µ is a functor homomorphism: µ ∘ fmap = fmap ∘ µ.

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

• µ is an applicative homomorphism: µ(pure a) = pure a and µ(imf <*> imx) = µ imf <*> µ imx.claim0.869
  Result for Image applicative specification.
• The specification for (⊸) is a category homomorphism (µ id = id, µ(g ∘ f) = µg ∘ µf), leading to a correct-by-construction implementation.claim0.848
  Demonstration on linear transformations.
• µ is a monoid homomorphism: µ distributes over monoid operations.claim0.844
  Derived result for Image monoid specification.
• Functor Homomorphismconcept0.747
• Steering vectors from µ(0→2) slightly outperform µ(1→2) for instruction discovery across datasets and modelsfinding0.745
  Shows that contrasting No Reflection with Triggered Reflection provides a stronger signal than Intrinsic vs Triggered.
• X → X[′′] on G and M are closure operators satisfying extensivity, idempotence, and monotonicity.finding0.715
• MCA provides functional intermediates: goal-directedness of modules pushes partial solutions toward attractors, resolving the problem of useful intermediates in evolution.claim0.702
  Subclaim.
• If a semantic function is a homomorphism with respect to a type class, the implemented instance automatically satisfies the class laws.hypothesis0.701
  Core hypothesis enabling 'laws for free': denotational semantics guarantee algebraic law satisfaction.