An Across-the-Board No-Go Theorem for Exact Yukawa Prediction

The Standard Model contains a set of continuous flavor parameters (Yukawa couplings) whose extreme hierarchies have long motivated the expectation that a deeper theory should predict their exact numerical values. This paper proves that this expectation is misplaced at the level of physical law.

Working within a closure-stable lawhood framework that is already strong enough to fix nontrivial numerical invariants elsewhere (including the quantum probability exponent, the fine-structure constant, and the cosmological constant), we prove an across-the-board no-go theorem for exact Yukawa prediction.

The physical Yukawa sector is shown to be a quotient parameter manifold, and non-fine-tuned admissibility requires viability on sets with nonempty interior. Under the no-silent-tie-breaking discipline, this blocks any law-level selector from outputting a unique Yukawa spectrum or exact mass ratio. We further show that although Yukawa data enter determinant-based law comparisons through coarse endomorphism invariants, even the strongest such Omega-projected scalar is not numerically fixed. Finally, we prove that conditioning on all other law-level invariants fixed by the framework does not collapse the Yukawa parameter space: exact Yukawa ratios are not implicitly determined by other constants.

The result applies to any physically lawful framework supporting stable records, unique probability, closure invariance, non-arbitrary selection, and non-fine-tuned admissibility. Exact Yukawa ratios are therefore not law-level quantities but realization-level data. Any proposal that predicts exact Yukawa numbers must either introduce additional record-visible selector structure or relax the axioms required for lawhood itself.