Measure preserved by the flow
Fourier-Laplacian eigenmodes for frequency domain analysis of graph and signal structures
StructuredDecompositions.jl sheaves on tree decompositions for FPT algorithms with bidirectional navigation
Koopman operator theory for infinite-dimensional linear lifting of nonlinear dynamics. Generates dynamics from observables.
SICMUtils/Emmy - Clojure library for symbolic mathematics, automatic differentiation, and classical mechanics. Bridges SICM concepts to executable computation via SRFI-compatible abstractions.
Intent taxonomy and morphisms across 15 amp threads
Reparameterization of time in flows
Naturality Factor Skill
Robustness of qualitative dynamics under perturbation
Triangle Metrics Skill
Universal properties: unique factorization.
Make all 69 cognitive moments happen simultaneously via parallel triadic fanout. Transforms sequential Given-When-Then into derivational ⊗ composition.
Coalgebraic observation of derivation streams with final coalgebra bisimulation for infinite trace verification.
Scalar function decreasing along trajectories
Ward Identity Checker
worldmat-tidar
Topos Generation Skill (PLUS +1)
Yang-Baxter equation for quantum integrable systems. Fusion procedure, R-matrices, cuboson weights, and partition function invariance under vertex crossings.
Manifold of points diverging from equilibrium
Möbius inversion on posets and lattices: alternating sums, chromatic polynomials, incidence algebras, and centrality predicates.
Convergence to common trajectory in coupled systems
low-discrepancy-sequences skill
Synthetic adjunctions in directed type theory for ∞-categorical universal constructions.
Bifurcation exchanging stability between equilibria
Local approximation of nonlinear dynamics
Automated resolution-based proof search via stellar resolution and bidirectional unification
Manifold of points converging to equilibrium
Stability via Lyapunov's direct method
Path traced by solution through phase space
Spectre monotile principles applied to Worldmat thread evolution with GF(3) conservation