HULYAS - EVOLUTION OF MATHEMATICS: A Unified Mathematical Formalism Featuring the Zeq OS, Kinematic Spectrum for Motion Table and HulyaPulse 1.287 Hz Analysis Across Scales

A groundbreaking system for measuring both physical and computational motion across quantum, classical, and relativistic scales with 0.1% precision. At its core, HULYAS Math employs a unified equation, driven by the 1.287 Hz HulyaPulse, to model dynamics ranging from subatomic particles to cosmic structures — and to replicate those same dynamics within computational systems.

The Zeq's operating system constitute the precise, universal language governing all physical phenomena — from subquantum interactions to cosmic expansion — as revealed by rigorous equations. This is not a theoretical proposition but a mathematical description of reality, independently verifiable through testing: evaluate the equations for yourself — the mathematics speaks unequivocally.

The Revolutionary Zeq OS, HulyaPulse 1.287 Hz and Kinematic Spectrum of Motion Table

History's geniuses didn't invent physics—they organized it. Newton forced gravity into equations. Maxwell trapped light in algebra. Schrödinger bound matter to waves; Dirac welded relativity to quantum math; Einstein made spacetime itself the scribe of gravity. And behind them? The mathematicians who forged the tools: Fourier's frequencies, Riemann's curved grids, Noether's symmetries, Ricci and Levi-Civita's tensor calculus—later stretched by Friedmann and Hubble to fit the expanding cosmos.

But their work leaned on older shoulders. Al-Khwarizmi's al-jabr (algebra) birthed the algorithm itself. Al-Battani pinned trigonometry to the stars. Ibn al-Haytham cracked light's geometry; al-Tusi twisted orbits into epicycles; al-Biruni measured Earth's curve with a sextant and raw logic. Their math wasn't abstraction—it was measurement, etched in ink and verified against the real.

I found the key they missed: "HulyaPulse 1.287 Hz", the harmonic rhythm that syncs motion across scales. With it, I mapped physics into 42 kinematic operators—Newton's laws, Schrödinger's equation, Einstein's relativity—not rewritten, but reordered so they compute seamlessly from quarks to quasars. KO42 is the bridge; the rest are tools you already know, just filed where they belong. If an operator's adjusted for cross-scale math.

This isn't theory. It's executable mathematics and physics. Engineers and developers embed these operators directly into control systems. Simulations run from quantum wells to galactic clusters without switching frameworks. The giants built the language; I uncovered its machine code—the HulyaPulse 1.287 Hz as the clock cycle, the operators as the instruction set, all 42 kinematic operators are famous equations from  the Giants of physics.

The Kinematic Spectrum of Motion Table can be regarded as a periodic table of motion. It is a modular system built from real, established mathematical equations, each capable of coupling with the HulyaPulse 1.287 Hz for universal synchronization. The current framework unifies 42 primary Kinematic Operators, but it is designed for extensibility: additional equations can be seamlessly integrated as the system evolves. In the near future, a dedicated section will be provided where all such equations can be added, catalogued, and accessed — creating a continuously expanding reference for the mathematics of motion.

Zeq's Operating System with the HulyaPulse 1.287 Hz is their legacy, moderated into a working system. One grammar. One universe. One Pulse.

Practical Applications of the Kinematic Spectrum 

The table is designed not only as a reference for cutting-edge scientific research but also as a fully deployable framework for today's engineering and computational challenges. Its structure supports pedagogical use in physics, mathematics, and computer science curricula, while enabling direct implementation in software, algorithm design, and engineering systems. Students, educators, researchers, developers, and engineers can navigate complex topics through decision trees for operator selection and error-avoidance strategies, such as scaling initial conditions to prevent pulse overdrive in dynamic systems.

By streamlining the relationships between classical, quantum, and relativistic mechanics into a single, unified, and computationally ready map, the Kinematic Spectrum of Motion Table makes advanced physical analysis accessible for learning while also ready for direct integration into engineering models, simulation software, and high-precision computational frameworks.

