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

The excluded edge gap and switch dependence

The excluded edge gap and switch dependence · lines 1726–1765

X-C-ST@1#eq:class-defect, X-C-ST@1#eq:edgegap, X-C-ST@1#eq:edge-integral

For arbitrary compact interior generators, the free class of (eq:variation) is

A [q^{'}] - A [q] = ϕ (R_{q^{'}} (Θ_{F} - Σ_{F} s [q])) .

The coordinate and switch mechanisms remain separate.

The inherited preflight gap for an initial-trivial compact $ξ$ is

ξ - w [K ξ] = E_{0, R} ((1 - σ) □ ξ) + E_{0, R} (σ^{'} a_{1}^{0 \cdot} [K ξ]) .

For the X-A-ST witness

ξ = α (t) β (x) \partial_{1}, 0 \neq = α \geq 0, supp α \subset (0, ε), \int β d^{3} x = 1,

the retained integrated gap is

\int_{R^{3}} (w^{1} [K ξ] - ξ^{1}) (t, x) d^{3} x = - \int_{0}^{ε} σ^{'} (s) α (s) d s < 0, ε \leq t \leq T_{*} .

This is supplied classical chart data XAST (:edge); the new maps do not alter the coordinate Cauchy prescription.

Displayed formulas in this passage

X-C-ST@1#eq:class-defect · line 1731
$A [q^{'}] - A [q] = ϕ (R_{q^{'}} (Θ_{F} - Σ_{F} s [q])) .$
X-C-ST@1#eq:edgegap · line 1742
$ξ - w [K ξ] = E_{0, R} ((1 - σ) □ ξ) + E_{0, R} (σ^{'} a_{1}^{0 \cdot} [K ξ]) .$
X-C-ST@1#eq:edge-integral · line 1756
$\int_{R^{3}} (w^{1} [K ξ] - ξ^{1}) (t, x) d^{3} x = - \int_{0}^{ε} σ^{'} (s) α (s) d s < 0, ε \leq t \leq T_{*} .$
unlabeled · line 1749
$ξ = α (t) β (x) \partial_{1}, 0 \neq = α \geq 0, supp α \subset (0, ε), \int β d^{3} x = 1,$