Clock pilot: from apparatus to identifiable parameters

01Question and provenance

Pilot ASD-RUN-CLOCK-001 connects ASD-PRED-001 to the clock-response task · Chinese original. It is a reproducible apparatus-model draft and leaves the registry at NEEDS THEORY.

Select two co-located $^{87}\mathrm{Sr}$ clocks on $^1S_0(F=9/2)\to{}^3P_0(F=9/2)$. The opposite-$m_F$ averaging protocol is described in the NIM evaluation paper (2015, hosted by BIPM). That paper supports the chosen transition/readout, not an ASD response.

02Fixed apparatus variables

Clock A has a horizontal north quantization axis; reference B points east. A shared interrogation laser uses two phase-stabilized fibre arms and a synchronous ratio estimator. Nominal heights agree; residual potential, magnetic/thermal/light shifts, servo and link phase remain explicit. Illustrative latitude is $40^\circ$, chosen background declination $30^\circ$, with 96 uniform samples in one nominal sidereal day. These are calculation inputs, not measurements or a claimed cosmic axis.

03Response with explicit unknowns

Use the existing geometric template $Q=(\mathbf n\cdot\mathbf b)^2-1/3$ in a candidate first-order readout model:

The susceptibilities, link response and covariance remain unknown. This dimensionless template is not an ASD atomic derivation. Opposite-$m_F$ averaging can cancel odd first-order contributions under its assumptions, not all directional or second-order Zeeman effects.

04Computed result

The design matrix $X=(Q_A,-Q_B,1)$ has rank 3 for the default geometry, rank 2 at zero background declination, and rank 2 for identical axes. Equal coefficients on identical axes cancel the shared response exactly. A null clock-ratio modulation alone therefore cannot exclude a common single-clock response.

These are identifiability results conditional on the template. The reference clock is not assumed unresponsive; geometry can be degenerate with the offset. No ASD frequency amplitude or observational fit is calculated.

05Next reviewable deliverable

Derive a directional susceptibility for this transition from ASD matter/field dynamics, or establish a symmetry that makes it vanish. Retain the reference and link responses. Then use measured sampling and covariance to assess uncertainty and power. Export the inputs, unknowns, rank checks, degenerate cases and code with the task.