Manuscript XX-C@1 · XX-C.tex · corollary · 7a8cab37

Corollary: Obstruction to a symmetric inverse-square two-rod covariance requirement

An intrinsic inverse-distance obstruction for two rods › The nonzero leading coefficient · lines 1605–1624 · proof included or linked

XX-C@1#cor:tailobstruction

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Suppose a two-rod covariance is defined, has the native canonical difference

W_{R R} (x, y) - W_{R R} (y, x)^{T} = i E_{R R} (x, y),

and both ordered terms satisfy an inverse-square spatial separation bound, uniformly for times in a compact interval containing the times used in Theorem thm:tworod. These requirements are inconsistent.

Proof. Their difference would be $O (r^{- 2})$ , contradicting Theorem thm:tworod.

Displayed formulas in this passage

unlabeled · line 1610
$W_{R R} (x, y) - W_{R R} (y, x)^{T} = i E_{R R} (x, y),$

Nearby in this section

lemma: Lemma: Rod-source normalization at zero spatial frequency
theorem: Theorem: Native two-rod inverse-distance tail
section: The nonzero leading coefficient
remark: Remark: Correct interpretation
section: The nonzero leading coefficient