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Amsterdam, The Netherlands: North-Holland, 1977","work_id":"d9dde3ce-4aac-46ca-8f1e-24bf2f9f144b","year":1977}],"snapshot_sha256":"26716f89c896b4536397909c2f411ea56d73bad8742557f7e3231d5e1301a4d0"},"source":{"id":"2605.17371","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:54:48.803896Z","id":"e7cea18e-2766-4c77-a26d-e6eb7c411931","model_set":{"reader":"grok-4.3"},"one_line_summary":"Algebraically resolves seven open problems on cyclic and negacyclic codes supporting designs via Cayley parametrizations, quotient transports, and corrected congruences, yielding existence criteria for ovoid codes and MDS constructions for 5-designs.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Cayley parametrizations and corrected projective-order congruences resolve seven open problems by giving exact existence criteria for constacyclic ovoid codes and constructions of negacyclic MDS codes that support complete 5-designs.","strongest_claim":"This paper gives a unified algebraic solution to seven open problems of Wang, Tang and Ding on cyclic, negacyclic and constacyclic codes supporting designs, including the exact existence criterion for constacyclic ovoid codes and constructions of consecutive-root negacyclic MDS codes yielding complete simple 5-designs.","weakest_assumption":"The Cayley parametrization of the unit circle reduces the trace-zero condition to a semilinear equation on PG(1,q) whose large root sets are exactly the F_{p^{gcd(m,s)}}-sublines, and the corrected projective-order congruence a=(q+1)c with c≡b mod (q-1) holds and applies to determine the orders for the ovoid code existence proof."}},"verdict_id":"e7cea18e-2766-4c77-a26d-e6eb7c411931"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:65060928ae693f61164aeaa03eb05bfa2a0103505c2f95256a9ddf94fcd2e1c4","target":"record","created_at":"2026-05-20T00:03:55Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0b11ca84c421dece5f83ca319442937cf732f72608e550cd5fbfcb9674d8467b","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.IT","submitted_at":"2026-05-17T10:27:58Z","title_canon_sha256":"4d825e2fd60fcb1be16d7d46ff3a64b4e2e3115ee1384a6a98168e5c2eeaf067"},"schema_version":"1.0","source":{"id":"2605.17371","kind":"arxiv","version":1}},"canonical_sha256":"c39d799b9fa59ae492a3d96be11b4a4a0a66414511a3935089e654a103c7fe65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c39d799b9fa59ae492a3d96be11b4a4a0a66414511a3935089e654a103c7fe65","first_computed_at":"2026-05-20T00:03:55.046133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:55.046133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T3RXc9834p1bYju6dLvylyssmiYK+FmYFNbaidGN/PbFdPUt2owXUnpiXk9N4yu2pXjI/JiqI7ZoVVNr0CaIBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:55.047106Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65060928ae693f61164aeaa03eb05bfa2a0103505c2f95256a9ddf94fcd2e1c4","sha256:18912da42e549789bbda9640824c874500879f68bbcc06db0660469882b2b237"],"state_sha256":"bc109a462fb427e0b54940de999f690181804801eec2102eac29144837423efc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f0IVfL7Xcqz32ReYJOZFO6Eeic0V8dY4xcTmVRWXjHQCctVdsJtLlSEmL0aiUmsu61w61R8CM2jIIruql71mBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:49:59.433428Z","bundle_sha256":"869fbd8e492faaacc33e55b424c5a03a26f934688559d9a51baea270d055642e"}}