Bipolar Triadic Neurosymbolic Framework: Deterministic Semantic Resonance

Warning

🚀 DEPRECATION NOTICE (Feb 2026) 🚀

This repository represents an early, theoretical exploration of the framework using analogies from theoretical physics and cosmology. While historically relevant, this code and theory have been superseded and rigorously formalized into pure discrete mathematics ($O(1)$ Algebra) for commercial and academic applications.

Please visit the active, production-ready repository: 👉 Triadic-Neurosymbolic-Engine 👈

The new engine features exact Topological Shortest-Path Auditing, interactive Streamlit dashboards, and reproducible industrial-scale benchmarks without relying on physical metaphors."The deterministic, prime-resonant future begins here."

This repository contains the reference implementation, validation datasets, and experimental logs for the Unified Semantic Engine, a neurosymbolic system that unifies Physics and Abstract Logic under a single deterministic law: Arithmetic Resonance ($K=1.0$).

🏆 Scientific Breakthroughs (v2.0.0)

This framework introduces the Unified Holographic Resonance Theory (UHRT), replacing floating-point statistical approximations with exact Prime Modular Arithmetic.

Domain	Discovery	Metric / Result
Physics	"Super-Dense" Topology	$\gamma = 1.11$ (Monarchy of Constants)
Semantics	High-Velocity Reasoning	2.82 Million analogies/sec (Peak)
Engineering	Semantic Compression	98.65% (2,300 bytes $\to$ 31 bytes)
Math	Calculus Emergence	Discrete sums converge to integral with $\epsilon = 0.016$
Unification	Low-Entropy Structure	Super Metric $\mathcal{UBS}_{UHM} = 0.0636$

📂 Repository Structure

The repository validates the theory across three layers: The Logic Core, Data Ingestion, and Scientific Validation.

.
├── LICENSE
├── README.md
├── paper/                                     # [PUBLICATION SOURCE]
│   ├── Deterministic Semantic Resonance.pdf   # Final Paper
│   └── Deterministic Semantic Resonance.tex   # Source LaTeX
├── triadic_framework/                         # [CORE LOGIC]
│   └── core/
│       ├── triadic_engine.py                  # Arithmetic Validator (K=1.0)
│       ├── concept_mapper.py                  # Prime Factorization Engine
│       ├── triadic_search.py                  # Combinatorial Explorer
│       ├── generic_inference.py               # Hybrid Solver (Multiplicative + Additive)
│       ├── dimensional_units.py               # Dimensional Guard [M L T]
│       ├── buss_bridge.py                     # Bipolar Bridge (Goldbach Decomposition)
│       └── additive_laws.py                   # Conservation Module
└── Notebooks/                                 # [VALIDATION & EXPERIMENTS]
    ├── Master_Experiment_Log.ipynb            # The Magnum Opus (Reproduces all metrics)
    ├── final_demo_unified.py                  # "Hello World": F=ma & King:Queen
    ├── calculus_convergence_test.py           # Proof of Calculus Emergence
    ├── validate_graph_topology.py             # Gamma=1.11 Validation
    ├── validate_romiti_discovery.py           # SOTA Replication (Plasma -> Quantum)
    ├── semantic_compressor.py                 # 98% Compression Algorithm
    ├── ingest_physics_db.py                   # Omnivorous Ingestor
    ├── final_physics_database.json            # Raw Physics Laws (~400 equations)
    └── glove.6B.50d.txt                       # Legacy Vector Data (User must download)

🔧 Component Details

1. Core Logic (triadic_framework/core/)

The deterministic "gears" of the engine.

triadic_engine.py: Arithmetic Validator. Calculates the "Simplicity Factor" ($K$). If $K=1.0$, the relationship is absolute Truth.

concept_mapper.py: Prime Factorization Engine. Maps semantic attributes to unique primes (e.g., $King = 2 \cdot 3 \cdot \dots$).

buss_bridge.py: Bipolar Bridge. Maps BUSS vector axes to Prime Factors via Goldbach Decomposition (Thesis + Antithesis).

generic_inference.py: Hybrid Solver. Combines multiplicative inference (Triads) with additive conservation laws ($E_{total} = KE + PE$).

dimensional_units.py: Dimensional Guard. Validates physical consistency (e.g., ensuring outputs match $[M L T^{-2}]$).

2. Validation & Experiments (Notebooks/)

The executable evidence cited in the paper.

Master_Experiment_Log.ipynb: The Magnum Opus. A single notebook that reproduces ALL charts, metrics, and discoveries presented in the paper.

final_demo_unified.py: "Hello World". Demonstrates Physics ($F=ma$) and Semantics ($King:Queen$) running on the same engine.

calculus_convergence_test.py: Proves that calculus emerges from discrete arithmetic ($\epsilon = 0.016$).

validate_graph_topology.py: Generates the Log-Log plot and PageRank analysis proving $\gamma=1.11$.

semantic_compressor.py: Demonstration of the 98% compression algorithm.

3. Data Ingestion

ingest_physics_db.py: Cleans and structures the raw physical laws from final_physics_database.json.

💾 External Datasets Documentation

This project relies on specific external datasets for validation and graph generation.

1. Physics Database (final_physics_database.json)

Used for: Graph Topology, Romiti Discovery, and Appendix C (Topological Analysis).

Description: A JSON database containing ~400 raw physical laws and constants.

Source: Derived from Romiti et al. (2025) or generated by ingest_physics_db.py.

Status: Included in repository (Notebooks/).

2. GloVe Word Embeddings (glove.6B.50d.txt)

Used for: Legacy Vector Comparison and Real World Validation (Appendix D).

Description: Pre-trained word vectors generated from Wikipedia 2014 + Gigaword 5.

Source: Stanford NLP Group.

Status: Download Required.

Installation Instructions for GloVe:

Download the zip file (~822MB): http://nlp.stanford.edu/data/glove.6B.zip

Extract glove.6B.50d.txt into the Notebooks/ directory.

Run final_demo_unified.py to verify integration.

📜 Publications & Citation

This code serves as the executable proof for the following research:

Unified Paper (v2.0):

J.ArturoOrnelasBrand. (2025). arturoornelasb/-Bipolar-Triadic-Neurosymbolic-Framework-: Bipolar Triadic Neurosymbolic Framework: Deterministic Semantic Resonance (v2.0.0). Zenodo. https://doi.org/10.5281/zenodo.17676514

Foundational Papers:

Ornelas Brand, J. A. (2025). Bipolar Universal Semantic Scale (BUSS) - V2.0. Zenodo. https://doi.org/10.5281/zenodo.17527818

Ornelas Brand, J. A. (2025). A Rigorous Triadic Framework for Neurosymbolic Reasoning. Zenodo. https://doi.org/10.5281/zenodo.17613664

Ornelas Brand, J. A. (2025). Unified Holographic Resonance Theory (UHRT). Zenodo. https://doi.org/10.5281/zenodo.17662886

🚧 Future Roadmap

Biological Resonance: Applying Prime Factorization to DNA sequences to detect "Genetic Glitches" and improve sequence analysis accuracy.

Narrative Entropy: Formalizing the variational principle of minimal entropy for multi-path reasoning.

License

This project is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

Copyright © 2025 José Arturo Ornelas Brand.