SGUFT G-closure V12 (SIN1): Adjudicable Spectral-Singularity Interior Toy via Variational Spectral Flow, Audited Regularization, and Finite-Energy Isolation — RUN_G_SINDEMO_0001_SIN1

This record archives the SGUFT G-closure V12 layer (SIN1), an adjudicable (PASS/FAIL) evidence package that upgrades the Chapter 10.3 spectral interior/singularity criterion into an evolvable toy with audited regularization control. A local exponential-tail strength β(r,τ) parameterizes the high-frequency spectral density ρ(ω,r,τ)=ω^{α0}exp(β(r,τ)ω). The evolution is defined by a variational spectral-flow surrogate S[β] and its gradient flow ∂τβ=−δS/δβ, aligning structurally with Chapter 10.10’s “spectral action variation → spectral flow” principle. The adjudication reports (i) divergence growth of the unregularized integral I0(Λ), (ii) convergence residuals under frozen heat-kernel and Laplace regularization families, (iii) a non-Schatten directional proxy Rp, (iv) a finite-energy isolation proxy R_iso, and (v) a horizon-area monotonicity proxy A_h(τ), with verdicts depending only on outputs plus audit/manifest under frozen thresholds. Upstream provenance is locked via a V10/BHX1 snapshot included in the evidence pack.