Manuscript IX-Free@1 · IX-Free.tex · section · 33b20e96

Analytical and algebraic distinctions

Sign, order, and verification audit › Analytical and algebraic distinctions · lines 1849–1875

The following implications are not used:

numerical finite part \neq \Rightarrow admitted polynomial output,

admitted labelled graph \neq \Rightarrow actual-functional binary map,

algebraic descent plus F9a \neq \Rightarrow F9b,

failed sufficient criterion \neq \Rightarrow nonexistence .

The proofs above address each completed implication through its separate kernel, admission, descent, or topological argument.

Displayed formulas in this passage

unlabeled · line 1852
$numerical finite part \neq \Rightarrow admitted polynomial output,$
unlabeled · line 1857
$admitted labelled graph \neq \Rightarrow actual-functional binary map,$
unlabeled · line 1862
$algebraic descent plus F9a \neq \Rightarrow F9b,$
unlabeled · line 1867
$failed sufficient criterion \neq \Rightarrow nonexistence .$