/events.json","paper":"https://pith.science/paper/INOG4GEJ"},"agent_actions":{"view_html":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ","download_json":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ.json","view_paper":"https://pith.science/paper/INOG4GEJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.01549&json=true","fetch_graph":"https://pith.science/api/pith-number/INOG4GEJBBP335EVH6WIDJRPPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/INOG4GEJBBP335EVH6WIDJRPPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ/action/storage_attestation","attest_author":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ/action/author_attestation","sign_citation":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ/action/citation_signature","submit_replication":"https://pith.science/pith/INOG4GEJBBP335EVH6WIDJRPPJ/action/replication_record"}},"created_at":"2026-07-05T10:10:29.563043+00:00","updated_at":"2026-07-05T10:10:29.563043+00:00"}