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

Problem, three models, and cutoff grammar

Problem, three models, and cutoff grammar · lines 204–250

The question is whether a specified classical functional admits a complete chain

classical functional ⟶ form or operator ⟶ instrument ⟶ record .

Each arrow requires its own definition and proof. A classical gauge-invariant expression does not automatically define an operator. A symmetric form cannot automatically be exponentiated. A unitary system channel does not by itself specify its controlled realization.

We answer this question in three named models. They are three models, not three approximations to one operator.

Model	Measured quantity	Representation
1: finite vacuum TT plane	A first-order inhomogeneous scalar correction	$L^{2} (R) \otimes Γ_{s} (L^{2} (R^{3}))$ .
2: dense vacuum TT	The same type of bilinear correction on an infinite-dimensional TT space	$Γ_{s} (h_{g}) \otimes Γ_{s} (h_{ϕ})$ .
3: sourced stress at $k = 0$	A curvature pairing of a prescribed linear response to scalar stress	$Γ_{s} (L^{2} (R^{3}))$ , without a graviton factor.

Figure fig:three-models separates the three classical quantities, representations, generators, and record endpoints.

Displayed formulas in this passage

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$classical functional ⟶ form or operator ⟶ instrument ⟶ record .$

Problem, three models, and cutoff grammar

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