Principia Fractalis: Fractal Resonance Ontology. A 1000+ page work exploring how mathematics, consciousness, and physical reality connect through a unified structure. Formally triple-verified in Lean 4, Coq, and L4L

A modular harmonic sieve for detecting nontrivial Riemann zeta zeros through phase-locked resonance, leveraging the interplay of base-3 and base-π spirals to isolate precise zero locations without statistical approximation. Ideal for mathematical research, numerical experiments, and algorithm development.

First explicit curvature correction formula for fractional Laplacians on curved manifolds. Complete proof via heat kernel expansion, validated computationally on S². Applications in anomalous diffusion, thermal field theory, and curved spacetime physics.

Consciousness axioms → complete physics: 15 papers mathematically deriving everything. Includes new calculus, C*-algebras, Millennium solutions. Pure mathematics despite names. All Zenodo archived. The mathematics is presented for examination.

Decoding cognitive states from fMRI brain networks using Spectral Graph Signal Processing (GSP) and High-Resolution Graph Fourier Transforms. Analysis of 88 subjects from the HCP S1200 dataset.

"$\hat{H} = xp + i\lambda(xe^{-x^2} + \epsilon \cos x)$ | Proving the spectral reality of Riemann Zeros through Half-Integer Topology and Maslov Index correction."

Exploring the relationship between conformal rigidity, spectral properties, and genus of graphs.

An experimental O(N) language model based on mathematical physics (Birman-Schwinger theory). A PyTorch implementation aiming to surpass Mamba in long-context stability and memory efficiency (O(N log N)) through Prime-Bump initialization and scattering theory routing.