CDIP v3.1 Cognitive Singularity Program Anchor Loss and Conditional Curvature Blow-up in a Geometric Model

This article upgrades an informal “CDIP cognitive singularity” argument into a publishable theorem program consistent with Zenodo release standards and CDIP v3.1 terminology. The central idea is that a physical-cognitive anchor may be modeled as a geometric regularizer in a state-space metric evolution. If that regularization is removed, curvature concentration may become possible.The rigorous core result is a conditional finite-time scalar-curvature blow-up theorem in a compact Riemannian setting: if anchor loss reduces the metric evolution to unnormalized Ricci flow, and if the initial maximum scalar curvature is strictly positive, then the maximum scalar curvature satisfies a Riccati-type lower bound and blows up in finite time. The proof uses the standard scalar-curvature evolution law together with the parabolic maximum principle.The article also explains why the original informal proof could not be accepted as a general Finsler theorem: it imported a Riemannian curvature-evolution formula into a Finsler setting without fixing the Ricci tensor, connection, strong-convexity preservation, or maximum-principle framework. Accordingly, the Finsler part is reformulated as a conjectural extension program, not as a proved theorem.Finally, the article gives a CDIP interpretation under an NI-2 posture. The theorem supports alerts-only geometric risk semantics and does not authorize threshold changes, gate reordering, verdict lifting, or Telomere/TEANT interactions. The result is therefore theorem-grade at the Riemannian level, explicitly conditional, and governance-compatible.