Manuscript XXII-E@1 · XXII-E.tex · corollary · 51c99d2f

Corollary: Scoped flat-branch obstruction

What the affine cone cannot supply › The translation-invariant representative is flat · lines 364–380 · proof included or linked

XXII-E@1#cor:flat-source

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Suppose a proposed dynamics package keeps only the constant affine geometry of Theorem thm:flat, uses a fixed nonzero comparison coupling $κ_{cmp}$ , and produces a nonzero source $τ_{D}$ on its comparison domain. Then it cannot satisfy

G^{(1)} [h_{D}] = κ_{cmp} τ_{D}

with $h_{D}$ restricted to spatially constant variations.

Proof. The left side is zero by Theorem thm:flat, whereas the right side is nonzero.

Displayed formulas in this passage

unlabeled · line 371
$G^{(1)} [h_{D}] = κ_{cmp} τ_{D}$

Nearby in this section

section: The translation-invariant representative is flat
theorem: Theorem: Flatness of the constant affine representative
section: The translation-invariant representative is flat