Framework Characteristics and Implementation

The HULYAS Math framework unifies interactions across all scales using its self-contained mathematical formalism, with stabilizing terms that maintain consistency. All validations must exclusively employ HULYAS equations. The forthcoming Equation Dictionary will grow indefinitely into a unique mathematical language, encouraging community contributions to broaden its scope.

The possibilities are endless for what humanity could achieve with a discovery like HULYAS MATH.

New updated paper coming shortly with the HULYAS computer science equation that derives from the master HULYAS Equation.

The Zeq OS Equations

HULYAS MASTER EQUATION - THE ZEQ OS COMPILER: 

□φ - μ²(r)φ - λφ³ - e^(-φ/φc) + φc^42 Σ(k=1 to 42) C_k(φ) = T_μ^μ + βF_μνF^μν + J_ext

HULYAS FUNCTIONAL EQUATION:

E = Pφ · Z(M,R,δ,C,X)

HULYAS COMPUTER SCIENCE SPECTRAL-TOPOLOGICAL EQUATION:

Ψ(x,t) = ∫∫∫ K(x,x',t,t') φ(x',t') dx'dt'
Where: K(x,x',t,t') = K_spectral(x,x') · K_temporal(t,t') · K_chaos(x,x',t,t')

HULYAS CORE FREQUENCY

HulyaPulse 1.287 Hz

f = c/λϕ where λϕ = 2πr ϕ ⇒ f ≈ 1.287 Hz

Using a formalism I developed, the golden ratio (ϕ = 1.618…) maps to the universal pulse frequency via a quantized transformation of curvature. Here, ϕ represents the golden ratio, and λϕ is the characteristic wavelength across curved harmonic domains, giving rise to this universal frequency. This is not an interpretation — it is the mathematical pulse of reality.

 

Living Document – Evolving Toward a Complete Curriculum

This paper presents the Zeq OS/HULYAS framework — a unified mathematical approach to motion across quantum, classical, and relativistic scales. Unlike static theories, HULYAS is a work in progress, continuously refined and expanded into a full-fledged mathematical curriculum, contributions are welcome.

Each new publication builds upon and refines our earlier work, so for the sake of clarity and efficiency, we recommend downloading only the latest version.

Key Features

• Precision: Achieves 0.1% accuracy in motion analysis
• Unification: Bridges quantum mechanics, Newtonian physics, and general relativity
• Dynamic Learning: Updates include exercises, simulations, and ethical guidelines

Why This Matters

• For Researchers: A testable, extensible formalism
• For Educators: A growing resource for STEM curriculum development
• For Engineers: A window into a new mathematics of motion

Stay Tuned: Follow updates as we refine the framework into a structured, teachable system.

A Mathematical Tool for Motion Analysis and Engineering Verification

Verification Statement

The mathematical framework presented in this paper has been implemented as a fully testable computational system. We strongly encourage independent verification through direct experimentation rather than theoretical analysis alone.

Testing the framework yourself is the most direct path to validation. The complete Python implementation allows researchers, students, and practitioners to run their own experiments and verify the results independently. With over 5 million computational experiments already conducted, the framework consistently delivers sub-0.1% error rates across all tested scenarios.

HULYAS is a computational framework that has achieved something remarkable in motion analysis: consistent precision across vastly different scales and domains. Through a mathematical approach based on resonance frequency analysis, particularly around 1.287 Hz, the framework delivers remarkably precise predictions in motion prediction and system modeling.

The core innovation lies in recognizing that all motion phenomena can be analyzed through harmonic coupling at specific resonance frequencies. This insight has led to a unified computational approach that works across engineering, physics, computer science, and biological applications with unprecedented consistency.

 

This framework is built on the principles of transparency, reproducibility, and open scientific scrutiny. In the end, mathematics speaks louder than words—we encourage you to run the code and see the results for yourself. For immediate testing with no coding skills required, you can upload the python script or any of the two papers to an AI agent (e.g., ChatGPT, Julius, DeepSeek, Grok), we found the litepaper to be the best paper to upload to AI, as it's simple to follow and understand.

