Fifth paper in the Gravitational Residual Coherence (GRC) series. This work asks whether the coherence field ψ, which organises 171 SPARC rotation curves between two parameter-free spectral attractors (R² = 0. 955), is merely a fitting degree of freedom or carries physical information not reconstructible from instantaneous observables. Five tests on 166 SPARC galaxies constrain the answer: (1) adding ψ to models already containing Vflat, fgas, Rd, and bulge yields ΔAIC = −24. 8 (BTFR), −43. 7 (RAR), −8. 4 (Mdyn/Mbar) ; (2) no random reassignment among 10, 000 permutations reproduces these gains (p 0. 39, p < 3×10⁻⁷) ; (4) among 573 matched pairs at fixed Vflat, the gas-rich member has higher ψ in 77% of cases; (5) the spectral weight function wf (k) = 1/ (1+k^0. 8) captures 86% of the predictive power of ψ while a linear predictor with identical inputs captures none, and this advantage transfers out of sample. The operator structure is selected by simultaneous constraints, not fitted. The hybrid operator (2 parameters per galaxy) outperforms a free exponential (3 parameters) by 15% in RMS. Only αK ∈ 0. 55, 0. 65 simultaneously satisfies fit quality, spectral efficiency, and non-trivial historical residual; the value αK = 3/5 lies at the centre. Population-stacked radial profiles confirm the predicted attractor geometry with R² = 0. 957 and ψₑff = 1. 03 (Phase I) versus ψₑff ≈ 0 (Phase III), demonstrating that the radial geometry of the composite operator survives population averaging. The irreducibility of ψ is stable under baryonic mass-to-light variations (ΔAIC < −20 and 0/1000 permutations across Ydisk = 0. 3–1. 0). The spectral flow β (ψ) = − (2−2αK) ψ (1−ψ) admits a unique linearising coordinate η = logit (ψ), in which the flow reduces to uniform translation at rate 4/5; individual galaxies differ in position along the flow, not in the underlying spectral-flow rate. A modal analysis shows that ⟨C⟩ is an exact zero mode of (−Δ) ^αK: when the disc dissolves, ⟨C⟩ freezes as a metastable relic, providing a mechanism for the high apparent M/L in gas-stripped dwarf spheroidals without requiring an additional dark matter component at galactic scales.
Jose Javier Meizoso Fernández (Sun,) studied this question.