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

Model 3 form and measured generator

Model 3: scalar stress form and exterior record › Regulated generators and coherent correspondence · lines 2929–2967

IV@1#fig:model3-form-hierarchy

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gravitationalscalaroperator / instrumenterror / restrictionsupport / scope

Unregulated metric-valued form

1. Algebraic Schwartz Fock vectors Ψ,X\Psi,\mathrm{X}
2. tμνΨ,X=⟨Ψ,:Tμν:X⟩t^{\Psi,\mathrm{X}}_{\mu\nu}=\langle\Psi,:T_{\mu\nu}:\mathrm{X}\rangle
3. jNWΨ,X=RNWtΨ,Xj^{\Psi,\mathrm{X}}_{\mathrm{NW}}=\mathcal{R}^{\mathrm{NW}}t^{\Psi,\mathrm{X}}
4. jNW(J)[Ψ,X]=∫J jNWΨ,Xj_{\mathrm{NW}}(J)[\Psi,\mathrm{X}]=\int J\, j^{\Psi,\mathrm{X}}_{\mathrm{NW}}

Separate cutoff branch

χΛ\chi_\Lambda on each scalar leg
BΛ(J)B_\Lambda(J)
ΠMBΛ(J)ΠM\Pi_M B_\Lambda(J)\Pi_M
eiτλBΛ,Me^{i\tau\lambda B_{\Lambda,M}}
bounded self-adjoint
Boundedness requires the kernel estimates, not number compression alone.
no graviton factor
no independent quantum metric field
no unregulated metric instrument

Model 3 representation hierarchy. Conserved normal-ordered stress matrix elements feed a specified classical response and define a metric-valued form. Momentum-kernel estimates produce a regulated quadratic operator, whose number compression is the bounded measured generator. No independent gravitational quantum degree of freedom is introduced.

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