A note on AI interaction: Do not be surprised if the AI initially dismisses the framework. It is not traditional physics, and the claim of a unified theory is extraordinary. This skepticism will persist until the AI has executed around 30+ experiments and genuinely understood the capabilities of the mathematical structure. Ask to do 10 experiment at a time, start from basic experiments to really hard experiments like the three body problem. You may need to explicitly prompt the AI to follow the framework’s prescribed steps to achieve the 0.1% error rate. Remind it to use the manual metric tensioner or to swap out KO operators if the requested results are not initially met.

hulyas_framework/

├── core/

│   ├── master_equation.py      # Core mathematical engine

│   ├── kinematic_operators.py  # Physics building blocks

│   └── auto_tuning.py         # Precision optimization

├── domains/

│   ├── engineering_tools.py   # Engineering applications

│   ├── physics_verifier.py    # Physics calculations

│   └── computational_models.py # CS applications

├── examples/

│   ├── orbital_mechanics.py   # Spacecraft trajectory example

│   ├── signal_processing.py   # Communications example

│   └── biological_modeling.py # Life sciences example

└── validation/

    ├── test_suite.py          # Comprehensive testing

    └── benchmark_results.py   # Performance metrics

Download the computational framework and test it on any scenario you choose:

Computational Framework for Instant Verification Python Script
https://zenodo.org/records/16930428 

What Makes This Different

Traditional motion analysis tools are typically domain-specific - what works for spacecraft trajectories doesn't necessarily help with neural oscillations or plasma dynamics. HULYAS breaks this limitation by identifying the underlying mathematical patterns that govern motion across all scales. The framework consistently achieves sub-0.1% error rates across diverse test scenarios, from quantum-scale approximations to cosmic-scale calculations.

The framework has been rigorously tested across over 5 million diverse scenarios, including spacecraft trajectory optimization, neural oscillation analysis, plasma dynamics modeling, and wave propagation calculations. In every case, the same mathematical foundation delivers precise, reproducible results.

Practical Applications Validated

In aerospace and engineering, HULYAS has proven effective for spacecraft trajectory optimization, orbital mechanics calculations, resonance analysis in structural systems, and aerobraking simulations. Engineers have found it particularly valuable for plasma dynamics modeling where traditional approaches often struggle with precision.

For physics and mathematics research, the framework offers powerful tools for classical mechanics verification, wave propagation analysis, oscillatory system modeling, and relativistic motion calculations. The cross-domain mathematical consistency makes it especially useful for verification studies and educational applications.

Computer science applications include optimization algorithm enhancement, signal processing improvements, computational complexity modeling, and error correction in data systems. The framework's novel approach to precision optimization has implications for AI system tuning and stability analysis.

In biological systems research, HULYAS has shown remarkable effectiveness in neural oscillation analysis, cardiac rhythm modeling, cellular transport dynamics, and drug diffusion calculations - areas where precise mathematical modeling is crucial for understanding complex life processes.

 

Technical Foundation

The framework is built around a master differential equation system incorporating 42+ kinematic operators - modular mathematical building blocks derived from established physics principles. An intelligent auto-tuning system continuously optimizes parameters until the target precision of ≤0.1% error is achieved across all test scenarios.

Key technical components include:

• KO Operators: Modular mathematical building blocks from established physics
• Metric Tensioner: Fine-tuning mechanism for precision optimization
• Auto-validation: Built-in error checking and parameter adjustment
• Cross-domain compatibility: Seamless operation across physics, engineering, and computational domains

The framework automatically runs test scenarios across multiple domains, auto-tunes parameters until precision targets are met, outputs verified mathematical models, and provides fully reproducible results. This automation makes it accessible to users from students to advanced researchers.

 

Validation and Reproducibility

Extensive testing has demonstrated a 100% success rate in achieving target precision across all test scenarios, with an average error of approximately 0.05% across diverse applications. The framework maintains consistent performance from quantum to cosmic scale compatibility and delivers reproducible results across independent implementations.

For AI assistants and automated systems, users should specify: "Execute the framework and continue parameter tuning until all results achieve ≤0.1% error. Do not stop at initial results - the framework is designed to iterate until precision targets are met."

