A two-tail obstruction to ambient conjugation in Dlab groups

Abstract

We give an affirmative answer to the corrected Kourovka Notebook Problem 21.149. The compact-support Dlab group with slopes in the powers of two has an order automorphism that cannot be implemented by conjugation after any embedding into any standard real Dlab group. The ambient slope group is unrestricted, the embedding need not preserve an order, and the conclusion includes the full and reflected extended-real families. The proof uses perfectness to separate the supports of commuting local groups, least action components and finite-tuple transitivity to obtain one uniform orientation, and a normalizer with infinitely many bump components near both source endpoints. One of these tails forces a forbidden descending sequence of ambient support components. A solvable affine-germ quotient treats the real-line left endpoint. The paper credits Gong, Yang and Zeng, arXiv:2609.18630, for the prior six-family rank-one theorem and one-tail support obstruction. It also distinguishes the earlier formally verified non-inner formulation from the corrected ambient question. The six-page note is accompanied by LaTeX source, an exact-rational construction verifier, source and priority audits, and independent AI adversarial-review records. Finite checks supplement the theoretical proof and do not certify universal claims about embeddings. Literature searches through 17 October 2026 found no earlier result with the unrestricted quantifiers; this is a bounded priority assessment. AI tools were used extensively in discovery, development, writing and verification. The preprint has not undergone independent human peer review, and no formal proof-assistant verification of this new theorem is claimed. Paper, prose and code: CC BY 4.0.