Separating Free Token Geometry from Raw Feature-Energy Routing: An OAPC Diagnostic Study

Fixed-grid tokenization couples uniform allocation with a factorized spatial geometry, so an apparent gain from adaptive placement may instead come from simply removing the grid constraint. We separate three questions: whether free-position geometry helps, whether content conditioning adds value beyond content-independent free geometry, and whether raw feature-energy routing is semantically useful. OAPC (Optimization-driven Adaptive Patch Centroids) is a deliberately non-amortized probe that optimizes N continuous centroids per input using raw-L2-energy-weighted spatial quantization. Randomized synthetic controls show that geometric and content-conditioned gains are budget-dependent rather than universal. On a stratified 300-image COCO diagnostic subset, raw energy improves the same projected optimizer over constant-density routing in 23 of 24 backbone-budget settings, yet projected OAPC beats a Lloyd-optimized uniform centroidal Voronoi control in only one setting by mean per-image relative MSE reduction. In a 1,500-image, two-backbone mask-prediction stress test, raw-energy routing is statistically unresolved against uniform-CVT on ResNet-50 and underperforms it on ConvNeXt-T; channel standardization removes the resolved deficit without establishing an advantage. Diagnostic GT-mask routing improves micro-IoU through architecture-matched decoders trained under the same protocol on both backbones, showing that aligned guidance can exploit the continuous placement mechanism. Free positions are flexible, but raw feature magnitude is not a stable semantic routing signal under this spatial-quantization objective across the representations tested.