CDIP v3.1 Berwald–Randers Singularity Theorem III Controlled β-Flow, Convexity Preservation, and Conditional Curvature Blow-up Under Anchor Loss

This paper advances the CDIP v3.1 cognitive-singularity program in the Berwald–Randers setting by introducing a controlled evolution law for the Randers one-form and proving new conditional preservation and blow-up results. The central problem is that, under anchor loss, unnormalized Ricci contraction of the base Riemannian metric can force premature failure of Randers strong convexity if the one-form is held fixed. We resolve this obstruction by introducing a natural Ricci-drag evolution law for the one-form, called the controlled β-flow, and proving that it preserves the Randers norm exactly along the flow.The paper then derives an explicit obstruction formula for preservation of the Berwald condition. This reduces the Berwald-preservation problem to a sharp compatibility condition involving covariant derivatives of the base Ricci tensor and the evolving one-form. As imme- diate corollaries, Berwald preservation follows in Einstein-type and Ricci-Codazzi regimes. Under these structural assumptions, together with anchor-loss reduction to unnormalized Ricci flow and positive initial maximum scalar curvature, we prove finite-time blow-up of the base Riemannian scalar curvature.A second theorem establishes finite-time blow-up of the Finsler scalar curvature itself under an additional comparison hypothesis. Two versions are given: a semipositivity version assuming nonnegative base Ricci tensor, and a more flexible pinching version involving a quantitative near-Riemannian comparison bound and a Ricci spectral pinching constant.This separates what is now rigorously proved from what remains open in the general Finsler setting.Finally, the paper states the precise CDIP interpretation under an NI-2 posture: the result supports only alerts-only geometric risk semantics, with no threshold changes, no gate changes, no verdict lifting, no write-back, and no Telomere/TEANT event interaction. The paper is therefore suitable as a Zenodo theorem note and as a mathematically disciplined extension of earlier CDIP v3.1 geometric-analysis releases.