From topology to first principles.
Spectral Causal Theory: derivations, verification, analysis, and publications.
The Golomb Universe
Formal verification of the logical incompatibility between the P=NP hypothesis and the Witten-Helffer-Sjöstrand tunneling theorems in spectral geometry. Implemented in Lean 4.
GNN-guided structure-aware mesh simplification framework
Lean 4 library characterizing the algebraic structure of metastability and consolidation in stochastic systems
Cosmochrony: A Structurally Constrained Pre-Geometric Framework for Emergent Physics
NLS/Gross–Pitaevskii on a lumpy torus — a spectral-geometry solver and a gallery of numerical experiments (solitons, collapse control, analog gravity/cosmology, quantum chaos, topological & Floquet transport), packaged as an MCP toolkit for numerically-grounded agent inference.
research
RIME: spectral, transport, accessibility, and observable-pipeline geometry for finite represented systems, with Rubik as a reproducible laboratory.
Computer-assisted proof of local minimality of the regular pentagon for the scale-invariant first Dirichlet eigenvalue
Newtonian Potentials from Projective Entropy in Three Dimensions
Causal Propagation and Gravitational Waves from Projective Spectral Dynamics
Operator-geometric framework for metabolic identifiability and metabolite panel design under partial observability using Human-GEM, proteomics-informed reaction weighting, and spectral geometry.
Counterexamples to Ashbaugh's higher-index PPW conjecture for Dirichlet Laplacian eigenvalue ratios, with exact-arithmetic verification.
BFS Shell Stratification and the Emergence of Four-Dimensional Lorentzian Geometry
Effective spacetime geometry from admissible non-injective projection, with thermodynamic scope explicitly delimited.
Дискретно-итерационный нелинейный симулятор фазовых объёмов матричных спектров.
Emergent Metricity from Spectral Connectivity
dual-view: a unified framework for 2-adic number systems, p-adic Newton dynamics, spectral geometry, gauge theory, and classical butterfly compilation
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