Manuscript XVI-I@1 · XVI-I.tex · section · a7046a8d

The compressed route

Root attachment: maps, wavefront test, and properness › The compressed route · lines 1425–1448

The decisive property is that the root has no nonzero wavefront covector with zero scalar-slot covector:

(y, x; p, 0) \in / WF (B) (p \neq = 0) .

The stronger $Z_{2}$ input guarantees it. If that input were withheld, the generic test (eq:root-condition) would remain an unresolved attachment obligation. Compactness alone would not replace it.

This compressed argument does not separately multiply every factor of an unfolded formula

E_{0}^{A} (y, z) A_{f, g} (z, x) .

That internal composition is used only through the already constructed root $B$ . No new claim about all unfolded partial-diagonal products is made.

Displayed formulas in this passage

unlabeled · line 1432
$(y, x; p, 0) \in / WF (B) (p \neq = 0) .$
unlabeled · line 1442
$E_{0}^{A} (y, z) A_{f, g} (z, x) .$

Nearby in this section

section: The compressed route
theorem: Theorem: Compressed attachment under the root cone input