Manuscript IV@1 · IV.tex · figure · 351cb2d7

Exterior curvature witness

Model 3: scalar stress form and exterior record › A compact exterior curvature current · lines 3095–3135

IV@1#fig:exterior-curvature-witness

gravitationalscalaroperator / instrumenterror / restrictionsupport / scope

(a)Uncut spacetime support

schematic. Scalar support

|x|\le r_0+|t|

\psi

sits outside that cone.

(b)Curvature certificate

j_{ij}(0,x)=\frac{E}{4\pi|x|}\delta_{ij}

R^{(1)}_{1212}(j)(0,x_*)=\frac{E}{4\pi r_*^3}>0

d=\int\psi R^{(1)}_{1212}(j)>0

(c)Conserved current

nonzero entries of

J_\psi

only

\partial_\mu J_\psi^{\mu\nu}=0

\int J_\psi h=\int\psi R^{(1)}_{1212}(h)

Momentum cutoff destroys exact compact spatial support. Only the pairing transfers:

d_\Lambda\ge d/2

for a selected finite

\Lambda

, not the exterior pointwise separation.

Exterior curvature witness for Model 3. A radial compact scalar preparation produces positive initial exterior curvature, giving a positive compact conserved-current pairing on a short future slab. Coherent expectation convergence transfers this pairing to a sufficiently large finite momentum cutoff, but not the uncut pointwise support separation.

Nearby in this section

section: A compact exterior curvature current