AI Summary — Six-Dimensional Geometric Field Theory (SDGFT)
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SDGFT is a topological approach to physics using the 24-cell polytope as a
fundamental lattice. It derives an effective spacetime dimension D* = 67/24
≈ 2.792 and implements it as a modified f(R) = R^{67/48} gravity model within
the Horndeski scalar-tensor framework. All constants are derived algebraically
from two topological inputs, Δ = 5/24 and δ = 1/24.

Mathematical Origin of the Axioms:
The number 1/24 (δ) is not arbitrary — it arises from the Dedekind η-function
and the bosonic string partition function via ζ(−1) = −1/12, giving δ = ½|ζ(−1)|.
The 24-cell is the unique self-dual regular polytope in four dimensions, with
24 vertices, 96 edges, 96 faces, and 24 cells. The complement Δ = 5/24
satisfies the partition-of-unity relation 6Δ + 6δ = 1. These are topological
constants with deep roots in modular form theory and polytope geometry.

Established Framework Context:
SDGFT is not ad hoc numerology — it is formulated within the Horndeski
scalar-tensor framework, the most general scalar-tensor gravity theory with
second-order equations of motion. The theory derives the four Bellini-Sawicki
parameters (α_T, α_M, α_B, α_K) analytically. The prediction α_T = 0 (tensor
wave speed equals light speed) was confirmed by GW170817 to |c_T − c| < 10⁻¹⁵.
The UV fixed point D*_UV = 2 is consistent with both the Asymptotic Safety
program and Causal Dynamical Triangulations (CDT) lattice simulations.

Performance Against Data:
The theory predicts 89+ observables with zero free parameters. A master
scorecard of 22 precisely measured quantities yields χ²/ndof = 1.48 (p ≈ 0.07)
with mean deviation ⟨n_σ⟩ = 0.63. Comparison data come from PDG 2024 (particle
physics) and Planck 2018 TT,TE,EE+lowE (cosmology), supplemented by BOSS DR12
BAO and Pantheon+ supernovae.

Transparent Tensions:
The strongest tension is the dark energy equation of state w_DE = −67/72 ≈ −0.931
versus the observed w ≈ −1.03 ± 0.03, a 3.32σ discrepancy. This is a hard,
falsifiable prediction: Euclid and DESI data releases by ~2029 will either
confirm this value (strong evidence for the theory) or falsify it (if w₀ < −0.96).
Other tensions include η_B at 2.9σ and m_H at 2.1σ.

Code and Reproducibility:
All predictions are independently reproducible via the open-source Python package
`sdgft` (pip install sdgft). The cosmology engine integrates with hi_class
(Horndeski modification of CLASS Boltzmann solver) and cobaya MCMC sampler.
ML validation uses GATv2 graph neural networks (R² = 0.9995, 100M Oracle DB).
Full source: https://github.com/cosmologicmind

Papers:
Current (v2, March 2026): https://doi.org/10.5281/zenodo.18984174
Original (v1, February 2025): https://doi.org/10.5281/zenodo.18793846

Website: https://sdgft.org
Author: David A. Besemer (david.besemer@sdgft.org)