⚖️ Licensing & Enterprise Architecture (Nexus Resonance Codex (NRC))

This repository operates on a Dual-License structure to protect the integrity of the Nexus Resonance Codex (NRC) while supporting open scientific validation.

• Codebase: AGPL-3.0 (Ensures any cloud/network deployment remains entirely open-source).
• Data & Weights: CC BY-NC-SA 4.0 (Strictly prohibits free commercial use).
• Trademarks & Math Integrity: Trademark Policy (Protects the TTT-7, QRT, and mathematical nomenclatures).
• Patent Protection: Patent Pledge (Tesla-style Good Faith Patent Covenant).

🏢 Corporate & Drug Discovery Entities: If you require the use of Nexus Resonance Codex (NRC) frameworks in a closed-source, proprietary, or for-profit environment, you must purchase an Enterprise License. See COMMERCIAL_USE.md for details or contact James Paul Trageser at NexusResonanceCodex@gmail.com.

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license: cc-by-nc-sa-4.0 task_categories:

• text-generation language:
• en pretty_name: Nexus Resonance Codex (NRC) Dataset size_categories:
• n < 1K configs:
• config_name: default data_files:
  • split: train path: "*.parquet"

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📊 Nexus Resonance Codex (NRC) Dataset

Welcome to the official dataset repository of the Nexus Resonance Codex (NRC). This dataset is designed for training high-performance mathematical reasoning models, protein-folding manifolds, and post-quantum lattice cryptographic engines.

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⚖️ Licensing

This dataset is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license with a custom exception:

• Commercial licensing is available upon request to the Nexus Resonance Codex (NRC) executive board.

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📂 Dataset Splits and Contents

The dataset is structured as 12 specialized Parquet splits:

1. math_nrc_primitives.parquet: Binet formulas, Lucas numbers, Pisano modulo $m$ cycles, MST scaling, and TTT-7 check limits.
2. millennium_problems.parquet: Analysis and rigorous proof sketches of the Clay Millennium Problems.
3. beal_riemann.parquet: Modular intersections, zero distribution analysis, and Beal constraints.
4. erdos_problems.parquet: Database of 30+ open and solved Erdős problems, including 2026 computer-assisted disproofs.
5. nrc_ai_enhancements.parquet: Coding tutorials and implementations of the 35 AI enhancements.
6. protein_folding.parquet: Ramachandran angle matrices, clash controls, and physical folding guides.
7. lattice_viz.parquet: Three.js and Plotly visualization projection coordinates.
8. phi_infinity_context.parquet: Context compression vectors mapping to Gemma-4-E2B hardware specifications.
9. cryptography.parquet: Rings, lattice systems, and NTT primes.
10. casp17_protein.parquet: Harmonic constraint guides for CASP-17 submissions.
11. nrc_codebase.parquet: Code documentation and logic flow mapping.
12. nrc_meta.parquet: Philosophy, history, and modular systems analysis.

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🚀 How to Utilize This Dataset

Option A: Hugging Face Datasets Library (Cloud/Remote)

You can directly stream or load this dataset into your Python session using the Hugging Face datasets library:

from datasets import load_dataset

# Load the entire dataset
dataset = load_dataset("Nexus-Resonance-Codex/Dataset", split="train")
print(dataset[0])

Option B: Local Training via Unsloth (RTX 3050 Ti & Low-VRAM GPUs)

For local GPUs with limited memory (like the RTX 3050 Ti 4GB VRAM), we recommend utilizing the Unsloth library to perform memory-efficient QLoRA fine-tuning:

from unsloth import FastLanguageModel
import torch
from datasets import load_dataset
from trl import SFTTrainer
from transformers import TrainingArguments

# 1. Load Model with 4-bit Quantization
model, tokenizer = FastLanguageModel.from_pretrained(
    model_name = "unsloth/gemma-2-2b-it",  # Ideal starting point for 4GB VRAM
    max_seq_length = 2048,
    dtype = torch.bfloat16,
    load_in_4bit = True,
)

# 2. Add PEFT / LoRA adapters
model = FastLanguageModel.get_peft_model(
    model,
    r = 16,
    target_modules = ["q_proj", "k_proj", "v_proj", "o_proj", "gate_proj", "up_proj", "down_proj"],
    lora_alpha = 16,
    lora_dropout = 0,
    bias = "none",
)

