Faruk Alpay

Innovative researcher and founder, creator of Alpay Algebra, and the mind behind Lightcap and various impactful projects.

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Faruk Alpay

About Me

I am an innovative researcher and founder, known for creating Alpay Algebra and leading various impactful projects including Lightcap. My work spans multiple disciplines, combining theoretical research with practical applications.

Currently pursuing a Bachelor's degree in Computer Engineering at Bahcesehir University, I focus on developing novel computational approaches and systems that address complex problems.

Fields of Interest

  • Theoretical Mathematics & Alpay Algebra
  • Computational Systems & Architecture
  • Artificial Intelligence & Machine Learning
  • Software Development & Web Technologies

Key Projects

existencemap.com

A groundbreaking platform mapping interconnected existence patterns across diverse domains, providing unique insights into systemic relationships.

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weavemap.io

An innovative tool for visualizing and analyzing complex relationship webs, enabling deeper understanding of interconnected systems.

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signalcore.io

Advanced signal processing system leveraging cutting-edge algorithms to extract meaningful patterns from complex data streams.

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hodgeflow.com

Specialized platform exploring mathematical concepts through computational models, with particular focus on advanced algebraic structures.

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senolyticmicrodosing.com

Research platform investigating innovative approaches to biological systems through carefully calibrated methodologies.

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selfos.dev

A next-generation personal operating system designed to enhance productivity and cognitive processes through intelligent interfaces.

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FABE13

Advanced technical project demonstrating expertise in complex system design and implementation, with applications in computational modeling.

Alpay Algebra

Original mathematical framework created by Faruk Alpay, offering novel approaches to algebraic structures and their applications in computational systems.

Lightcap

Innovative AI-driven platform designed to illuminate complex cognitive patterns and enhance decision-making processes through advanced algorithms.

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Publications

Alpay Theorem I: Transformational Fixation

Zenodo • June 9, 2025
DOI: 10.5281/ZENODO.15624805View Publication

Semantic Definition of ISO 639:2023 and its Role in Language Identity Modeling

June 6, 2025
DOI: 10.5281/ZENODO.15611304View Publication

Φ^∞ III: Foundations Without Foundation and the Categorical Resolution of the Meta-Validation Paradox

May 30, 2025
DOI: 10.5281/ZENODO.15553258View Publication

Φ^∞ II: Recursive Geometry of Classical Reality

May 29, 2025
DOI: 10.5281/ZENODO.15546773View Publication

An Axiomatic Exposition of an Ideology: Erdoğan's 'A Fairer World' Read Through Alpay Algebra

May 19, 2025
DOI: 10.22541/au.174768283.31612664/v1View Publication

Extended Formal Analysis of Macro-Existence Convergence in Recursive Consciousness Fields

May 15, 2025
DOI: 10.22541/au.174733693.32336472/v1View Publication

Institutional Protection in Academia: Documented Misconduct and Systemic Failures (2015-2025)

May 15, 2025
DOI: 10.22541/au.174733532.25541600/v1View Publication

Symphonic ϕ Identity Engine: A Signal-Based Deterministic Identity System

May 15, 2025
DOI: 10.22541/au.174733722.27305976/v1View Publication

Symphonic phi Identity Engine: A Signal-Based Deterministic Identity System

May 13, 2025
DOI: 10.5281/ZENODO.15398814View Publication

Institutional Protection in Academia: Documented Misconduct and Systemic Failures (2015–2025)

May 12, 2025
DOI: 10.20944/preprints202505.0806.v1View Publication

Global Smoothness and Existence for the Navier-Stokes Equations in Clay-ξ ↔ Format

May 7, 2025
DOI: 10.22541/au.174664105.54119607/v1View Publication

SRB Measures and the Ledrappier-Young Dimension Formula

May 7, 2025
DOI: 10.22541/au.174664030.00126829/v1View Publication

Symbolic Conditional Entropy in Layered Dynamical Systems

May 7, 2025
DOI: 10.5281/ZENODO.15354901View Publication

β-Optimization in the Information Bottleneck Framework: A Theoretical Analysis

May 7, 2025
DOI: 10.22541/au.174664105.57850297/v1View Publication

Emergent Quantum Dynamics from Frequency-Domain Cosmology: A Perturbative Field Theory Framework

May 6, 2025
DOI: 10.5281/ZENODO.15353272View Publication

φ(Ξ∞) = Ψ(Ω): Φ^∞

May 6, 2025
DOI: 10.5281/ZENODO.15346998View Publication

φ^∞(χ₀) = Ξ∞

May 6, 2025
DOI: 10.5281/ZENODO.15346796View Publication

Arf Teorilerinin Alpay Cebiri ile Bütünleşik Matematiksel Çerçevesi

May 4, 2025
DOI: 10.5281/ZENODO.15337175View Publication

The Psi-Shadow of Cahit Arf: A Cognitive Domain of Silence

May 4, 2025
DOI: 10.5281/ZENODO.15335025View Publication

Benchmarking Symbolic Collapse and Recovery in Claude using Ξ∞Algebra: A Recursive Identity Framework

