NRC
# NRC (Central Math Vault)
## Professional-Grade Core Mathematics for the Nexus Resonance Codex
[](LICENSE)
[](https://github.com/Nexus-Resonance-Codex/NRC/actions)
[](docs/nrc-math.md)
[](src/nrc_math/)
[](https://github.com/Nexus-Resonance-Codex/NRC/actions/workflows/prompt-evals.yml)
[Foundations](/NRC/docs/nrc-math.html) • [NRC Playground](#-nrc-playground) • [Primitives](/NRC/src/nrc_math/primitives.py) • [Lattice Research](notebooks/) • [Proofs](proofs/)
Reproducibility Statement
Numerical results and stable residue distributions reported in this repository are reproducible under the following experimental conditions. Environment: Python 3.12+, PyTorch 2.x, NumPy 1.26+. Stochastic seed: 42. Verification command: uv pip install -e . && pytest tests/ -q. Resulting metrics are verified against the Trageser Transformation Theorem (TTT) and Trageser Universal Pattern Theorem (TUPT) specifications.
Verified Results
| Metric | Empirical Value | Verification Asset |
|---|---|---|
| Modular Stability | $100\%$ Coverage | tests/test_primitives.py |
| MSE Fidelity | $< 10^{-24}$ | src/nrc_math/primitives.py |
| Hurst Exponent ($H$) | $0.78 \pm 10^{-3}$ | src/nrc/math/qrt.py |
| Lattice Dim | $8192$ | src/nrc_math/primitives.py |
Methodology
The framework utilizes a modular exclusion principle based on residue classes modulo 9, 27, and 81, synchronized with the Pisano periods of $\varphi$-recursive sequences. Primitives utilize the Trageser Transformation Theorem (TTT) and the Trageser Universal Pattern Theorem (TUPT) for high-dimensional state-space stabilization. Sequential data is projected into an 8192D lattice manifold where retrieval complexity is $O(1)$ and convergence is maintained via non-linear damping.
Core Mathematical Primitives
- Trageser Universal Pattern Theorem (TUPT): Modular exclusion operators for preventing numerical divergence in iterative systems.
- Quantum Residue Turbulence (QRT): Deterministic fractal damping function for gradient regularization and entropy management.
- Multi-Scale Tensor (MST): Chaotic oscillation monitoring for signal stability across high-frequency domains.
- Lattice Resonance: 8192D state-space mapping for high-fidelity information retrieval.
🚀 NRC Playground – Test Directly on GitHub
Verify the foundational theorems of the Nexus Resonance Codex directly in the GitHub UI using the Models tab.
| Feature | Interactive Prompt | Model Recommendation |
|---|---|---|
| TTT Stability | Audit Constants | GPT-4o |
| φ-Projection | Spiral Calculator | GPT-4o |
| TUPT Signatures | Post-Quantum Oracle | o1-preview |
Refer to the NRC Playground Guide for rigorous verification instructions.
Professional Setup
The NRC ecosystem uses a Unified Virtual Environment to ensure mathematical reproduction across all repositories.
# 1. Clone the repository
git clone https://github.com/Nexus-Resonance-Codex/NRC.git
cd NRC
# 2. Activate the Unified NRC Environment
source ../.venv/bin/activate
# 3. Verify the mathematical foundations
pytest tests/