A Coupled Weak-Field Topological Model for the Turin Shroud Image Formation and Spatial Radiocarbon Anomalies

Abstract The Turin Shroud remains one of the most extensively studied archaeological textiles, yet the physical origin of its superficial body image and the interpretation of its radiocarbon measurements remain unresolved problems in heritage science and materials physics. Here we propose a quantitatively constrained multiscale framework coupling weak-field transport dynamics, superficial cellulose perturbation, oxidation-mediated fibrillar modification, and localized isotopic variability within a unified phenomenological model. The framework is formulated explicitly within a low-energy, non-catastrophic regime designed to remain compatible with experimentally established constraints, including extreme image superficiality, fibril-level discontinuity, absence of bulk thermal degradation, and preservation of cellulose structural integrity. The transport regime is modeled through diffusion–attenuation dynamics leading to shallow near-surface energy deposition and bounded mesoscale heterogeneity. Coupled perturbative interactions are shown to produce correlated spatial fields linking image intensity, cellulose crystallinity reduction, oxidation topology, and localized isotopic response. Importantly, the framework does not invoke neutron bursts, large-scale nuclear conversion, or macroscopic heating processes. Nor does it claim invalidation of existing accelerator mass spectrometry (AMS) measurements. Instead, the model investigates whether bounded physicochemical heterogeneity may contribute to localized sampling variability under experimentally admissible conditions. The theory generates explicit experimentally testable predictions involving Raman spectroscopy, FTIR mapping, WAXS/XRD crystallinity gradients, SEM/AFM superficial morphology, and spatially resolved AMS covariance analysis. The proposed framework is therefore presented as a falsifiable and mechanism-agnostic experimental roadmap for future multiscale investigation of the Turin Shroud.