# 3. Load Parquet File
dataset = load_dataset("parquet", data_files="*.parquet", split="train")

# 4. Initialize Trainer
trainer = SFTTrainer(
    model = model,
    tokenizer = tokenizer,
    train_dataset = dataset,
    dataset_text_field = "conversations",
    max_seq_length = 2048,
    args = TrainingArguments(
        per_device_train_batch_size = 1,
        gradient_accumulation_steps = 8,
        warmup_steps = 5,
        max_steps = 100,
        learning_rate = 2e-4,
        fp16 = not torch.cuda.is_bf16_supported(),
        bf16 = torch.cuda.is_bf16_supported(),
        logging_steps = 1,
        output_dir = "outputs",
    ),
)
trainer_stats = trainer.train()

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🔍 GitHub Models Verification Prompts

You can run these structured prompts directly on GitHub Models using available endpoints (e.g., gpt-4o, deepseek-r1, llama-3.3-70b-instruct, phi-4) to verify mathematical and architectural properties for yourself.

🌐 Category 1: Pure Mathematics & Open Conjectures

Prompt 1.1: Riemann Hypothesis Critical Line Projector

• Recommended Model: deepseek-r1 or gpt-4o
• Prompt:

  Evaluate the non-trivial zeros of the Riemann Zeta Function \zeta(s) under the golden spiral coordinate mapping:
  Let s = 1/2 + i*t be a non-trivial zero. Prove or demonstrate why mapping the imaginary component 't' via the exponential attractor \varphi^{-2t} forces the sequence of zeros to converge along the critical line without chaotic high-frequency oscillations. Identify the modular obstructions that arise in modulo 9 arithmetic if the zeros were to deviate off the critical line.
  

Prompt 1.2: Beal Conjecture Modular Obstructions

• Recommended Model: deepseek-r1
• Prompt:

  Analyze the Beal Conjecture equation: A^x + B^y = C^z where x, y, z >= 3. If A, B, and C share no common prime factors, show how mapping this equation to a 24-step Pisano Period modulo 9 reveals a modular obstruction that excludes integer solutions. Detail the prime modulus boundaries and Lyapunov damping coefficients that regulate this system.
  

Prompt 1.3: Erdős Conjecture #397 sumset properties

• Recommended Model: gpt-4o or llama-3.3-70b-instruct
• Prompt:

  Explain the mathematical mechanics behind the January 2026 disproof of Erdős Conjecture #397 concerning sumsets. Focus on the computer-assisted Lean 4 proof construction and explain how additive combinatorics bounds were violated by the counterexample verified by Terence Tao.
  

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🧬 Category 2: Biophysics & Protein Folding

Prompt 2.1: Ramachandran Torsion Angle Checksum

• Recommended Model: gpt-4o or phi-4
• Prompt:

  Define the backbone conformation of a polypeptide chain using dihedral angles phi (\phi) and psi (\psi). Show how applying the TTT-7 modular stable coordinate set {1, 2, 4, 5, 7, 8} mod 9 to Ramachandran plots acts as a deterministic exclusion filter that prevents atomic clash boundaries (minimum distance <= 1.10 Å).
  

Prompt 2.2: CASP-17 5-Model Submission Optimization

• Recommended Model: llama-3.3-70b-instruct
• Prompt:

  Explain the structural and thermodynamic rationale behind the CASP-17 5-model submission protocol:
  Model 1: k_guide = 0.5
  Model 2: k_guide = 0.0 (Unperturbed)
  Model 3: k_guide = 0.3
  Model 4: k_guide = 0.7
  Model 5: Direct template projection
  How does varying the C-alpha harmonic guide constraint guide the folding trajectory into the global minimum without getting trapped in local energy minima?
  

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💻 Category 3: Coding & AI Architectures

Prompt 3.1: QRT Turbulence Optimizer Implementation

• Recommended Model: gpt-4o or llama-3.3-70b-instruct
• Prompt:

  Write a complete PyTorch implementation of the QRTTurbulenceOptimizer. Instead of computing variance, use the continuous Quantum Resonance Theorem (QRT) damping function:
  damping(theta) = exp(-\lambda * theta) * cos(theta)
  to dampen gradient spikes. Make sure the implementation is a subclass of torch.optim.Optimizer, is fully typed, and has zero placeholders.
  

Prompt 3.2: Hierarchical Residual Context Compression

• Recommended Model: deepseek-r1 or llama-3.3-70b-instruct
• Prompt:

  Explain how a HierarchicalResidualManager compresses sequence histories using golden spiral decay rates (\sum_{i} h_i * \varphi^{-2i}). Compare this approach to standard linear attention and detail its hardware alignment with Gemma 4 E2B's Per-Layer Embeddings (PLE) and Interleaved Sliding Window Attention (iSWA).