Negative result: integral ansatz with uniform window does not reproduce MHQ coherence survival curve in Allen-Cahn / Wright-Fisher dynamics

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Authors: Arturo Cerezo
Cited by: 10
References: 3

Abstract

Within the Radial Coherential Dynamics (RCD) program, an attempt is made to construct a phenomenological thermodynamic 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, Neg(coh, γ), on IBM ibm_fez superconducting hardware (Heron r2). A minimal integral functional with uniform spatial window and single-point global normalization is declared ex ante, with full predeclaration of seven parameters, two predeclared branches of the dissipative coupling κ ∈ {1, 0.1}, three predeclared forms of the channel response function R(C), and falsifiable kill-switch criteria registered prior to any simulation. Three numerical kill switches are executed: (i) integrator sanity check passes cleanly across both κ branches; (ii) main bridge validation fails — the principal branch saturates while the perturbative branch grows monotonically, opposite to experimental trend; (iii) robustness to R(C) ∈ {C, C(1-C), C^2} fails uniformly with all three forms producing strong negative Pearson correlations with experiment (-0.72 to -0.90). Cross-platform reproducibility (sandbox versus Mac Studio) is verified to four decimal places. The closed-form negative conclusion is registered: the integral functional with uniform window measures total accumulated loss of C, not coherence survival as captured by MHQ. This rules out a non-trivial region of bridge ansätze without invalidating either the underlying field dynamics or the experimental signature. This is a registered negative result with full ex-ante kill-switch protocol and cross-platform numerical reproducibility. It does not invalidate the underlying Wright-Fisher / Allen-Cahn coherential dynamics nor the MHQ experimental measurement; it falsifies one specific phenomenological identification. The negative result is reported because such results are scientifically valuable and underrepresented in the literature.

Fields of Study & Subjects

Fluid Dynamics and Turbulent Flows Magnetic confinement fusion research Solidification and crystal growth phenomena

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
7 May 2026
Language
EN
Document type
Preprint