Identifies tangled geodesics in proof dependency graphs via Möbius inversion.
Propagator-based parallel structure for exploiting knowledge differentials
Matrix of partial derivatives for linearization
Lawvere theories: categorical universal algebra.
Derangement-CRDT Skill
Local Compositionality Gadget
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
GF(3)-balanced random walk through Lean proof states. Use when generating formal proof chains with parallel triad verification. Invokes 3 agents (Generator +1, Coordinator 0, Validator -1) to traverse proof space via prime geodesics.
Hedges' 4-kind lattice for bidirectional programming - covariant/contravariant/invariant/bivariant types with GF(3) correspondence
Rezk types (complete Segal spaces). Local univalence: categorical isomorphisms ≃ type-theoretic identities.
Segal spaces: ∞-categories via simplicial spaces.
Fixed points where vector field vanishes
Surjective map intertwining two dynamical systems
Natural transformations: morphisms of functors.
Elements of ∞-Category Theory (Riehl-Verity) for foundational ∞-categorical
Naturality Factor Skill
Monoidal categories: ⊗, I, α, λ, ρ.
Stability classification via Jacobian eigenvalues
GAP (Groups, Algorithms, Programming) system integration for computational discrete algebra. Generates group-theoretic structures, character tables, and algebraic objects for the Plurigrid ecosystem.
Homotopical algebra via weak equivalences, fibrations, cofibrations, Quillen adjunctions, and homotopy (co)limits
Dialectica Skill (ERGODIC 0)
IMO Gold Medal level Lean4 theorem proving via Harmonic API
low-discrepancy-sequences skill