Manuscript I-B-G@2 · I-B-G-v2.tex · section · 3b4d700f

The independent retained-shadow condition

Supported replacement of flat-completion operators › The independent retained-shadow condition · lines 1764–1808

I-B-G@2#eq:shadow

Theorem thm:transfer is a kernel comparison. A companion calculation also has its own support contract. Write the developed slab as

M_{T_{lab}} = [0, T_{lab}] \times R^{3} .

For a retained observation region $O$ , the X-B-ST contract uses

D_{*} = J_{η}^{-} (O) \cap M_{T_{lab}} ⋐ dev (U) .

Tests belong to $O$ ; the required coordinate, interaction, and propagation calculations belong to the retained shadow, or to a specified compact neighbourhood of it CheungXBST (:supported, :host).

The IX-A-ST presentation instead makes the reserve explicit:

V = (0, T_{lab}) \times B_{r_{0}}, K_{*} = [0, T_{lab}] \times B_{r_{0} + T_{lab}},

inside a developed region containing

(- δ, H) \times B_{R}, R > r_{0} + T_{lab}, H > T_{lab} .

Its closure used in the calculation must stay off $W$ CheungIXAST (:support). Here $r_{0}, R$ are Euclidean laboratory radii around its developed centre; they are not the polar radius $r$ from the apex.

Displayed formulas in this passage

I-B-G@2#eq:shadow · line 1775
$D_{*} = J_{η}^{-} (O) \cap M_{T_{lab}} ⋐ dev (U) .$
unlabeled · line 1769
$M_{T_{lab}} = [0, T_{lab}] \times R^{3} .$
unlabeled · line 1791
$V = (0, T_{lab}) \times B_{r_{0}}, K_{*} = [0, T_{lab}] \times B_{r_{0} + T_{lab}},$
unlabeled · line 1797
$(- δ, H) \times B_{R}, R > r_{0} + T_{lab}, H > T_{lab} .$

The independent retained-shadow condition

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