Discrete 3D+3D Temporal Geometry: A Unified Framework for Galactic Dynamics, Cosmology, and Quantum Coherence

How I Built a Unified Geometric Theory of Spacetime... and Why I'm Asking the Scientific Community to Falsify It

My name is Simone Calzighetti. I am not a professor, nor a university researcher. I don't have a PhD, nor a laboratory. I am a theoretical physics enthusiast — and on September 14, 2025, I had an intuition about discrete mathematics and three-dimensional space that has evolved into a complete theoretical framework.

I have developed a geometric theory of spacetime with six dimensions and metric signature (−,+,+,+,−,−): three spatial and three temporal (3D+3D). Two temporal dimensions are compactified on a torus T² with modular parameter τ = i/φ (where φ is the golden ratio), at scales L₂ ≈ 9.5 light-years and L₃ ≈ 6.0 light-years. This generates emergent gravitational effects that explain phenomena attributed to dark matter and dark energy — without exotic particles, through pure geometry.

The Work Done

With the help of artificial intelligence — particularly Lucy (Claude, Anthropic), Vega (GPT, OpenAI), and Gemini (Google) — I have developed:

60+ academic papers (~1000 pages) covering: mathematical foundations, galactic dynamics, gravitational lensing, cosmic web structure, 6D thermodynamics, quantum decoherence, black holes, chronology protection, baryogenesis, gravitational waves, complete fermion spectrum, gauge couplings, neutrino masses, and UV completion.

All 42 Standard Model parameters derived from geometry with zero free parameters:

• Fine structure constant: α⁻¹ = 137.036 (0.001% precision)
• Weinberg angle: sin²θ_W = (3−φ)/6 = 0.2303 (0.4% precision)
• Strong coupling: α_s = 1/(2φ³) = 0.1180 (0.1% precision)
• Complete fermion mass hierarchies via Koide formulas on T²
• CKM and PMNS mixing matrices from fixed points on T²(i/φ)
• Higgs self-coupling: λ_H = 1/(2φ³)
• Cosmological constant: derived from T² Casimir energy
• Average precision across all 42 parameters: 1.2%

Empirical validation on real data:

• SPARC galaxy rotation curves: 175 galaxies, RMS = 15 km/s, zero free parameters per galaxy
• WALLABY HI survey: independent confirmation on separate galaxy sample
• 85 SLACS gravitational lensing systems: Einstein radius deficit predicted and observed (4σ detection)
• NANOGrav pulsar timing: detected periods T₂ = 30 years and T₃ = 19 years consistent with compactification scales
• Solar System constraints: compatibility with Cassini, Lunar Laser Ranging, Mercury perihelion
• Cosmic web structure at characteristic scale λ₁₃ = 0.856 Mpc following the φ-ladder hierarchy

Rigorous mathematical foundations:

• UV completion via asymptotic safety with Gaussian-like fixed point (only 2 relevant operators)
• Parameter Regress Theorem (Theorem 2.5): formal proof using the Implicit Function Theorem that 4D theories have an irreducible floor of d_free ≥ 19 free parameters — formalized in four independent mathematical frameworks (differential, moduli space, algebraic-geometric, functional)
• Complete 6D Lagrangian with Kaluza-Klein reduction to the Standard Model
• Quantum entanglement derived from causal propagation through compactified temporal dimensions
• Uniqueness theorem: τ = i/φ is the unique modular parameter satisfying all physical constraints simultaneously

Pre-registered predictions for upcoming experiments:

• Dark energy equation of state: w₀ = −0.80 ± 0.05 (DESI/Euclid, 2026)
• Growth rate index: γ = 0.567 ± 0.02 (DESI, 2026)
• Neutrino mass sum: Σm_ν ≈ 60 meV (KATRIN, 2027)
• Atmospheric mixing angle: sin²θ₂₃ = φ/3 = 0.539 (DUNE, 2028)
• Null WIMP detection (LZ/XENONnT, 2026)
• 15 specific predictions deposited BEFORE data release

Why I Cannot Validate It Alone

I lack the academic credentials to guarantee absolute mathematical correctness of every step. I have no access to experimental instruments for independent tests. I have worked with AI as my primary collaborator — which introduces risks of systematic biases that might escape my notice.

What I Am Asking

I explicitly request the scientific community to:

1. Verify the mathematical derivations
2. Criticize the physical assumptions
3. Refute the predictions with data
4. Improve the framework where necessary
5. Falsify the theory using the five kill switches provided in this repository

I have uploaded all documents, codes, simulations, and predictions. Every claim is accompanied by explicit formulas and verifiable data. Key predictions were deposited on Zenodo BEFORE the release of observational data, to prevent post-hoc fitting.

I am not seeking confirmation: I am seeking truth.

If this theory is wrong, I want to know why — and learn from the mistake. If it is correct, I want it to be rigorously tested. If it is partially valid, I want it to be refined by minds more expert than mine.

The Five Kill Switches

This theory can be destroyed. Here is how:

If any ONE kill switch is triggered at > 5σ, the theory is falsified.

Repository Contents

This release contains:

• 4 root documents: README, LICENSE (MIT), canonical parameter dictionary, falsification criteria
• 2 foundational papers: logical inevitability of 6D, Parameter Regress Theorem (4D structural analysis)
• 6 mathematical core papers: golden ratio derivation, axiom-to-theorem chain, α⁻¹ = 137 closure, complete 6D Lagrangian, spectral theory
• 5 galactic dynamics papers: SPARC validation (175 galaxies), WALLABY confirmation, NGC 3198 case study, robustness analysis
• 4 cosmology papers: cosmic web, cosmological constant, dark energy tests, 15 pre-registered predictions
• 4 reproducibility files: Python codes for SPARC fits, robustness verification, Euclid mock testing, requirements.txt

All papers in PDF format. All codes executable with standard Python (numpy, scipy, matplotlib, astropy).

Science is not certainty. It is openness, dialogue, falsifiability. This is my contribution — offered in complete transparency, with humility, and with the hope that someone with the appropriate expertise will take a look.

The truth belongs to science. We are asking the community to test it.

Simone Calzighetti 3D+3D Laboratory, Abbiategrasso, Italy simone.calzighetti@3dplus3d.it www.3dplus3d.it

February 2026 — Theory Origin: September 14, 2025