Universal Binary Principle (UBP) Framework v3.2+

Euan Craig, New Zealand September 3, 2025

Abstract

The Universal Binary Principle (UBP) Framework provides a deterministic, information- centric model that seeks to computationally simulate and analyze fundamental aspects
of reality through the manipulation of binary state toggles within high-dimensional spaces. Built upon axiomatic principles, modular software architecture, and rigorous coherence metrics, the UBP offers a foundation for scientifically exploring both physical
and non-classical domains with precision and extensibility [1].

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1 Introduction

The Universal Binary Principle (UBP) postulates that all observable phenomena emerge from discrete binary state changes, termed toggles, operating within multidimensional man- ifolds. The goal of the framework is to realize a fully rigorous, extensible system enabling new forms of computational experimentation—calculating, discovering, and validating real- ities not attainable with conventional methods. By encoding information in nuanced 24-bit OffBits and integrating persistent, content-addressable storage with advanced error correc- tion, UBP bridges data science, quantum modeling, and fundamental physics under a unified formalism [2].

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Core Principles of the UBP Framework

OffBit: The atomic binary unit. Each OffBit contains 24 bits partitioned into identity, dynamic state, and relational context. Unlike conventional bits, OffBits capture poten- tiality and layered properties.

6D Bitfield Spatial Mapping: All OffBits reside on a dynamic 6D spatial manifold, supporting the representation and simulation of complex relationships beyond classical 3D mapping. Mapping parameters adapt to hardware profiles and experiments.

HexDictionary Universal Storage: Persistent, content-addressable repository indexed by SHA256; supports immutability and reproducibility of all computational states and experiment outputs. Data is compressed (gzip), with standardized metadata for rich querying.

BitTab Encoding: Specialized 24-bit encoding translates physical or informational prop- erties (such as atomic number, valence, block) into binary strings for experiment and simulation.

Multi-Realm Physics Integration: UBP supports quantum, electromagnetic, gravita- tional, biological, cosmological, nuclear, and plasma realms. Each realm receives unique resonance parameters, error correction, and toggle behaviors.

Framework Modules Overview

The UBP is modular, with each submodule building toward full functionality:

• ubp config.py, system constants.py: Central nervous system housing all UBP, math- ematical, and physical constants; supports dynamic configuration across hardware.

• state.py: Implements OffBit and MutableBitfield (6D arrays for binary states).

• toggle ops.py: Toggle algebra (AND, XOR, resonance, entanglement, superposition, spin transition).

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• kernels.py: Provides resonance kernel, coherence calculations, global coherence invari- ants.

• energy.py: The UBP energy equation:
  E = M × C × (R × Sopt) × PGCI × Oobserver × c∞ × Ispin × X(wijMij)

• metrics.py: NRCI (Non-Random Coherence Index), Coherence Pressure, Fractal Dimen- sion, Spatial Resonance Index.

• global coherence.py: Computes global phase-locking using weighted frequency averages.

• enhanced nrci.py: Advanced NRCI, Golay-Leech integration, temporal weighting.

• observer scaling.py: Models observer intent and purpose tensor interactions.

• carfe.py: Implements Cycloid Adelic Recursive Expansive Field Equation (CARFE) for nonlinear dynamic system evolution.

• dot theory.py: Encodes purpose tensor mathematics and intentionality.

• spin transition.py: Quantum spin dynamics, Zitterbewegung modeling, quantum in-

  formation quantification.

• p adic correction.py, glr base.py, level 7 global golay.py: Multi-realm error cor- rection, BCH, Hamming, Golay codes, p-adic lifting, adelic corrections.

• prime resonance.py: Prime-based coordinate systems tuned via Riemann zeta zeros.

• tgic.py: Triad graph constraints, Leech lattice, dodecahedral projections, enforcing geo-

  metric coherence (3/6/9 rules).

• hardware emulation.py, hardware profiles.py: Simulate different hardware profiles and architectures.

• ubp lisp.py: S-expression based ontology, executing UBP primitives via a native lan- guage.

• crv database.py, enhanced crv selector.py: Dynamic resonance value management, CRV optimization.

• htr engine.py: Harmonic Toggle Resonance engine for physical and abstract resonance behaviors.

• ubp pattern analysis.py, ubp 256 study evolution.py, visualize crv patterns.py: Pattern generation/analysis, storing and visualizing cymatic-like coherence states.

• materials research.py: Predictive modeling of materials (e.g. tensile strength in alloys) based on resonance and coherence.

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• rgdl.py: Resonance Geometry Definition Language for dynamic geometry generation and emergent 3D field export.

• optimize route.py: TSP solver leveraging resonance and NRCI optimization.

• detect anomaly.py: NRCI-based anomaly detection in real time signals.

• runtime.py: Virtual Machine managing high-level state, semantic execution, simulation orchestration.

• Utility modules (cli.py, dsl.py, etc.): automation, command-line, and persistent state management.

4 The UBP Self-Contained Formula

The central computational pipeline of UBP is:
U(x) = H−1 R C Φt ERT1(x)




where:

• T1(x): BitTab 24-bit encoding of input x; b1−8 identity, b9−16 dynamic state, b17−24 rela- tional context.

• ER(x): Realm-specific error correction; e.g., BCH, Hamming, Golay, p-adic, and Fibonacci strategies selected per R.

• Φt: Evolution operator, Φt(b) = exp(tLCARFE) ∗ b, LCARFE = λC + μA + νR.

• C : Coherence maximization (NRCI), parameter tuning for λ, μ, ν to maximize N RC I (Φ, T ).

• R[f]: Rune protocol, fixed point closure via self-evaluating UBP-Lisp expressions.

• H−1: HexDictionary retrieval of outputs and augmentation with all NRCI-coherent his- torical states.

5 Design Philosophy

UBP emphasizes:

• Scientific rigor: All computations are based on mathematically exact models rather than approximations.

• Completeness: Each module is fully functional; no placeholder or mock algorithms.

• Persistence: Robust SHA256-indexed content-addressable storage enables transparency and reproducibility.

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• Modularity: Logical separation of concerns among modules for independent development and validation.

• Adaptability: Dynamic optimization for hardware, experiment types, and realm switch- ing.

• Discovery: Uncover novel relationships and structures via binary, resonant, and coherence- driven analysis.

6 Example: Materials Modeling with UBP

The UBP framework has been demonstrated on atomic-scale modeling of resonant steel. Us- ing a BCC lattice simulation, the Harmonic Resonance Transfer engine calculated NRCI of 0.9219, and the Resonant Geometry Definition Language engine produced a unique material ”fingerprint.” The experiment highlighted the framework’s ability to link elemental prop- erties, atomic structure, classical mechanics, and resonance analytics within one workflow [2].

7 Conclusion

UBP v3.2+ represents a leap toward unified computation grounded in fundamental binary information, modular architecture, error correction, and resonance-driven modeling. Its fully implemented modules and scientifically rigorous design provide new tools for physical modeling, discovery, and experimental science.

References

[1] Universal Binary Principle: A Meta-Temporal Framework for a Computational Reality. Technical Whitepaper, Euan R A Craig, 2025.

[2] A Computational Framework for Atomic-Scale Material Modeling: A Case Study on Resonant Steel using UBP, Euan R A Craig, 2025.

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