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

Version 1.9.2 of the Radial Unitary Geometry (GRU) Hypothesis.

NEW IN v1.9.2 — Structural tests (A.30–A.33) + methodological honesty note:

• A.30 — Rotational invariance: GRU is 21.1× more rotationally invariant than octant-based analysis (GRU std=0.0083, range [1.058,1.089] vs octants std=0.1756, range [1.352,1.923]; same CDT geometry, 8 origins/angles). This is the operational meaning of "octant-blind": frame-of-reference independence.
• A.31 — Node efficiency: GRU visits 8× fewer nodes than octant analysis (e.g. 800 vs 6,400 for N=40×20) producing a more stable observable.
• A.32 — Dimensional decomposition: d_s(full)=1.969 ≈ d_s(spine)+d_s(S¹)=1.045+1.089=2.134 (residual 0.16). Explicitly flagged as heuristic, not exactly additive — the residual quantifies non-separable coupling.
• A.33 — Three regimes with diagnostic column: N<10 confinement (d_s undefined); 10<N<65 Bohr zone (topological echo contaminates UV window — large errors are diagnostic, not defects); N≥65 clean UV escape (d_s→1.0). The N=65 threshold is independently confirmed by three analyses (A.7 topological crossover, A.10–11 echo, A.33) — an intrinsic property of discrete S¹ geometry, not parameter tuning. Protocol v4 (SIGMAMAX∝√N, NWALKS∝N) proposed for N>100.
• Methodological honesty note (GRU_nota_metodologica.html): explicit statement of what is numerically supported, what remains interpretation, and what is open. Position: "GRU is promising, falsifiable, and partially validated numerically" — a new observable, not a closed theory.

CONSOLIDATED RESULTS (v1.9.0–v1.9.1):

• Toy S¹ (A.6): d_s(λ=0)=1.0007±0.0321 vs d_s(λ=1)=1.9818±0.1020 — 9.2σ
• CDT 2D real (A.21, 60 geometries): d_s(spine)=1.019±0.015 — spine vs full: 15.8σ
• T-scan (A.23): d_s(T=320)=1.006±0.022 — P1 RESOLVED
• Spectral law (A.24): λ_n≈n², error 4.9% — P5 RESOLVED
• CDT (2+1)D (A.25): d_s=1.0489±0.0287 (6 seeds)
• Toy S³×ℝ (A.26): d_s=1.0428±0.0157
• Robustness (A.27): 236/240=98% across 240 configs
• Causal sets (A.28): d_s=1.0640±0.0368, 5/5
• Holographic encoding (A.29): Corr_λ=0.957±0.003
• C.1 CMB / C.2 LISA: program-level predictions with explicit falsification criteria; quantitative calibration with standard pipelines (CAMB/Planck, LISA waveforms) in progress.

KEY DISTINCTION: d_s≈1 refers to the GRU SPINE, not the full CDT graph. Full graph recovers d_s→2 (CDT 2D), consistent with CDT standard. GRU refines, not contradicts, the consensus.

VERSION HISTORY:
v1.0 (May 23, 2026): GRU Hypothesis and conceptual motivation in LQC/CDT.
v1.8.x: numerical consolidation on discrete S¹ (open chain→S¹ correction, N≥65 threshold, dimensional-flow validation).
v1.9.0: integration with real CDT Monte Carlo (2D, 3D) and 4D toy, R operator as octant-blind post-processing without modifying the Regge action.
v1.9.1: external-critique battery (240-config robustness, causal sets, holography) and first CMB/LISA phenomenological connections.
v1.9.2 (this version): structural tests A.30–A.33, methodological honesty note, and minor documentation fixes (title tag, SIGMAMAX value in A.33 corrected to 80) — no numerical results affected.

REPOSITORY CONTENT (24 files):

• GRU_v1_9_2_web.html — complete HTML (A.1–A.33 + C.1 + C.2, ~1.2 MB)
• GRU_v1.9.2_completo.pdf — complete PDF
• GRU_v1_9_2_short.html / GRU_v1.9.2_short.pdf — short paper (arXiv-ready)
• GRU_nota_metodologica.html — NEW: methodological honesty note
• GRU_zona_bohr_analisis.html — NEW: Bohr zone regime analysis (A.33)
• GRU_invarianza_rotacional.py — NEW: A.30 (21.1× invariance)
• GRU_eficiencia_nodos.py — NEW: A.31 (8× fewer nodes)
• GRU_descomposicion_1mas1.py — NEW: A.32 (heuristic 1+1)
• GRU_regimenes_S1.py — NEW: A.33 (three regimes)
• README_INSTALL.md — updated replication guide for v1.9.2 (Phases 0–4: toy models, CDT 2D/3D real, post-processing, and structural tests) with expected d_s(spine) values for S¹, S³×ℝ, CDT 2D, CDT 3D, and causal sets
• + 14 files inherited from v1.9.1 (scripts A.21–A.29, C.1–C.2, configs, setup)

Previous versions: v1.9.1 DOI 10.5281/zenodo.20635841 | v1.9.0 DOI 10.5281/zenodo.20574763
DOI: 10.5281/zenodo.20650400