Fractal Curvature Matter and Selection-Matched TNG-Cluster Subhalo Lensing Efficiency

Recent multiscale cluster-lensing analyses have sharpened a small-scale tension for collisionless cold dark matter (CDM): the subhalo mass function and tidal truncation radii can remain broadly compatible with CDM, while the projected radial distribution, inner density structure, and galaxy-galaxy strong lensing (GGSL) incidence show a much stronger internal signal than expected. Natarajan, Chiang, and Dutra (2026) report that GGSL from subhalo cores exceeds CDM expectations by nearly an order of magnitude and requires steep internal slopes, while the same subhalos behave more collisionlessly in their outskirts. This paper develops Paper II of the Fractal Consistency Law (FCL) / Fractal Curvature Matter (FCM) program: a real-data proxy audit using TNG-Cluster API products, selection-matched satellite catalogs, regularized environmental activation, analytic SIS cross-sections, finite-grid multi-SIS ray-tracing proxies, and bootstrap covariance estimates. The paper does not claim a full Lenstool reproduction or final empirical validation. Rather, it asks whether a regularized FCL-FCM kernel can transform selection-matched TNG satellites into GGSL-efficient internal lenses while keeping the outer halo nearly CDM-like. The principal result is that a bounded environmental kernel yields an internal lensing-efficiency boost of 9.289 ± 0.188 at the proxy level, and the subsequent SIS GGSL proxy gives a bootstrap-stable global internal enhancement of 9.1466 ± 0.0293 with outer enhancement 1.3598 ± 0.0263. The result supports a precise interpretation: FCL-FCM need not multiply subhalos; it must activate the gravitational efficiency of already selected internal satellites in high-curvature cluster environments. The discussion is extended by treating core-collapsed self-interacting dark matter (SIDM) as the closest particle-physics competitor: both frameworks identify compact dark perturbers as the required phenomenological object, but they differ in whether compactness is generated by gravothermal self-interaction or by localized geometric curvature activation.