FROM OPERATOR ALGEBRAS TO OBSERVATORIES: Mass-Locked Singularity Resolution, Ion Trap Emulation, and Pre-Registered Tests of Non-Hermitian Algebraic Gravity

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 f_min 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 R_crit; (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 R_crit = (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 t_max = 0.08/γ(R_crit) 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 − R_crit|^{−1/2} (D5). Results (1) R_crit = (288π)¹⁄⁴ M¹⁄² is free-parameter-independent: for M ~ 10⁶ M_☉, R_crit ~ 1.6×10⁴ ℓ_P, 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 S_vN = v_E t ln q, with v_E bounded by the MSS scrambling rate, making r = 16/κ(t_k)² a derived bound rather than an assumption. (4) The LISA linear template is analytically valid for t ≤ t_max ≈ 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