Manuscript VII-J-ST@1 · VII-J-ST.tex · proposition · f1f1d82c

Proposition: Robust port margin

Causal embedding, realized routes, and robustness › The conservative slicing-parameter speed · lines 795–824 · proof included or linked

VII-J-ST@1#prop:robust, VII-J-ST@1#eq:robust

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In a convex regular developed chart, let a nominal slice-time gap be $h$ , nominal spatial endpoint distance at most $D$ , spatial localization radii $r_{-}, r_{+}$ , slicing-time errors at most $ε_{s}$ at each endpoint, and additional dimensionless geometric-time errors at most $ε_{τ}$ at each endpoint. All endpoint choices remain causally admissible if

h - (1 + λ) D \geq (1 + λ) (r_{-} + r_{+}) + 2 ε_{s} + 2 ε_{τ} .

Strict inequality gives positive slack.

Proof. The actual spatial distance is at most $D + r_{-} + r_{+}$ , and the actual slicing gap is at least $h - 2 ε_{s}$ . The two-family estimate gives actual geometric-time difference at least

h - 2 ε_{s} - λ (D + r_{-} + r_{+}) - 2 ε_{τ} .

Under (eq:robust) it exceeds the actual spatial distance. The straight developed segment is available within the chart.

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VII-J-ST@1#eq:robust · line 804
$h - (1 + λ) D \geq (1 + λ) (r_{-} + r_{+}) + 2 ε_{s} + 2 ε_{τ} .$
unlabeled · line 818
$h - 2 ε_{s} - λ (D + r_{-} + r_{+}) - 2 ε_{τ} .$

Proposition: Robust port margin

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