Operationalizing Informational Invariance: A Probabilistic Model for Pattern Persistence Under Adversarial Attack

This paper presents an operational model for the concept of informational invariance, proposed in previous work (Vidal Porto, 2026a, 2026b). The model quantifies pattern persistence through a probabilistic score I'(x) = (Pcorr - Padv)/(Pcorr + Padv + ε), where Pcorr is the frequency of an element in correlated (preserved) versions and Padv its frequency in adversarial (attacked) versions. Three adversarial scenarios are defined: upper bound (attack on the original), realistic (attack on the correlated version), and baseline (blind attack). From these scenarios, we define Trans-Lesional Regenerative Capacity Cr = lim(Simorig → 0) (Simrec - Simorig)/(1 - Simorig) and Invariant Robustness Rinv = Cr(Realistic) / Cr(Upper Bound). Binary grid simulations show Cr(Realistic) = 68.3%, Cr(Upper Bound) = 51.7%, and Rinv = 1.32. Validation on the MNIST dataset of handwritten digits yields Cr(Realistic) = 6.1%, Cr(Upper Bound) = 0.1%, and Rinv = 75.63, demonstrating that the invariant is substantially more robust in realistic scenarios. The results confirm the hypotheses of previous work and provide a testable foundation for future applications in medical imaging and biological systems.