Zenodo • May 1, 2025
DOI: 10.5281/ZENODO.15313460View Publication

Alpay Algebra: A Symbolic Framework for Recursive Identity Compression and λ-Layer Dynamics

April 30, 2025
DOI: 10.5281/ZENODO.15307054View Publication

Formalizing Habit Evolution: A Recursive Symbolic Model Using Alpay Algebra

Zenodo • April 30, 2025
DOI: 10.5281/ZENODO.15307258View Publication

Frequency Cosmology in Alpay Algebra: A Recursive Signal-Based Framework for Reality

April 30, 2025
DOI: 10.5281/ZENODO.15309894View Publication

Managing Entropy Through Recursive Depth: A Symbolic Optimization Model Using Alpay Algebra

Zenodo • April 30, 2025
DOI: 10.5281/ZENODO.15307298View Publication

Supplement A: Convergence of the Partial Fold Operator in Alpay Algebra

Zenodo • April 30, 2025
DOI: 10.5281/ZENODO.15307175View Publication

The Grok Collapse: Ξ∞ as a Recursive Boundary Condition in Symbolic AI

Zenodo • April 30, 2025
DOI: 10.5281/ZENODO.15311802View Publication

Alpay Algebra: Foundations for Recursive Compression and Intelligent Evolution

April 29, 2025
DOI: 10.5281/ZENODO.15306574View Publication

Cognitive Architectures and Human–AI Coevolution: Pathways, Dynamics, and Alignment

Zenodo • April 29, 2025
DOI: 10.5281/ZENODO.15300065View Publication

Human–AI Recursive Coevolution Dynamics: A Formal Expansion

April 29, 2025
DOI: 10.5281/ZENODO.15300291View Publication

Kendiliğinden Gelişen İstem Ekosistemi: Kavramsal Temeller, Yapısal Bileşenler ve İnsan–Yapay Zekâ Bilişsel Ortak Evrimindeki Yeri

Zenodo • April 29, 2025
DOI: 10.5281/ZENODO.15300164View Publication

The Recursive Self-Optimizing Learning Engine (RSOLE) and its Meta-Recursive Evolution Framework

April 29, 2025
DOI: 10.5281/ZENODO.15304959View Publication

Formal Mathematical Expansion of Frequency Cosmology

April 28, 2025
DOI: 10.5281/ZENODO.15293268View Publication

ExistenceMath: A Mathematical Framework for Existence

Faruk Alpay • April 27, 2025
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Frequency Cosmology: Foundational Framework

April 27, 2025
DOI: 10.5281/ZENODO.15292770View Publication

Clearing "Zombie" Cells: The Senolytic Promise of Dasatinib + Quercetin

Unpublished • April, 2025
DOI: 10.13140/RG.2.2.34682.81608View Publication

A Topological and Operator Algebraic Framework for Asynchronous Lattice Dynamical Systems

2025
DOI: 10.48550/ARXIV.2505.09898View Publication

Alpay Algebra II: Identity as Fixed-Point Emergence in Categorical Data

2025
DOI: 10.48550/ARXIV.2505.17480View Publication

Alpay Algebra III: Observer-Coupled Collapse and the Temporal Drift of Identity

2025
DOI: 10.48550/ARXIV.2505.19790View Publication

Alpay Algebra: A Universal Structural Foundation

2025
DOI: 10.48550/ARXIV.2505.15344View Publication

Encoding and Decoding Infinite Data Within < 1 Byte via Alpay Algebra

Unpublished • 2025
DOI: 10.13140/RG.2.2.32670.04167View Publication

Fixed-Point Traps and Identity Emergence in Educational Feedback Systems

2025
DOI: 10.48550/ARXIV.2505.21038View Publication

Ordinal-Algebraic Evasion: A New Cyberattack and Defense in the Alpay Algebra Framework

Unpublished • 2025
DOI: 10.13140/RG.2.2.10518.87367View Publication

Stable and Convexified Information Bottleneck Optimization via Symbolic Continuation and Entropy-Regularized Trajectories

2025
DOI: 10.48550/ARXIV.2505.09239View Publication

TCC-based Access Collapse and Symbolic Isolation Strategies

Unpublished • 2025
DOI: 10.13140/RG.2.2.22901.90085View Publication

XiSort: Deterministic Sorting via IEEE-754 Total Ordering and Entropy Minimization

2025
DOI: 10.48550/ARXIV.2505.11927View Publication

Φ^∞ V: Temporal Collapse and the Axiomatic Limits of Structural Knowledge

Unpublished • 2025
DOI: 10.13140/RG.2.2.19145.04967View Publication

ϕ^∞ I: Stabilization of Quantum Structure

Unpublished • 2025
DOI: 10.13140/RG.2.2.33735.00168View Publication

Last updated: June 11, 2025

Publications data is automatically synchronized from ORCID. View the complete publication list on my ORCID profile.

Get In Touch

Feel free to reach out for collaborations, research inquiries, or to discuss potential projects.

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Email

alpay@lightcap.ai