Manuscript X-C-ST@1 · X-C-ST.tex · proposition · b679954e

Proposition: Propagation without edge repair

The excluded edge gap and switch dependence · lines 1766–1790 · proof included or linked

X-C-ST@1#prop:edge, X-C-ST@1#eq:propagated-edge

Suppose an excluded edge transformation has generators supported in an already existing interaction plateau, so $g = 1$ near $K_{F}$ . Then

δ_{F} A_{1} δ_{F} A_{2} = ϕ (θ_{1}), = ϕ (θ_{2} - L_{1, g} [h^{'}] E_{A} θ_{1}) .

The second term in the latter expression is the propagated first-order gap. The independent term $θ_{2}$ is still the full second-coordinate test difference in (eq:theta).

Proof. Under the stated interaction-plateau condition $S_{1} = S_{2} = 0$ . Pass (eq:var1)–(eq:var2) to free-field classes. The compact $P_{m}$ -terms vanish and the displayed formulae remain.

Displayed formulas in this passage

X-C-ST@1#eq:propagated-edge · line 1771
$δ_{F} A_{1} δ_{F} A_{2} = ϕ (θ_{1}), = ϕ (θ_{2} - L_{1, g} [h^{'}] E_{A} θ_{1}) .$

Proposition: Propagation without edge repair

Displayed formulas in this passage

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