Geometría Radial como Base del Espacio Físico: Una Hipótesis sobre la Reducción Dimensional desde el Origen

Version 1.8.9 of the Radial Unitary Geometry (GRU) Hypothesis. This version introduces the first validation of the octant-blind protocol (A.15) on a real CDT simulation (A.21), invariance verification under UV rescaling (§6.1.3), Fisher test for spectral dimension (§6.1.4), corrected Bianchi I reduction factor (§6.2.1), and corrected topological echo ratio (A.11).

Central result (invariant):
d_s(λ_t=0) = 1.0136 ± 0.009 ✓ | Separation: 25.4σ

A.21 — First validation on real CDT (JorenB/2d-cdt):
The octant-blind protocol A.15 applied to 10 independent CDT geometries generated with the official simulator of Brunekreef, Görlich & Loll (github.com/JorenB/2d-cdt, arXiv:2310.16744; λ=ln(2)=0.693147, V=2000 triangles, T=40 slices, seeds: 42, 123, 314, 456, 777, 789, 1000, 1234, 5678, 9999) produces:
d_s = 1.0282 ± 0.0250 (N=10, SEM=0.0079)
IC 95% = [1.0104, 1.0461] | Δ vs A.15 reference = 1.2σ
10/10 geometries satisfy GRU criterion |d_s − 1| < 0.15 ✓
This is the first test of GRU on formal CDT triangulations without modifying the Regge action or Monte Carlo sampler.

§6.1.3 — UV invariance under rescaling:
d_s(τ=0) strictly invariant for NRADIAL=60→960 (dispersion=0.000000) — rules out finite-size artifact.

§6.1.4 — Fisher / Likelihood Ratio Test:
Using the full Laplacian spectrum of S¹: Λ=+1012.7 (N=120, τ=0) — STRONG evidence for GRU over CDT (Jeffreys criterion |Λ|>10). Note: Fisher test for τ=1 requires ~80 real graph eigenvalues — future work.

§6.2.1 — Bianchi I reduction factor corrected:
Numerical verification with Z²³ group (5000 random triples, seed=42): Var(V)=0 exactly; H antisymmetric under s¹s²s³=−1. Reduction factor = 4× (not 8× as stated in v1.8.7). Real computational savings in LQC integrals: 75%.

A.11 corrected:
Topological echo ratio P(2N)/P(N) → 1/√2 ≈ 0.7071 in the limit N→∞ (corrects erroneous value 0.465 from v1.8.4).

Repository Content v1.8.9:
GRU_v1.8.9_completo.pdf — complete PDF with A.21, §6.1.3–6.1.4, §6.2.1, A.11 corrected
GRU_v1_8_9_web.html — complete interactive HTML (A.1–A.21)
GRU_A21_cdt_real_brunekreef.py — A.21 script: octant-blind on JorenB/2d-cdt (10 seeds)
GRU_CDT_real_postprocessing.py — standalone protocol for any CDT adjacency file
GRU_A11_eco_topologico_corregido.py — A.11 corrected: ratio → 1/√2
GRU_bianchi_signs_demo.py — §6.2.1: factor 4× verification
Previous scripts A.1–A.20 available in v1.8.8 record: 10.5281/zenodo.20502213

DOI: 10.5281/zenodo.20535537

Version 1.8.9 introduces the first formal CDT validation of the GRU octant-blind protocol (10 independent geometries, 10/10 criterion satisfied). Pending: full (2+1)D CDT with causal foliation, formal derivation of R̂ operator, and quantitative C₂ suppression factor.

Note (June 2026): A.21 updated from 5 roots to 10 independent CDT geometries (seeds 42–9999). ds corrected to 1.0282 ± 0.0250, IC 95% = [1.0104, 1.0461]. Script GRU_A21_cdt_real_brunekreef.py updated accordingly.