UFT-F Spectral Framework: Resolutions of Gödel's Incompleteness, Informational Cosmology Simulations, and AGI Synthesis

This repository synthesizes three core extensions of the Unified Field Theory-F (UFT-F) Spectral Framework, building on prior validations (Zenodo 17566371, 17583962).

1. Unconditional Completion: Resolves Gödel's Incompleteness Theorems via transcendental closure with the Anti-Collision Identity (AACI) axiom, enabling F' ⊢ Con(F) through spectral equivalence.

2. UFT-F Hybrid Simulation (information.pdf): Ring-sector Green kernel with Base-24 harmonics detects discrete angular quantization in informational halo density (99.5% concentration in sectors 1/24), confirming ACI stability (L¹ norm = 7232.0091 < ∞). Predicts Δℓ ≈ 24 modulation in halo/CMB power spectra.

3. AGI Synthesis: Maps UFT-F identities (spectral map Φ, ACI stability, inverse spectral reasoning) to LeCun's foundational AGI goals (world models, stable priors, efficient planning), providing a Q-constructible blueprint for robust neural-spectral architectures.

All components enforce dimensional closure and transcendental universality via c_{UFT-F}. Reproducible code included. Related: Dark matter NFW derivations (separate repo). 

## Overview
The UFT-F framework unifies arithmetic (TNC/BSD resolution), spectral geometry, informational cosmology, logic (Gödel completion), and AGI priors via the spectral map Φ: M → H_M = -Δ_M + V_M(x).

## Key Components
- **Godel.pdf**: Proves GIT I/II resolution via AACI axiom (‖Ψ_M‖_{L¹} < ∞) as transcendental prior.
- **information.pdf**: 2D simulations reveal Base-24 artifacts in ρ_info(r,θ), stable under ACI/LIC.
- **AGI.pdf**: Actionable 4-phase plan for AGI, linking to LeCun's world models/stability/reasoning.

## Related Works
- Empirical ACI validation: [10.5281/zenodo.17583962](https://doi.org/10.5281/zenodo.17583962)
- TNC resolution: [10.5281/zenodo.17566371](https://doi.org/10.5281/zenodo.17566371) 
- Dark matter extensions:  the dark_matter.pdf can be found here https://zenodo.org/records/17566371

## Reproduction
Python 3 + NumPy/SciPy. See code zips for O(1) factoring and Schrödinger kernels.