arXiv:2610.34788v1 Announce Type: new Abstract: Quick Response (QR) code deblurring must ultimately recover the encoded payload, yet how accurately the underlying camera motion must be estimated remains an open question. To address this question, we formulate motion-blurred QR recovery within a unified mathematical framework of identifiability and systematically measure the decoding tolerance to perturbations in motion length, direction, rotation or scaling centre, and speed profile. These controlled experiments reveal three structural laws: 1) parameter tolerances shrink rapidly as blur amplitude grows and are tightest under uniform speed, whereas accelerating motion is substantially more forgiving; 2) length tolerance can differ markedly between underestimation and overestimation; 3) errors that are individually benign interact strongly and prevent decoding when combined. Guided by these findings, we propose a grey-box recovery pipeline in which two compact networks predict an initial corner trajectory, followed by tolerance-guided candidate search, alternating image-and-path fitting, and regularised linear inversion. On a new benchmark of 955 handheld motion-blurred photographs captured across four phone models and four motion categories, our method recovers the exact payload on 93.1% of the images, outperforming the strongest fine-tuned deblurring network at 83.6% and reducing the decoding error rate by 58.0%.