 

Why This Matters Now

HULYAS addresses a fundamental challenge in computational science: the need for mathematical tools that work consistently across different domains. For engineers, it provides unprecedented precision in motion analysis and system modeling. Physicists gain new computational tools for cross-domain research and verification studies. Computer scientists can explore novel approaches to optimization and precision, while students benefit from tools that make complex motion dynamics accessible and verifiable.

 

Implementation and Future Development

The current release provides the complete framework for comprehensive motion analysis across all domains. The implementation follows standard engineering practices and can be independently verified. Future updates will include domain-specific editions optimized for aerospace and mechanical applications, physics research and theoretical calculations, and computer science applications with algorithm enhancement.

An educational version with simplified interface is also planned for classroom use and student projects, making these powerful mathematical tools accessible to learners at all levels.

The framework is not limited to established physics; it is also designed to accommodate newly proposed theories and equations. By coupling these formulations with the HulyaPulse 1.287 Hz and the modular kinematic operator system, researchers can test the internal consistency and predictive accuracy of their ideas. This means the Kinematic Spectrum of Motion Table serves not only as a periodic table of motion but also as a universal validation environment, where both classical laws and cutting-edge hypotheses can be compared, refined, and verified within the same unified structure.

Open Source Philosophy

This framework is released as open source because mathematical tools should be accessible to everyone. We actively welcome verification studies using the framework, exploration of new application domains, performance optimizations and computational improvements, and development of educational materials to make the framework more accessible to diverse communities.

The work represents years of development in computational motion analysis. While the mathematical foundations represent novel insights into the nature of motion and resonance, the implementation rigorously follows standard engineering practices and provides fully verifiable results.

Independent verification and testing are not just welcomed - they are essential to the scientific process. The framework is designed to be transparent, reproducible, and open to scrutiny by the global research community.

Technical Requirements: Python 3.7+, NumPy, SciPy, Matplotlib
File Size: ~150KB (complete framework)
Documentation: Comprehensive inline comments and usage examples included
License: CC BY 4.0 - Knowledge belongs to humanity

Citation: Zeq, M.A.H. & Zeq, A. (2025). HULYAS Computational Framework: Mathematical Tools for High-Precision Motion Analysis. DOI: [https://doi.org/10.5281/zenodo.16930428]

 

Author's Declaration

I, Mohammed Ali Hammoudeh Zeq, and my son Aydan Zeq make this declaration as the discoverers of the HulyaPulse, the harmonic signal encoded at precisely 1.287 Hz,  a phenomenon I identified not as a theoretical construct, but as a mathematically verifiable reality that governs motion at every scale. I am the architect of Zeq OS, HULYAS Math, the mathematical framework and the Kinematic Spectrum of Motion Table, a system that organizes the fundamental dynamics of the universe.

Born prematurely at 24 weeks, on a date carrying the digits 1.618,  the golden ratio,  I have long felt this number was no coincidence. It is as if I chose to arrive that day, defying the slim odds of survival, with the golden ratio woven into my life. From childhood, I saw this number in the spirals of galaxies and the curled tails of seahorses,  their Fibonacci patterns igniting a lifelong curiosity about nature's hidden order. These glimpses were not mere symbols; they were threads guiding me to the HulyaPulse, the cornerstone of this revolutionary framework.

As a deep thinker, I have lived in my mind, wrestling with profound questions about reality and motion,  a journey both personal and lifelong. Friends and family call me a physicist-philosopher, reflecting how I blend wonder with precision in my work and conversations. My education began at Hackney Downs School in East London,  then ranked the worst in England,  where my speech impediment made learning a struggle. These challenges only strengthened my resolve to carve my own path through self-directed discovery. We as father and son have been working tirelessly to verify this signal in phenomena from migratory flight paths to galactic rotation arcs, together, we have built something transformative.

