Technical Report v1.15: When comp_* Features Match, Does SSIM Still Equal 1.0? A Four-Model Test of the Converse, Its Mechanism, and a General Theorem

Technical Report v1.13 asked whether an SSIM score match guarantees content agreement, and found that it does not, always. This report tests the converse: if a reconstruction's eight independently-measured quality features (comp_*) match the ground truth's own features exactly, does SSIM still equal 1.0? There is no mathematical necessity for this to hold -- the Pixel Identity Theorem, established and confirmed across all four models in this series (Technical Reports v1.12, v1.12.1, and v1.14), proves only the reverse direction (SSIM=1.0 -> pixel-identical -> comp_* match) -- so this report tests the converse empirically, at full dataset scale, across four AI upscaling models. Restricting to blocks where all eight features match GT exactly, the answer is again conditionally yes, not universally so: SwinIR sits at 99.97% SSIM=1.0, but Upscayl High-Fidelity has 63.05% of its feature-matched blocks below SSIM=0.5, with Standard (42.23% exact) and Digital-Art (53.33% exact) in between. Tracing the mechanism resolves not just that this happens but exactly why: across the entire feature-matched population, in all four models, the SSIM contrast term C is proven -- algebraically, not just observed -- to equal exactly 1.0 whenever sigma_gt=sigma_notta (a new general theorem, not restricted to the masking regime), and the structure term S sits at or extremely close to 1.0 throughout. What remains free to vary is the luminance term L alone, and its spread is the entire content of the observed score divergence. The root cause is structural: none of the eight comp_* features measures luminance at all, so 8-feature agreement can constrain C and S but says nothing about L. Together with Technical Report v1.13, this establishes the argument in both directions: neither an SSIM score match nor a comp_* feature match, alone, guarantees the other -- both must be used together for a fuller picture of reconstruction quality. Every finding is computed against independent, from-scratch verification databases (one per model, built by this project's no-join pipeline, first established in Technical Report v1.12), via a single consolidated, copy-paste-ready SQL script covering all four models in one continuous screen recording (no cross-model join is needed anywhere in this report's logic, avoiding the memory-pressure risk noted in Technical Report v1.13 for its own cross-model comparison). The complete verification SQL, including the fully-expanded 4-model script, is included to enable independent reproduction. Dataset and Mandatory Citation:- Source: NIH ChestX-ray8 (Hospital-scale chest x-ray database)- Citation: Wang, X., Peng, Y., Lu, L., Lu, Z., Bagheri, M., & Summers, R. M. (2017). "ChestX-ray8: Hospital-scale chest x-ray database and benchmarks on weakly-supervised classification and localization of common thoracic diseases." Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 3462–3471. - Download: https://nihcc.app.box.com/v/ChestXray-NIHCC Contact : s.shiny.n.works@gmail.com