Topological phase transitions in information-coupled gravity: Spontaneous scalarization and Kodama-state resolution of the IRW singularity

We present a unified scalar-tensor and dynamical Chern-Simons (dCS) framework for the Information-Recipe Warp (IRW) relation. Eliminating unbounded divergences found in prior models, we implement a self-interacting quartic potential V (ϕ) that regulates the scalar field vacuum. We unpack the precise calculus mapping the conformal coupling to the effective gravitational constant, demonstrating the stability of the expansion. By defining the exact thermody-namic boundaries of the stellar core during collapse, we show how the depletion of the electron fraction (Ye) acts as a trigger. Unlike Vainshtein screening, which suppresses scalar effects in high-density regions, the IRW model explicitly activates geometric modifications as Ye → 0, leading to spontaneous scalarization. To resolve the ensuing singularity, we perform a Hamiltonian analysis in Ashtekar variables. We translate the advanced gauge theory of the SO(3, 1) spin connection into a physically intuitive model, demonstrating how the Kodama wavefunctional replaces the infinite point singularity with a finite, non-contractible toroidal manifold (S1 × S1).