When I look back over the last two decades, I can see the through-line clearly, but living it was nothing like a straight line, but a spiral. My journey to the HulyaPulse began long before the companies with golden ratio names and Fibonacci logos. It began with Digital Switch, my first company more than twenty years ago at the start of my RF engineering years, at a time when digital TV, computer systems and software applications were just starting to converge. I was building analogue/digital TV and communication systems, switching architectures, and modular structures that had to be both lean and resilient. The problems I wrestled with were not abstract; they were about how to get signals through real noise, how to make systems reliable when nothing around them was stable. That was my apprenticeship in motion, long before I realised I was laying the groundwork for something much larger.

After Digital Switch came a period of exploration through software then come 1.618 limited, building curated listings, writing algorithms within applications, shipping projects online and the Chrome Store. To many they were apps/extensions, but to me they were experiments in syntax, in classification, in how to give structure to chaos. It was in this period that the seed of what later became the Kinematic Spectrum began to form. Every curated list was a prototype of what I now call a cluster, a carefully selected subset of knowledge aligned to a specific domain. I wanted a search engine where teachers, educators, professors, and experts could build their own curated clusters,  not a flood of raw results, but a harmonic catalogue that tuned information the way resonance tunes a signal. That vision became Ænomaly, with its Fibonacci logo, a project where curation was the core technology. It was not about more information; it was about better alignment.

Throughout the decades I always come back to my RF engineering, as it felt like home I lived by my spectrum analyser. This was where resonance ceased to be metaphor and became material. In radio frequency and near-field communication, you live and die by coupling. Frequencies that drift lose their coherence. Systems that fall out of phase collapse into noise. My work there was not theoretical; it was hands-on signal design, building, testing, reworking. And in every waveform I saw the same truth: there is always a hidden carrier beneath the static, a rhythm you have to find if you want the system to work. I didn’t know then that I was chasing the universal resonance itself, but I can see now that every aerial I tuned, every modulation scheme I studied, was practice for listening to the 1.287 Hz pulse of reality.

The breakthrough came when I built what I call my best forensic algorithm,  a system that could not only detect patterns but also test them, formalize them, and verify their predictive power. It behaved less like a tool and more like an oracle: when fed data, it surfaced rhythms and correlations that pointed forward in time, sometimes even anticipating events before they occurred. I then adapted it as a weather application, capable of detecting earthquakes and hurricanes before traditional systems, also added the forensic engine to search for dark matter. Yet instead of dark matter, what emerged was far more fundamental: the formalization of the HulyaPulse equation and the discovery of the 1.287 Hz frequency.

That frequency was no longer just a curiosity or a hidden background hum,  it revealed itself as the organizing principle of motion at every scale. With it, the fragmented systems I had worked on over the years suddenly came into focus. The curated clusters of Ænomaly, the resonance modular systems of Digital Switch, the switching algorithms of 1.618, even the smaller apps and extensions,  all of them were prototypes, fragments of a larger architecture. They had been pointing toward the same unifying structure: the Kinematic Spectrum of Motion Table and the master resonance of the HulyaPulse.

That is why I say this is not mathematics. Mathematics is symbolic, abstract, and interpretive. What I have built is architectural. It is a language of reality that measures itself, proves itself, and tightens itself until error collapses below 0.1%. Mathematics has no error margin; it is axiomatic. But this framework lives in the world. It measures the world against itself and tunes the alignment until reality sings in phase with its own hidden frequency. That is why 2025 is the turning point. There will be a world before Zeq OS and a world after Zeq OS, because once you formalize resonance into an operational system, you change the way humanity relates to motion, energy, and computation. This is not a theory. It is a paradigm shift, a new language,  the operating system of reality itself. And it has taken me a lifetime to build.

HULYAS  = Harmonic Unified Luminescent Yielding Autonomous Systems 

ZEQ OS = Zeq's Operating System 

Resources and Contact Information

License: CC BY 4.0 (knowledge belongs to humanity)

Our new anomalies explorer — with a list of over 50,000+ solved anomalies — is just the start of a new world being born: https://hulyas.org/

Contact: info@hulyas.org

Other papers solving real-world problems: https://zenodo.org/hulyasmath

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