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

Three represented models

Problem, three models, and cutoff grammar · lines 251–289

IV@1#fig:three-models

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gravitationalscalaroperator / instrumenterror / restrictionsupport / scope

Common measurement pattern; different models.

Model 1
ℓ0,f+qℓe,f+πℓr,f\ell_{0,f}+q\ell_{e,f}+\pi\ell_{r,f}
formal coefficient bookkeeping
H1=L2(R)⊗Γs(L2(R3))\mathcal H_1=L^2(\mathbb R)\otimes\Gamma_s(L^2(\mathbb R^3))
essentially self-adjoint numerical quadratic polynomial
c1−eεc_1-e_\varepsilon
Model 2
Bf(k,ϕ)\mathcal B_f(k,\phi)
vacuum-TT bilinear
H2=Γs(hg)⊗Γs(hϕ)\mathcal H_2=\Gamma_s(\mathfrak h_g)\otimes\Gamma_s(\mathfrak h_\phi)
bounded number-compressed generator
c2−eM−eR(M)c_2-e_M-e_R(M)
Model 3
∫J RNWT(ϕ)\int J\,\mathcal R^{\mathrm{NW}}T(\phi)
sourced curvature pairing
Γs(L2(R3))\Gamma_s(L^2(\mathbb R^3))
scalar Fock space only
bounded compression of a quadratic scalar response
c3−eM(3)c_3-e_M^{(3)}

Model 3 measures sourced curvature, not the first-order scalar correction.

Three distinct represented models. Models 1 and 2 represent vacuum-gravity scalar corrections, whereas Model 3 represents a curvature pairing of a prescribed scalar-stress response. The common binary-instrument construction does not identify their Hilbert spaces, generators, or classical sources.

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