A Phase-A Audit of a Cross-Scale Response Bridge between Galaxy Dynamics, Solar-System Constraints, and Precision-Clock Residuals

We present a phase-A audit of a cross-scale response framework that connects galaxy-scale mass discrepancies, Solar-System post-Newtonian constraints, and precision-clock residuals through a common state sector Z. The observables on the three scales are not identied with Z directly, but are treated as distinct projections G[Z,ρb], P[Z,ρ⊙], C[Z,geometry] of the same underlying response sector. On a bridge-ready SPARC subsample of 139 galaxies, the trigger axis x≡log10(gbar/a0) supports a robust monotone ordering of the dimensionless mass discrepancy Ξgal= gobs/gbar−1, with Spearman rank correlation ρs ≈−0.74. Fixed- parameter saturating and logistic families of Z(x) calibrated on the galaxy side survive transfer into a solar integral proxy of Solar-System projections without recalibration of the Z-sector, yielding proxy-level post-Newtonian projections below current Cassini and lunar- laser-ranging bounds. An extended audit along the exact-SPICE EarthSunCassini signal path spanning deterministic geometry-derived kernel projectors, time-resolved channel proxies, minimal two-way ts, and cross-family reference control leaves the transferred state-sector response small and dynamically stable across all tested stages, with the best-case kernel projection approximately eight decades below the Cassini proxy bound. The cross- family stage makes the structural limit of a public-data audit explicit: a radio-science-based γ-extraction is not reconstructable from publicly archived ephemerides alone and is therefore agged as a collaboration-stage task. The high-g asymptotic used in the clock-side audit is set by the saturating benchmark, log10 Zsat(x) ≈−0.094−0.583 x; the currently parame- terized logistic benchmark does not share this asymptotic level and is carried through the audit only where its status is independent of the high-g extrapolation. On the clock side, we use the SrSr bre-linked comparison of Lisdat et al. (2016) as the rst genuine residual benchmark, with ΞLisdat clock = (4.7 ±5.0) ×10−17 after an explicit GR/geopotential correction of (−247.4 ±0.4) ×10−17. This immediately excludes the identication Ξclock = Z: the Lisdat residual lies approximately ten decades below the high-g asymptotic level of Z. A rst structure-related laboratory projection operator closes about 6.45 of these decades but still overshoots the measured residual by about 3.4 decades. Subsequent transfer tests of the laboratory operator class against further architectural classes further characterize this projec- tion. The two-site Grotti et al. (2018) transportable-clock comparison excludes any universal form of the projection: an explicit Lisdat-type link term is structurally incompatible with a two-site architecture at approximately three decades of signicance, while a reduced no-link form is compatible but not positively validated. The redundant Boulder Atomic Clock Op- tical Network (BACON Collaboration, 2021), which simultaneously measures three optical frequency ratios, admits a narrow but geometrically compact strict-structural-success sector characterized by vanishing remote coupling, near-unit pair symmetry, and a small residual local amplitude, reproducing both the absolute scales and the internal rank ordering of the three ratios. The three tested architectures therefore populate three qualitatively dierent reductions of a common operator class rather than a single universal laboratory operator. A 1fair comparison conrms that the standard loglog radial acceleration relation remains em- pirically more compact than the Ξ-representation used here. We therefore frame the present work not as a completed closure but as a decision-oriented status audit: the common state sector remains viable at the present audit level, the direct clock identication is excluded, the solar projection is structurally plausible, and the clock-side projection is populated by three architecturally distinct reductions rather than by a single universal operator. The data are consistent with a common state sector Z and a small architecture-dependent operator family {Cclosure , C2site , Cnetwork}, with the derivation of these reductions from an underly- ing principle, and a realistic signal-path audit of the Solar-System branch, identied as the leading open problems.