λEnter Calculus CompanionRegistered manuscripts, kept distinct

Manuscript V@1 · V.tex · figure · e7ddf37d

Specified inverse and cubic composition

Contrast: the Newton–wave cubic form › Option A inverse and its constraints · lines 3183–3213

V@1#fig:Option-A-composition

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metricscalarrepresented quantumdefect / unresolvedsupport / scope
conserved scalar stress Q=T(ϕ)Q=T(\phi)
Option A, used
position (a,0,0)(a,0,0), velocity (0,0,Bij)(0,0,B_{ij})
j=RAT(ϕ)j=\mathcal R^A T(\phi) — field degree two
Bf(j,ϕ)B_f(j,\phi) — field degree three

j=jinit+jsrcj=j^{\mathrm{init}}+j^{\mathrm{src}}. Constraint-compatible D(j)=0D(j)=0, LEj=QL_{\mathrm E}j=Q.

Option B, comparison only
position (a,−Vi,0)(a,-V_i,0), velocity (−∂iVi,0,0)(-\partial_i V_i,0,0)

Same sourced wave integral. Different initial data, so the inverse maps generally differ. Scalar responses are not labeled equal. Not substituted into the theorem.

not the external metric
not Qe+ΠrQe+\Pi r
not R1,1R_{1,1}

Specified inverse and cubic composition. Option A combines constraint-compatible Newton initial data with the sourced wave integral. Feeding scalar stress into this inverse and then into the scalar response gives a cubic functional. Option B has different initial data and is not substituted into the theorem. Neither reconstructed metric is the metric argument defining the earlier retarded coefficients.

Nearby in this section