We construct an explicit affine group G = F_29^2 semidirect H, with H isomorphic to SL_2(5), of order 100920 for which b_f(G) = b(G) = 3 < 4 = mu′(G). Here b(G) is the largest size of an inclusion-minimal base over all permutation representations, including nonfaithful and intransitive actions, and mu′(G) is the largest size of an independent subset, whether or not it generates G. This gives a negative answer to P. J. Cameron's Kourovka Notebook Problem 16.45.

The upper bound is structural and does not enumerate the full subgroup lattice of the affine group. Every subgroup missing the translation subgroup has faithful base invariant at most two, and every nontrivial normal subgroup contains the translations. Explicit witnesses attain both bounds. The intersection associated with the independent four-set is a nonnormal subgroup of order two, exposing the normal-bottom obstruction.

This record contains the revised preprint and its self-contained source and verification archive: editable LaTeX, exact group specifications, certificates, standard-library Python and C++17 verifiers, an additional independently written checker, research provenance, and separate structural, computational, and primary-source audit reports. Exact checks reconstruct all 76 complement subgroups, check 1215450 four-member families and 67525 three-member families, and verify the affine witnesses and the characteristic-11 boundary example.

Author: Alec Kriebel (ORCID 0009-0001-9320-500X). This publication revision and its verification were prepared with OpenAI Codex and separate AI audit agents. One matrix-product order was corrected from six to three; the generated subgroup still has order twelve, and the theorem is unchanged. No unresolved substantive gap was identified within the recorded audit scope. This is an unrefereed preprint, not external human peer review or complete proof-assistant verification. The foundational formulations are attributed to Cameron, including his published 2024 account. No minimum-order claim is made, and the bounded priority search does not guarantee novelty.

Version 1.0.1 clarifies the projective-pair and intersection-order arguments and prevents obsolete output files from entering rebuilt upload kits. The mathematical construction and theorem are unchanged. The source package includes two new sequential adversarial reviews and the disposition of their findings. The second fresh reviewer found zero actionable issues after the repairs.
