Manuscript VI@1 · VI.tex · proposition · b5b60afb

Proposition: Quantitative failure of quotient approximation

The finite obstruction certificate › The evaluated two-representative table · lines 2741–2755 · proof included or linked

For any function $F$ of the common quotient label,

max {∣ F - A_{f, g}^{(1)} (0, ϕ_{0}) ∣, ∣ F - A_{f, g}^{(1)} (K ξ, ϕ_{0}) ∣} \geq \frac{a _{f}}{2} \geq \frac{1}{4} .

Proof. The two candidate values differ by $a_{f}$ . Insert the common value $F$ between them and apply the triangle inequality.

Displayed formulas in this passage

unlabeled · line 2743
$max {∣ F - A_{f, g}^{(1)} (0, ϕ_{0}) ∣, ∣ F - A_{f, g}^{(1)} (K ξ, ϕ_{0}) ∣} \geq \frac{a _{f}}{2} \geq \frac{1}{4} .$