Stochastic Rupture as an Informational Renormalization Group Flow: Collapse, Gravity, and the Koide Formula from a Single Variational Principle

We present a reformulation of Stochastic Rupture (SR) in which all physical structure—collapse, gravity, dark sectors, and the Koide formula—emerges from a single variational principle: the extremization of entropy production under the con- straint of the Bekenstein holographic bound. The saturation field χ is promoted from a phenomenological bookkeeping variable to the generator of an informational renormalization group (RG) flow, Oˆ χ, whose spectral properties determine the preferred collapse basis, the functional form of the feedback F(χ), the decoherence rate, the effective gravitational coupling, and the scalar spectral index ns. The constant η = 2/3 arises as the dimensional compression exponent of the RG flow from volume-law to area-law entanglement; the same value appears in the Koide formula as the spectral projection of Oˆ χ onto three active flavor modes, eliminating the need for numerical coincidence as an argument. The framework has one postu- late, zero free parameters (all constants are stability eigenvalues of the flow), and a falsifiable prediction—Regime IV, entanglement-driven collapse without spatial superposition—absent from CSL and Di´osi–Penrose.