Abstract

We construct represented binary measurements in three separate models. On a fixed nondegenerate transverse-traceless plane, a first-order inhomogeneous scalar correction becomes a quadratic oscillator–field operator. It is essentially self-adjoint, a smooth initial-time-edge regulator can be removed, and two gravitational coherent preparations with the same scalar factor yield a positive Ramsey contrast. On an infinite-dimensional vacuum transverse-traceless completion, the analogous bilinear functional has explicit four-leg kernels. Their spectral masks can be removed in operator norm after a fixed particle-number compression, with separate Hilbert–Schmidt and operator-norm coefficient estimates and a controlled record remainder. Independently, a specified Newton–wave response to normal-ordered massive scalar stress defines a metric-valued form on scalar Fock space. A compact exterior curvature pairing gives a positive vacuum–coherent record at fixed scalar momentum cutoff and sufficiently large finite number cutoff. Every record theorem includes an exact zero-interpolation control. The three representations, sources, and cutoffs are not identified. The measured dense-TT and sourced models retain their number cutoffs, and all apparatuses are global controlled-unitary instruments.