Manuscript XVI-K@1 · XVI-K.tex · assumption · aa7553bb

Assumption: Fixed preparation and selected source

Setting, explicit interfaces, and normalization › Inherited interfaces · lines 285–308

XVI-K@1#ass:preparation

Fix $0 < ε < T$ , preparation data $f, g$ , and a smooth time-only ramp satisfying

σ_{ε} (t) = 0 (t \leq 0), σ_{ε} (t) = 1 (t \geq ε) .

Fix independently $χ_{I} \in C_{c}^{\infty} (M; R)$ .

The supplied XII-C source interface is

J_{D}^{μν} = σ_{ε} J_{3}^{μν} + 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ_{ε} - 2 M_{2}^{μν ρ} \partial_{ρ} σ_{ε} .

Only the middle summand is retained here. Its finite algebraic definition is given in (eq:C2)–(eq:source). The identification with that summand is inherited; no audit of the complete cubic Euler source is claimed.

Displayed formulas in this passage

unlabeled · line 289
$σ_{ε} (t) = 0 (t \leq 0), σ_{ε} (t) = 1 (t \geq ε) .$
unlabeled · line 297
$J_{D}^{μν} = σ_{ε} J_{3}^{μν} + 2 C_{2}^{μν α β} \partial_{α} \partial_{β} σ_{ε} - 2 M_{2}^{μν ρ} \partial_{ρ} σ_{ε} .$

Assumption: Fixed preparation and selected source

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