Kinetic Blindness in Gradient-Based Phenomenological Bridges: A Structural Limitation in Cuaderno 7 v0.5
Abstract
Within the Radial Coherential Dynamics (RCD) program, we test whether a phenomenological macroscopic bridge between the dynamics of a coherential scalar field C(x,t) — governed by an Allen-Cahn drift with multiplicative Wright-Fisher noise — and the experimentally measured Margenau-Hill quasiprobability negativity on IBM superconducting hardware can be constructed using differential observables based on spatial gradients of C. Three independent observables in the gradient family are evaluated: an instantaneous integral S_nabla[C] = ∫|∇C|² dx, a temporal-integral form W_int accumulating the instantaneous form across the simulation window, and a pointwise maximum S_nabla_max[C] = max_x |∂_x C|. All three observables are normalized as differential ratios between coherent and control preparations. Synthetic tests with three controlled decay regimes (exponential, linear, threshold) show Pearson correlation between exponential and linear regime curves of +0.9995, +0.9999, and +0.9995 respectively for the three observables — virtually identical kinetic responses for functionally distinct decay forms. We conclude that gradient-based phenomenological observables with differential cociente normalization are structurally kinetic-blind: they detect monotonic decrease of structure but cannot distinguish the form of the decay. High correlation with an experimental survival curve is not sufficient evidence of kinetic agreement when both curves are monotone. This closes the gradient family as a candidate for the macroscopic-microscopic phenomenological bridge in this program, while leaving open non-gradient observables and microscopic-dictionary derivations as future routes. The result extends the previous registered negative result of v1.0 (Zenodo 10.5281/zenodo.20073982) from a specific observable failure to a structural limitation of an entire observable family, with full ex-ante kill-switch protocol and synthetic adversarial testing.
Fields of Study & Subjects
Advanced Thermodynamics and Statistical Mechanics
Particle physics theoretical and experimental studies
Model Reduction and Neural Networks
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 8 May 2026
- Language
- EN
- Document type
- Preprint