A Mathematician Lurking in the TechUnderWorld

A Mathematician Lurking in the TechUnderWorld

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November 2025

Hyperreal Programming in Action
How dual numbers, jets, and hyperreals fix broken AI
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Jose Crespo PhD
A New Mathematical Operating System for AI
From Flat Gradients to Jet Geometry: Differentiating the Space Instead of the Network
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Jose Crespo PhD
Holonomy, From Einstein to Deep Learning
Born in Einstein’s geometry of gravity, holonomy now gives us the language to measure curvature in neural networks and explain why flat Euclidean AI…
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Jose Crespo PhD
Why AI Isn’t Flat: The Hidden Curvature
Holonomy, Jacobians, and Curvature Emerging from Flat Space
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Jose Crespo PhD
THE TWO ALGEBRAS FOR AI - AND WHY EVERYONE USES THE WRONG ONE
Build Worlds, Not Limits: The Jet Algebra Playbook.
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Jose Crespo PhD
The Winding Numbers: Topology’s Answer to the Birthday Paradox in Current AI
How to Avoid Hallucinations by Preventing Collisions
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Jose Crespo PhD
Mathematical Core Equations: AI JEPA’s Failures vs. AI-Toroidal Truth
Technical Notes for My Article: LLMs Are Already Dead — The New AI Killed Them.
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Jose Crespo PhD
The Mathematical Myopia of New AI Architectures — and How to Correct Their Glasses
Technical Notes for my Article: LLMs Are Already Dead — The New AI Killed Them.
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Jose Crespo PhD
JEPA-AI:Core Technologies & Programming Stack
Technical Notes for My Article: LLMs Are Already Dead — The New AI Killed Them.
 • 
Jose Crespo PhD

February 2024

© 2025 Jose Crespo
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