Depth-Coordinate CHSH Correlations: Characterization and Exclusion of an A3c Resonance-Transform Family

We characterize a depth-coordinate resonance-transform construction — the A3c family — for Bell-type correlations, and determine precisely how it relates to the quantum singlet. Under its normalized probability rule the family is Bell-violating and non-signalling, yet not rotationally invariant: its correlations depend on the average analyzer angle, not only on the relative angle. We show that the contamination is already present in the joint-angle amplitude before the probability map and survives the principal internal repair routes examined here: renormalization, scalar-phase modulation, and the faithful branch-coupled C1c construction. Within the explicitly defined A3c subclass, these routes do not produce a rotationally invariant singlet correlation. It is removable only by hardcoding the relative angle, which is an imposition rather than a derived symmetry. Characterizing the couplings shows the family exhibits behavior across the classical, quantum-strength, and post-quantum CHSH regimes, including a post-quantum correlation object that is non-signalling under the stipulated normalized probability rule, whose super-Tsirelson behavior is the same orientation dependence read through CHSH. The orientation-independent singlet is not recovered within A3c; recovering it is the aim of a different, representation-complete readout of the relational sector, which we delimit as future work. Throughout, the depth coordinate is a formal parameter; this is a characterization-and-exclusion result, not a physical theory. Code: the accompanying C1a reproducibility suite (routeA_c1a_suite.zip) is licensed MIT; this manuscript is licensed CC BY 4.0.