Structured Abstract Background The Non-Hermitian Algebraic Gravity framework (NH-ALG) Mattos, 2026, resolves gravitational and cosmological singularities via a topological Exceptional Point (EP) transition in a Type III₁ von Neumann algebraic substrate, deriving from first principles a minimum geometric sampling frequency fₘin and predicting a secular t·exp (−γt) gravitational wave ringdown envelope. Gap The flagship paper does not derive: (a) the explicit dissipation rate trajectory γ (R) and a mass-locked, free-parameter-independent critical radius Rcrit; (b) a laboratory-accessible EP emulation protocol with hardware-level specification; (c) a microscopic derivation of the cosmological slow-roll model; (d) proof that the secular signature survives the Liouvillian density-matrix mapping; (e) an analytic LISA template validity window; (f) a full pre-registered analysis pipeline with Fisher information parameter covariance. Approach Taking the NH-ALG framework as established, we derive γ (R) = 9/ (8πR⁴) and anchor Rcrit = (288π) ¹⁄⁴ M¹⁄² to the Bekenstein area quantization Δ = 1/ (8πM) ; prove the secular t-multiplier is invariant under the Kronecker vec (ρ) mapping of the Liouvillian (Theorem T1) ; derive κ (t) ∝ t^−1 from MSS-bounded Random Tensor Network entropy growth (D4*) ; prove the LISA linear template validity window tₘax = 0. 08/γ (Rcrit) analytically (D6) ; specify a hardware-level ¹⁷¹Yb⁺ ion trap protocol with an extended noise criterion covering laser phase, magnetic, and motional channels; and prove Hausdorff pseudospectrum convergence with universal power law κ (V) ∝ |R − Rcrit|^−1/2 (D5). Results (1) Rcrit = (288π) ¹⁄⁴ M¹⁄² is free-parameter-independent: for M ~ 10⁶ M_☉, Rcrit ~ 1. 6×10⁴ ℓP, within the semiclassical validity range. (2) The secular t·e^−γt is proven invariant under vec (ρ) vectorization (Theorem T1). (3) κ (t) ∝ t^−1 is derived from RTN entropy growth SᵥN = vE t ln q, with vE bounded by the MSS scrambling rate, making r = 16/κ (tₖ) ² a derived bound rather than an assumption. (4) The LISA linear template is analytically valid for t ≤ tₘax ≈ 0. 81 s for M ~ 10⁶ M_☉ (D6), covering the full ringdown window. (5) The extended ion trap noise criterion incorporates Lamb-Dicke motional and magnetic channels, raising the threshold by 2. 4% while remaining achievable with commercial equipment. (6) The Hausdorff proof eliminates the truncation-artifact objection: the EP is a topological branch-point singularity independent of matrix dimension. Implications NH-ALG is the only quantum gravity framework with a mass-locked, free-parameter-independent threshold; three pre-registered, independently falsifiable predictions across laboratory (2026), CMB (2032), and LISA (2035) platforms; an analytically proven template validity window; a microscopically derived slow-roll model; and a Hausdorff-proven truncation convergence. The path from operator algebras to observatories is quantitatively complete. Keywords: NH-ALG; non-Hermitian quantum gravity; exceptional points; Type III₁ von Neumann algebra; Liouvillian vectorization; ¹⁷¹Yb⁺ ion trap; CMB tensor-to-scalar ratio; LISA ringdown; Random Tensor Network; Bekenstein area quantization; Fisher information matrix; Hausdorff pseudospectrum; pre-registration; Bayes factor; Alguilas-AI Method ALGUILAS-AI Dialectical Engine
José Caetano de Mattos (Wed,) studied this question.