We present Version 6 of the crystallization index (χ), a dimensionless, baryon-only modification of gravity that quantifies structural persistence through compactness, coherence, and asymmetry. The response law
μ(χ) = 1 + μ₀ · χ / (1 + χ)
The preregistered falsifiers include:
Monotonicity of anomalies with χ.
Nulls for compact, symmetric systems.
Morphology-based splits at fixed baryonic mass.
Lensing–dynamics lockstep under a single μ₀.
Saturation of anomalies at cluster scales (μ ≤ 1+μ₀).
Using SPARC rotation curves, we fix μ₀ = 3.5 ± 0.2. This same value successfully reproduces:
Monotonic scaling of anomalies with χ across 175 disk galaxies.
Strong-lensing rescalings in BELLS (μeff ≈ 1.5) and SLACS (μeff ≈ 1.1).
Stacked weak-lensing profiles from SDSS, DES Y1, and KiDS-1000.
Cluster weak lensing in CLASH and DES/KiDS stacks, with μeff ≈ 1.2–1.6, below the saturation ceiling.
Together, these results demonstrate closure across galaxies, strong lenses, weak lensing, and clusters using a single preregistered parameter. Either falsification or survival with forthcoming Euclid and Rubin (LSST) surveys will decisively sharpen the space of viable theories of gravitation.