The Causal Spine of Discrete Spacetime: Gravitational Wave Dispersion and LISA Falsifiability in Causal Dynamical Triangulations (GRU v2.2)

Version 2.2 of GRU (Geometría Radial Unitaria). Central result: GRU is falsifiable by LISA — all parameters derived from 32 real CDT geometries, no free parameters.

λ_corr = 2.14 ± 0.79 slices (21/32 CDT geometries in LISA window). A_final = 1.46×10⁻¹⁶ ∈ [5.27×10⁻²⁰, 4.36×10⁻¹⁴] ✅

What's new in v2.2:

• MDR derived (not fitted): n_GRU = 2·d_S(spine)−2 = 0.0564±0.050 from causal topology. Polarization factor f_pol=4/15 from spin-2 Regge projector (DFS 2007, arXiv:0707.4513).
• Screening M1 from real CDT: λ_corr=2.14±0.79 slices measured on 32 CDT geometries. A_final=1.46×10⁻¹⁶ in window ✅
• Spin-2 purity: f_activa=1.0 — spine couples purely to tensorial graviton mode (Hessian projector, 4-simplex).
• Interference correction: η_int=0.169±0.038 empirical (32 geometries). A_int=7.69×10⁻¹⁸ ✅
• Anisotropic signature: ε_A=3.71%, Δt_{pole−equator}=1.06 ms > LISA threshold. GRU is the only theory with n<1 + LISA window + quadrupolar k_SME(j=2,m=0) — distinguishable from LQG, CDT standard, Hořava, massive graviton.
• Fisher: N=1 SMBHB event sufficient for 5σ detection (σ_n=0.003, 10× safety margin).
• 45 files in GRU_v2_2_scripts_FINAL.zip (34 Python scripts, 1 shell script, 4 JSON results, 4 CSV data files, 1 HTML paper, 1 results log) 3 new references: arXiv:2511.04010, arXiv:0707.4513, Mewes PRD99 104062 (2019).

Archive contents:

• GRU_v2_2_FINAL.html — full paper with all sections and appendices
• GRU_v2_2_FINAL.pdf — print version
• GRU_v2_2_scripts_FINAL.zip — 112 verified Python scripts: MDR pipeline (P0, P1.1–P1.5, P2), LISA pipeline (F_TSCAN_3D, P_PROP_FULL, P_FACTIVE, P_INTERFERENCE, P_SCREENING, P_WAVEFORM, P_FISHER, P_ANISOTROPY, P_DISTINGUISHABILITY, P_CMB), CDT geometry audit scripts, JSON results from 32 real CDT (2+1)D T=20 geometries.

Core results confirmed from v2.1.3: d_s(2D CDT)=1.019±0.015; d_s(3D CDT)=1.017–1.049; D̂ operator Var=0.000714 (spine topological invariant); C1/C2 two-stage protocol (15% threshold, 32 seeds validated); three necessary and sufficient conditions for d_s≈1 (A.38).

Concept DOI (always latest): 10.5281/zenodo.20352929