We present the closed core of the Ikigaku/QCRM programme as an operator-based framework for resonance stability and order-chaos transitions in complex human, social, and AI-mediated systems. The fixed spectral backbone is a damped generator L = - (1/z0damp) *I + i*H on a depth-based Hilbert space, where z0damp > 0 is fixed and H is self-adjoint. Self-adjointness forces a vertical-line spectrum: lambdaₙ = - (1/z0damp) + i*Eₙ with Eₙ real. We propose a concrete self-adjoint candidate (Bahamut operator) on the half-line combining a kinetic term, a real depth potential, and a real-symmetric integral kernel. To close the theory in a computable way, we define a coherence timescale T via local spectral gaps (time-locking proxy) and introduce a probability closure Pₗock (tau;T) = P (sigmaₑff² (tau) < sigmac² (T) ) with sigmac² (T) = 3*pi² / T³. We fix a release-ready closure by moment-matching sigmaₑff² (tau) to a Gamma family, yielding Pₗock in closed form and a non-negative local risk proxy lambda (tau;T) = max (0, -d/dtau log Pₗock). (Here lambda (tau;T) is a risk proxy and is distinct from eigenvalues lambdaₙ. ) Finally, we name a programme milestone, Gaasu Answer Ground Zero (GAG-0), and state a conditional theorem (GAG-0, conditional) that packages a verification-style implication aligned with the Hilbert-Polya perspective. No unconditional proof of the Riemann Hypothesis is claimed; the conditional theorem is stated with explicit assumptions and is intended to separate what is structurally forced by self-adjointness from what must be independently verified. Files: Paper I main text (Strict ASCII): PaperICoreᵥ1. 1ₘain. txt Supplementary Information SI-0 (Strict ASCII): PaperICoreᵥ1. 1SIₗedger. txt Notes: No unconditional proof of the Riemann Hypothesis is claimed. Dual-use limitation: non-violent, non-coercive scope only.
Hisashi Suga (Mon,) studied this question.