Asymptotic behavior of trajectories (ω/α-limit sets)
Invariant set repelling nearby trajectories
Navigate skill graphs via deterministic random walks. Fuses derivational chains, algebraic structure, color determinism, and bidirectional flow for skill recombination.
Matrix of partial derivatives for linearization
Quillen model categories: (C,W,F) structures.
Janus and reversible languages: run programs backwards, time-symmetric computation.
Sets preserved by the flow
Triadic skill (coordination)
APL/BQN rank polymorphism: implicit iteration via array rank, no explicit loops.
Existence and uniqueness of solutions to ODEs with initial conditions
Operads: multi-input operations.
Presheaves: contravariant Set-valued functors.
Invariance principle for asymptotic stability
Obstruction Learning Skill
Dynamic structures via polynomial functor arrangements from Topos Institute
No eigenvalues on imaginary axis (robust dynamics)
Closed trajectory in phase space
Planar Isotopy Screen Mapping
Harmonic centrality gadgets with GF(3) conservation for topological transport of ablative case structure via abelian extensions of ℚ
Fixed phase relationship in oscillators
Systems varying with external parameters
Hesse-inspired interdisciplinary synthesis game with Badiou triangle
Right adjoints preserve limits. RAPL.
Symmetric bifurcation with symmetry breaking
Free Monad Generation Skill (PLUS +1)
Ordered Locales (Heunen-van der Schaaf 2024): Point-free topology with direction. Frame + compatible preorder with open cone conditions.
Colored operads for multi-input composition, associahedra, A-infinity structure, and homotopy algebra
Time averages equal space averages
Rezk types (complete Segal spaces). Local univalence: categorical isomorphisms ≃ type-theoretic identities.
Segal spaces: ∞-categories via simplicial spaces.