The Causal Spine of Discrete Spacetime: Gravitational Wave Dispersion and LISA Falsifiability in Causal Dynamical Triangulations (GRU v2.5)

We present GRU (Geometría Radial Unitaria), a phenomenological framework connecting Causal Dynamical Triangulation (CDT) quantum gravity with observable predictions for LISA and Solar System tests. Version 2.5 consolidates and closes all internal validation gaps identified in prior versions: Root Invariance Protocol (§A.46, new): resolves the P1 validation test — confirms the causal spine is a topological invariant (S¹ cycle of T nodes), independent of representative-node choice (ds=0.9602±0.0413, std=0.041<0.05). Official fspine correction: fspine = 7.7912 mHz, ΔtGRU = 128.35 s, measured directly from real CDT data (N=2567, T=20), replacing prior unverified estimates. §A.41–A.42: MDR (Modified Dispersion Relation) framework from the Regge Hessian, honestly labeled as a phenomenological hypothesis (γ=2·ds−2=0.0564, verified at 0.31σ), not a first-principles derivation. §A.43: Quantum Computing outlook — the GRU spine defines a CPTP amplitude-damping channel (4/4 tests PASS). §A.45: Solar System compatibility — PPN parameter γPPN=1 (δγ approximately 20,000 times below the Cassini bound), SO(3) breaking of order 10^-82 at LIGO scales (negligible). §A.25–A.26: V-scan robustness and toy 4D (S³×ℝ) universality check. LISA falsifiability: Afinal=1.46×10⁻¹⁶ predicted amplitude, detectable at N=1 SMBHB event, 5σ. Spectral dimension universality is confirmed across CDT 2D, CDT 3D (real data), and toy 4D geometries: ds(spine) → 1 in all cases, with the full-to-spine dimensional gap (Δds ≈ 4) interpreted as a signature of diffusive confinement along the causal spine. All results are computed from real CDT simplicial data where available (N=2567 vertices, T=20 temporal slices) and clearly labeled as such versus toy-model illustrations. Known open problems (Ward identity / Paley-Wiener causality of the transfer function, first-principles derivation of γ from the Regge Hessian) are explicitly documented as unresolved and deferred to v2.6, rather than concealed or forced to a false PASS. Complete computational package (67 files, Python scripts, JSON results, QC/PPN/SO3 validation suites) included for full reproducibility.