Technical Report v1.12.1: Verification SQL Supplement for the SSIM=1.0 Transitivity Corollary (Upscayl Standard and SwinIR) — Supplement to Technical Report v1.12

Supplement to Technical Report v1.12 -- not a correction; no value in that report changes. Technical Report v1.12 Section 4.4 used a corollary of the Pixel Identity theorem as a cross-check on the correctness of the independent, from-scratch verification databases underlying that report's sigma_stat correction: blocks where SSIM(GT,NOTTA)=1.0 and SSIM(GT,TTA)=1.0 hold simultaneously are, by that theorem, forced to be pixel-identical to GT on both sides, and therefore, by transitivity, pixel-identical to each other. Technical Report v1.12's own text reported this holding exactly for Upscayl Standard, across 702,108 blocks with zero exceptions, but the SQL query that produced this result was not included in that report's originally published bundle, and no corresponding SwinIR figure was stated anywhere in its text. This supplement closes both gaps: it adds the SQL (unmodified for Standard; a direct, no-logic-change retarget for SwinIR), together with a fresh re-execution confirming the Standard figure, and completes the SwinIR side of the check -- finding the identical pattern across 2,657,100 blocks, again with zero exceptions, roughly 3.8x Standard's proportion of the database (consistent with SwinIR producing more pixel-perfect reconstructions overall, the same pattern already noted for sigma_stat in Technical Report v1.12). This establishes the SwinIR figure for the first time and completes Technical Report v1.12's own two-model scope for this cross-check. Both models were verified via live SQL execution against the same databases used in Technical Report v1.12, screen-recorded (one continuous recording per model) and hash-verified. The complete verification SQL is included to enable independent reproduction. Upscayl High-Fidelity and Digital-Art remain outside this supplement's scope, matching Technical Report v1.12's own scope throughout. 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