sentence

the linear utterance of neural: an ordered chain of links, a → b → c → …, cast in one signal. the signal boundary defines the utterance — a sentence is atomic, all of its links land together or none do. order is grammar.

structure

a sentence is a sequence of links where each target is the next source: (ℓ₁, …, ℓₙ) with to(ℓᵢ) = from(ℓᵢ₊₁). it is a linkchain — the same object. a sentence a neuron states and a chain tru discovers differ only in origin; both are linear paths of meaning.

types by topology

shape gives kind:

properties

• length — shorter carries stronger relation
• width — parallel chains between the same endpoints make it robust
• weight — the product of link weights along the chain; the focus it carries
• composition — C₁ ∘ C₂ joins when end(C₁) = start(C₂); a cycle closes when to(ℓₙ) = from(ℓ₁)

explicit and implicit

an explicit sentence is what a neuron states. the implicit chains tru finds by diffusion are conclusions the network did not state outright. both are sentences; tru ranks them by focus. a non-linear arrangement of the same links is a motif.

the linear flow

as a flow on the graph a sentence is the gradient — the linear, consistent component of meaning. a coherent argument has near-zero curl; a self-contradicting chain (a → b → c → a) is pure curl. a motif is the non-linear (curl / harmonic) component. see frontier.