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For an attractor with one adiabatic clock and a regular Bunch-Davies vacuum, a long comoving curvature perturbation ${\zeta }_L$ acts at leading order as a spatial dilation. The single-field inflation squeezed-limit consistency relation therefore fixesFor the local convention $\zeta ={\zeta }_G+(3/5)f_{\mathrm{NL}}({\zeta }_G^2-⟨{\zeta }_G^2⟩)$, comparison with its squeezed primordial bispectrum givesThe matter-era negative gravitational potential is $\phi =3\zeta /5$, so this is also the conventional $f_{\mathrm{NL}}$ of part (i). In single-field slow-roll inflation, the spectral tilt is small and the effective local coupling is of slow-roll size, typically of order $10^{-2}$ for a tilt of a few percent. This is a statement about the normalized coupling: the squeezed primordial bispectrum still contains the large long-mode power spectrum.

Formally putting this small coupling into the local template of part (ii) predicts only a tiny correction on accessible scales, rather than an order-unity local signal. For a physical halo abundance there is a stronger qualification. The consistency-relation modulation at fixed coordinate wavelength is a dilation; the coordinate size of a fixed physical halo must be dilated too. Those responses cancel. This is the absence of primordial scale-dependent halo bias in single-clock inflation: the leading consistency-relation term produces no physical $k^{-2}$ halo bias. The first physical long-mode response contains two spatial derivatives, so dividing it by ${\delta }_L\propto k_L^2{\phi }_L$ does not produce the local-template enhancement. Thus the leading primordial large-scale galaxy power spectrum remains the Gaussian-bias result, apart from ordinary transfer, bias, and projection effects.

The cancellation can be seen with a top-hat filter. At fixed local time, a constant long curvature rescales physical lengths by $e^{{\zeta }_L}$, so the coordinate radius of a fixed physical halo is $R_c=e^{-{\zeta }_L}{R}_0$, and the coordinate short density contrast is ${\delta }_s(\mathbf{x})={\delta }_s^{(0)}(e^{{\zeta }_L}\mathbf{x})$. Changing variables $\mathbf{y}=e^{{\zeta }_L}\mathbf{x}$ givesThus the smoothed field and its variance at fixed physical mass are unchanged by the constant long mode.

The assumptions matter: a non-attractor such as ultra-slow-roll inflation, additional fluctuating fields, or an excited initial state need not obey this squeezed-limit conclusion. A sizable physical local modulation would test the stated single-clock attractor assumptions, rather than every possible one-field model.