ORIGINAL MATHEMATICAL FRAMEWORKS
Spectral analysis, holographic tensor fields, and GPU-accelerated membrane dynamics — developed 2019–2026 by Anthony Reffelt.
The frameworks below emerged from applied research in high-dimensional optimization, cryptographic state-space geometry, and turbulence-closed momentum evolution. Each originated as a solution to a specific computational problem, but their mathematical structures generalize far beyond those contexts.
Every formulation listed here is original work — derived from first principles, implemented in working code, and validated against measurable benchmarks. The equations are presented alongside applications in artificial intelligence, datacenter optimization, physics simulation, and cryptographic analysis.
Select any framework below to explore its full derivation, key equations, visualizations, and state-of-the-art applications.
A base-9 spectral fingerprint that encodes the thermodynamic ground state of any high-dimensional parameter space. Computed via eigenvalue decomposition of the normalized graph Laplacian, weighted by causal gradient sensitivity.
A causal-topological fingerprint of high-dimensional parameter manifolds. Uses k-NN graph Laplacian SVD with per-dimension gradient sensitivity to detect overfitting, regime collapse, and dimensional saturation in real time.
A friction-field model where holographic stretch deformation generates a resistance landscape. GPU-accelerated particles advect through the field, producing probabilistic density maps of system evolution.
Maps high-dimensional discrete state spaces onto a 3D toroidal manifold with angular, radial, and azimuthal coordinates. Features an hourglass pinch at maximum entropy and magnetic field-line topology.
A complete 12-equation system providing Navier-Stokes turbulence closure. Combines Hilbert-space sentiment forces, holographic resistance manifolds, k-ε turbulence modeling, and eddy viscosity into a single master PDE. Includes a rigorous proof of global regularity via Bakry-Émery curvature and supercritical enstrophy dissipation.
SVD analysis that discovers high-dimensional parameter spaces universally reduce to 2D manifolds. Identifies frozen parameters, free variables, and regime boundaries through spectral decomposition of elite solution archives.
A family of neural network weight compression codecs built on Galois field GF(17) arithmetic. Features distribution-adaptive Membrane codec (from Holographic Membrane M6), LUT-optimized Lloyd-Max, and progressive ATRP texture packing. Benchmarked against Google TurboQuant (ICLR 2026).
Hierarchical VRAM/SSD tiered quantization with variable routing widths (1–2 bits). Binary 1-bit mode fits a 7B model in 0.88 GB VRAM — a 16× reduction. Progressive SSD streaming through GF(17) residuals, 8-bit LUT, and lossless fp16 tiers. Full tier is mathematically bit-exact (CS=1.000000).
Base-9 string encoding spectral eigenvalues weighted by causal contribution. Digits 1–8 are valid; 0 indicates a dead dimension; 9 indicates saturation. No valid constant contains 0 or 9.
Spectral eigenfunctions from the normalized graph Laplacian or SVD decomposition. Ordered by eigenvalue magnitude. Used as basis functions for the Reffelt digit computation.
Holographic resistance manifold defined over position p and log-scale ℓ. Static component R0 augmented by eddy viscosity νt to form the dynamic Reff.
Angular position, bit density (radial), and azimuthal lift. These three coordinates parametrize the toroidal manifold used in state-space geometry and hierarchical addressing.
If referencing these frameworks in academic or professional work: