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

Version 1.9.0 of the Radial Unitary Geometry (GRU) Hypothesis.

CENTRAL RESULTS:

• Toy model S¹ (A.6 v2.1): d_s(λ=0) = 1.0007 ± 0.0321 vs d_s(λ=1) = 1.9818 ± 0.1020 — separation 9.2σ
• CDT real (A.21, 60 geometries): d_s(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): d_s = 1.013 ± 0.004 stable across λ=0.50–0.693 (extended phase)
• T-scan CDT (A.23, T=20–320): d_s(T=320) = 1.006 ± 0.022 — P1 RESOLVED: d_s→1.0 at T→∞ confirmed with adaptive protocol v3
• Spectral law (A.24): λ_n ≈ 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): d_s(spine) = 1.0489 ± 0.0287 (6 seeds ensemble); seed=42: 1.0165±0.0222; T=40→d_s=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): d_s(spine) = 1.0428 ± 0.0157 — universality confirmed in 4D toy model.

KEY DISTINCTION: d_s≈1 refers to the GRU SPINE (temporal subgraph), not the full CDT graph. The full graph recovers d_s→2 in UV (CDT 2D) and d_s≈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→∞: d_s(T=320)=1.006±0.022 → convergence to 1.0 confirmed ✓
• P3 — GRU vs consensus: GRU refines d_s→2, does not contradict ✓
• P4 — Protocol variability: range 0.98–1.03, robust ✓
• P5 — Spectral law λ_n≈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: d_s≈1.013 stable for λ∈[0.50,0.693]
• A.23 — T-scan T=20–320: convergence to d_s=1.0 confirmed with protocol v3
• A.24 — Spectral law λ_n≈n² validated with direct Laplacian eigenvalues
• A.25 — GRU universal in CDT (2+1)D: d_s=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): d_s=1.0428±0.0157 — blind prediction for CDT (3+1)D real.
• §6 — Open methodological question: “Is d_s=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):

• d_s(spine) > 1.15 in ≥80% of CDT geometries → GRU refuted
• d_s(T=320) > 1.05 with correct protocol → refuted (tested: 1.006 ✓)
• d_s(spine, 3D CDT) > 1.15 → refuted (tested: 1.0489 ✓)
• d_s(spine, toy 4D) > 1.15 → refuted (tested: 1.0428 ✓)
• External replication reports d_s > 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: d_s 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.20535537
DOI: 10.5281/zenodo.20574763