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

This paper introduces the Radial Unitary Geometry (GRU) Hypothesis: under spherical symmetry, the physically irreducible variable of quantum spacetime is a single scalar radial coordinate r ≥ 0. The diagnostic observable is the spectral dimension d_s extracted from heat kernels on discrete graphs. Central result (invariant across all versions):d_s(λ=0) = 1.0007 ± 0.0321 → interval [0.969, 1.033] contains 1.0 ✓d_s(λ=1) = 1.9818 ± 0.1020 → interval [1.880, 2.084] contains 2.0 ✓Statistical separation: 9.2σ (discovery threshold in physics: 5σ) New in v1.8.7 — S²×ℝ Octant-Blind Protocol and Temporal Dimension Scan: A.15a — GRU_A15_s2xR_lambda_scan.py: Three critical bugs fixed from original S²×ℝ script. With octant-blind protocol (colapsar=True, one node per shell):• GRU pure (λ_θ=0, λ_t=0, colapsar=True): d_s = 1.0136 ± 0.009 ✓ GRU• +Temporal: d_s = 1.647 • +Angular S²: d_s = 1.780 • Complete S²×ℝ: d_s = 2.594Monotonic flow: 1.01 → 1.65 → 1.78 → 2.59 ✓ — each degree of freedom adds one effective dimension. A.15b — GRU_A15_temporal_dimension_scan.py: λ_t diagonal scan on collapsed radial chain.Critical window: λ_t∈[0.50,0.70] → d_s = 2.0205 ± 0.0385 (Giasemidis recovered).λ_t=0.0: d_s=1.0136 (GRU pure) → λ_t=0.2–0.4: unstable (phase transition) → λ_t=0.5–0.7: d_s≈2.02 → λ_t=1.0: d_s=1.78 (overconnected).Causal time is not maximal but an optimal intermediate coupling regime. GRU_CDT_postprocessing.py: Octant-blind protocol as CDT post-processing. Accepts any CDT adjacency list. No modification to Regge action, Monte Carlo sampler, or causal foliation required.Usage: python GRU_CDT_postprocessing.py adjacency.txt Three independent justifications for N_RADIAL ≥ 65:(A.7) topological crossover — (A.10–A.11) echo exits UV window — (A.13d–A.14) confinement at r=0 breaks at N≥65. Technical objections addressed (§7):• Diff(M): GRU is spectral spectroscopy, not gravitational quantization.• Lorentz: d_s is a random-walker observable, not spacetime dimension.• Unitarity: GRU uses classical random walks, not quantum Hamiltonians.• RG: N<40 confinement is an operational limit. Connection to Asymptotic Safety is future work. Note on Caceffo-Clemente (arXiv:2010.07179): GRU does not contradict their result that the dual graph spectral dimension does not generally agree with the continuum Laplace-Beltrami spectrum. GRU measures a different observable — the effective radial dimension after BFS shell collapse (octant-blind protocol) — which is defined by construction and independent of LB convergence. GRU asks: "what effective dimension remains when angular and temporal connectivity are suppressed?" not "what is the physical spectral dimension of CDT spacetime?". Extension using FEM on the collapsed manifold is proposed as future work. See §7 of the consolidated report for full discussion. A.16 (in preparation): Laplacian spectrum on octant-blind collapsed graph recovers λ₁∝1/N² with <1% error, while full CDT graph shows 17–20% discrepancy — directly addressing Caceffo-Clemente (arXiv:2010.07179). Full results to appear in v1.8.8. Repository Content v1.8.7:GRU_v1.8.7_completo.pdf — complete print version with A.13–A.15, §7 objections and 20 Colab verification figuresGRU_v1_8_7_web.html — interactive web version (1MB) with all scripts A.1–A.15 embeddedGRU_v1_8_7_consolidated_report.html — supplementary report for reviewers and collaborators (recommended first read)GRU_A15_s2xR_lambda_scan.py — A.15a corrected octant-blind λ-scan S²×ℝGRU_A15_temporal_dimension_scan.py — A.15b λ_t diagonal scan, critical window [0.50,0.70]GRU_CDT_postprocessing.py — octant-blind protocol for real CDT triangulationsAll v1.8.6 scripts unchanged (A.1–A.14, available in v1.8.6 record). DOI: 10.5281/zenodo.20472915 Version 1.8.7 freezes the GRU hypothesis with complete robustness analysis on toy models and a concrete post-processing protocol for validation on formal CDT triangulations. Pending independent validation by external CDT collaborators.