Track A6–A7: forward instrument and robust viability

The projective instrument has the mathematical isometry $\psi \mapsto {\sum }_x|x⟩\otimes {\Pi }_x\psi$. No conformational Ramsey apparatus is thereby engineered.

For an independently justified additive-noise measurement,

This is a forward POVM. On an $L^2$ frequency band, stable inversion requires $\inf \text{abs}\hat{\nu }>0$. A zero-free multiplier gives uniqueness on classes whose Fourier differences it does not annihilate, but unrestricted stability does not follow. Gaussian multipliers decay at high frequencies. At $\epsilon =1/2$, the present detector destroys the score signal completely.

For a calibrated response $y_h=B{a}_h+hs+r_h$, weights with $B^{\mathsf{T}}w=0$ give

A retained invariant signal exists exactly when $s\notin \mathrm{range}B$. Thus a contrast can cancel the proposed gravitational response as well as the nuisance, as emphasized by En01-C CheungEn01C.

For unbounded setting-dependent records, randomize setting $i$ with probability $p_i>0$, clip at $L>0$, and use

If ${\mathbb{E}}_h{Z}_i^2\le M_{h,i}$, clipping reduces an oriented mean-contrast gap $G_T$ by at most

since $\text{abs}z-c_L(z)\le z^2/L$. Independent common erasure multiplies the nonconstant gap by its observation probability; arbitrary missingness must be included in the complete law.