AWAKEN Research Program

Research Papers

Rigorous analysis of foundational questions in mathematics, logic, and artificial intelligence.

The Hidden Intersections

A Locale-Theoretic Resolution of the Banach-Tarski Paradox

How point-free topology reveals that the Banach-Tarski pieces were never truly disjoint — and the paradox dissolves. Works in full ZFC without rejecting the Axiom of Choice.

~30 pages | Full ZFC | 2025

Logic

The Most Misunderstood Theorem

Gödel's Incompleteness Theorems: Scope Inversion

How Gödel's incompleteness theorems became a cultural weapon — and why almost everything you've heard about them is wrong. 70–80% of published mathematics is untouched.

18,000+ words | ~80 references | 2025

AI & Linguistics

The Semantic Compiler

Formal Semantic Structure in Natural Language

What if language has formal semantic structure — and we can compute it? An exploration treating natural language as multiplexed semantic signals requiring formal compilation.

~400 semantic atoms | 8 ontological categories | Active research

AWAKEN Research Program|Created through human-AI collaboration