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Theory69(2023), no. 3, 1988–1999","work_id":"c2ac7962-dc93-4dc6-afe6-6e5afe2ed1b5","year":2023},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Faruk G¨ olo˘ glu and Lukas K¨ olsch,An exponential bound on the number of non-isotopic commutative semifields, Transactions of the American Mathematical Society376(2023), no. 03, 1683–1716","work_id":"e6995eb3-7e54-474f-9236-5b3e06677922","year":2023}],"snapshot_sha256":"2d063511783c48f70a2fcf898624d56e59cbaafdf00eba046571aed042c05c15"},"source":{"id":"2605.17545","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:13:42.162201Z","id":"9e6fb6cb-b277-495c-a6fd-7a1e5ae384ba","model_set":{"reader":"grok-4.3"},"one_line_summary":"Explicit constructions of triprojective APN permutations on vector spaces of odd dimensions divisible by three, plus non-bijective APN functions on even dimensions.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A triprojective structure induced by GL(3, 2^m) produces almost perfect nonlinear permutations on vector spaces of every odd dimension divisible by three.","strongest_claim":"We give a large family of almost perfect nonlinear (APN) permutations of finite vector spaces of every odd dimension divisible by three.","weakest_assumption":"The triprojective structure induced by the general linear group GL(3, 2^m) on the vector space produces functions satisfying the APN differential uniformity condition for the stated dimensions."}},"verdict_id":"9e6fb6cb-b277-495c-a6fd-7a1e5ae384ba"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:399d42b195c8d751795f38f95a1550f7daeaab85332b8aec805bb7dedc6113b7","target":"record","created_at":"2026-05-20T00:04:45Z","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":"31b206c4e71e38613eba4310d7fa3fd4118557c96f0a29256fd1164d3fb0510c","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T16:58:00Z","title_canon_sha256":"453ae5e1380c08edc9ad3ced7005de066b84f5a1857a3f69806a94aac47ec0c3"},"schema_version":"1.0","source":{"id":"2605.17545","kind":"arxiv","version":1}},"canonical_sha256":"5793b12418dfbf7d1af90aa7d2e980ec3f44fe19275a7eb3c3a55829e6ebdd54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5793b12418dfbf7d1af90aa7d2e980ec3f44fe19275a7eb3c3a55829e6ebdd54","first_computed_at":"2026-05-20T00:04:45.075052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:45.075052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xZPB/bF5+zAM5CUCIKAlmr7SFDnW6X8OnaRtEqZKM5FkDk5cMkfrJmEiuPVM9S5MccqU1kJ1BI8/+0L5rAfQCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:45.075929Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:399d42b195c8d751795f38f95a1550f7daeaab85332b8aec805bb7dedc6113b7","sha256:05485867da4391088d3c4554f10173cf4f4efc452c67bcbaf129035de2f78def"],"state_sha256":"22063e16f6961152e8ea93cbbc7d07bb1a7f9cc0c401e7af76076d9709a1f3df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYZuf8xSvy4SjTpMoa3fCYi3EXjFn3aBXAcNRJQb+VA2OB6j7x0QN/PdjcVmx4ps3hH3wfJlhY7PgRzSE76hAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:56:27.398265Z","bundle_sha256":"e247f2b4f42d3a9ea42d41ee43053a8fd8e6d06e34d14b71dd1dc93a37859f20"}}