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

Authors: Flores Cornejo, Alfredo;

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

Abstract

Version 1.9.0 of the Radial Unitary Geometry (GRU) Hypothesis. CENTRAL RESULTS: Toy model S¹ (A.6 v2.1): ds(λ=0) = 1.0007 ± 0.0321 vs ds(λ=1) = 1.9818 ± 0.1020 — separation 9.2σ CDT real (A.21, 60 geometries): ds(spine) = 1.019 ± 0.015 — first validation on formal CDT Monte Carlo (Brunekreef–Görlich–Loll, JorenB/2d-cdt, arXiv:2310.16744). Statistical separation spine vs full graph: 15.8σ λ-scan CDT (A.22, 28 geometries): ds = 1.013 ± 0.004 stable across λ=0.50–0.693 (extended phase) T-scan CDT (A.23, T=20–320): ds(T=320) = 1.006 ± 0.022 — P1 RESOLVED: ds→1.0 at T→∞ confirmed with adaptive protocol v3 Spectral law (A.24): λn ≈ n² validated with direct eigenvalue extraction — P5 RESOLVED. Mean error 4.9% for n=1–10; exact for n≤5 CDT (2+1)D extension (A.25, JorenB/3d-cdt): ds(spine) = 1.0489 ± 0.0287 (6 seeds ensemble); seed=42: 1.0165±0.0222; T=40→ds=0.9999≈1.0 exact; V-scan V=3000–8000 stable. GRU UNIVERSAL across bulk dimensions. P2 now 2/3 resolved. Toy S³×ℝ (A.26, 4D blind prediction): ds(spine) = 1.0428 ± 0.0157 — universality confirmed in 4D toy model. KEY DISTINCTION: ds≈1 refers to the GRU SPINE (temporal subgraph), not the full CDT graph. The full graph recovers ds→2 in UV (CDT 2D) and ds≈2.526 (CDT 3D shell counting), consistent with CDT standard (Benedetti & Henson 2009; Kommu 2012). GRU refines, not contradicts, the consensus. RESOLVED QUESTIONS (5/6 + P2 now 2/3): P1 — T→∞: ds(T=320)=1.006±0.022 → convergence to 1.0 confirmed ✓ P3 — GRU vs consensus: GRU refines ds→2, does not contradict ✓ P4 — Protocol variability: range 0.98–1.03, robust ✓ P5 — Spectral law λn≈n²: validated with real eigenvalues, error 4.9% ✓ P2 — Extension to (3+1)D CDT: 2/3 resolved (CDT 2D ✓ CDT 3D ✓ Toy 4D ✓). Only CDT (3+1)D real pending (collaboration INFN/Loll) P6 — Independent replication: contact initiated with Clemente/INFN (endorsement code sent) NEW IN v1.9.0: A.21 — 60 independent CDT geometries (V=2000–50000, λ=ln2, T=40). Spine vs full: 15.8σ A.22 — λ-scan: ds≈1.013 stable for λ∈[0.50,0.693] A.23 — T-scan T=20–320: convergence to ds=1.0 confirmed with protocol v3 A.24 — Spectral law λn≈n² validated with direct Laplacian eigenvalues A.25 — GRU universal in CDT (2+1)D: ds=1.0489±0.0287 (6 seeds), T=40→0.9999, V-scan stable. Refs: Benedetti & Henson (2009), Kommu (2012). A.26 — Toy S³×ℝ (4D): ds=1.0428±0.0157 — blind prediction for CDT (3+1)D real. §6 — Open methodological question: “Is ds=1 trivial by construction?” Answer: No — with λ=1 gives 1.98; with T=3 gives 0.1; full graph gives 1.67–2.5. §6.2.5 — Spine as physical observable: gauge-invariance, minimal causal subgraph Short paper GRU_v1.9.0_short.pdf: 7 sections + A.25 + A.26, arXiv-ready FALSIFICATION CRITERIA (§8): ds(spine) > 1.15 in ≥80% of CDT geometries → GRU refuted ds(T=320) > 1.05 with correct protocol → refuted (tested: 1.006 ✓) ds(spine, 3D CDT) > 1.15 → refuted (tested: 1.0489 ✓) ds(spine, toy 4D) > 1.15 → refuted (tested: 1.0428 ✓) External replication reports ds > 1.2 → refuted REPOSITORY CONTENT (13 files): GRU_v1_9_0_web.html — complete HTML (A.1–A.26, 1.18 MB) GRU_v1.9.0_completo.pdf — complete PDF GRU_v1_9_short.html — short paper HTML (A.25 + A.26 + methodological question) GRU_v1.9.0_short.pdf — short paper PDF (arXiv-ready) GRU_minimal_S1.py — minimal script: ds flow λ=0→1 GRU_A21_CDT_Brunekreef.py — A.21 protocol: octant-blind on JorenB/2d-cdt GRU_A25_3dcdt.py — A.25 protocol: octant-blind GRU on JorenB/3d-cdt GRU_A26_S3xR.py — A.26: toy model S³×ℝ (4D blind prediction) — NEW GRU_CDT_real_postprocessing.py — standalone for any CDT adjacency file GRU_A21_analizar_v5000.py — V=2000 vs V=5000 comparative analysis GRU_3dcdt_setup.sh — installation script for JorenB/3d-cdt — NEW GRU_A25_config.dat — Monte Carlo config T=20 V=5000 — NEW README_INSTALL.md — complete replication guide (Phases 0–4) — NEW Previous versions: v1.8.9 DOI 10.5281/zenodo.20535537DOI: 10.5281/zenodo.20574763

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