Biophysical Foundations of Coherence Collapse in Cancer: An Indeterminacy Gradient Formalization

This paper develops the biophysical foundations of the Multilevel Recursive Coherence (MRC) framework applied to cancer. We formalize the tumor as a pathological attractor---a stable configuration of low coherence characterized by degraded saturation of gradient indeterminacy (I-G) relations. We introduce the tissue hash $H(\mathbf{r},t)$ as the local electromagnetic signature of coherence, and show how the tumor's aberrant emissions degrade the signal-to-noise ratio (SNR) of the intercellular communication field, propagating decoherence through the microenvironment.

 This propagation is modeled by a diffusion equation with a tumor source term, leading to a progressive collapse of the attractor landscape that explains systemic deterioration even in the absence of extensive metastasis. We derive a tumor coherence index $C_{\text{tumor}}$ that quantifies the degree of I-G degradation across four biophysical dimensions: spatial organization, temporal coordination, thermal entropy production, and chiral architecture.

We further extend the diffusion model to incorporate the bidirectional tumor-nerve interaction recently demonstrated by Thiel et al. (2025), formalizing neural hijacking as active amplification of the pathological attractor through the organism's own coherence infrastructure.

Seven falsifiable predictions are proposed, linking SNR thresholds, spectral tumor signatures, therapeutic windows, and stochastic reverse transitions to the MRC framework. This work provides the mathematical substrate for understanding cancer as a systemic coherence disease and opens new avenues for diagnosis and intervention based on electromagnetic restoration.