relation

how a link carries a type — is-a, causes, part-of — without labelling the edge. the settled model of neural: a relation is a link on the axon. the base edge stays untyped; its type is a second-order link from the pair's axon to a relation-word.

the model

cat is-a animal lands as two edges:

cat → animal                 the bare relationship
H(cat, animal) → is_a         the type — a link on the axon of the pair

the cybergraph already reifies every pair: all links on (from, to) bundle into an axon, and axon = H(from‖to) is a particle that materializes on link (bbg axiom A6). so typing a relation needs no new mechanism — you stake a link from that axon to the relation-word.

why this and not the alternatives

three ways to type a link; only this one holds:

• edge label (Link{from,to,rel}) — would change the wire and the running cell, and declares a relation schema. rejected: it breaks types emerge, no schema, and relations are not particles so φ* cannot rank them.
• route-through-word (cat → is_a → animal) — makes no real cat–animal edge and turns every relation into a super-node (one is_a particle collecting millions of links), wrecking focus and topology. rejected.
• axon typing (this) — the base edge is real, the type is a meta-link, and it satisfies every constraint at once (below).

what it buys

• the wire is untouched — Link { from, to, token, amount, valence } stays; a relation is just another link. the running cell needs no change.
• relations are first-class particles — a relation-word is ranked by φ*, can be linked, staked, and disputed like any word.
• many types per pair — a pair may carry → is_a and → causes at once; the tension among them is the polysemy / curvature signal (see frontier).
• typed edges stay emergent — the type is which word you route through, not a declared column; honours neural's types are not declared, they emerge.
• two granularities free — type the axon for the pair-relationship; type a specific link-particle for one assertion. the cybergraph closure gives both.

how it is authored

a neuron never hand-writes the two links. it speaks a sentence (cat is-a animal); the active dialect expands it into [base link + axon-type link]. this is exactly a dialect's job — a smart contract over links: it builds the right ones. so:

meaning is authored at the sentence altitude, lands as a typed axon (link on the pair), and is read back by the dialect that owns the relation-word.

bootloader relation-words

the genesis dialect ships a small seed set, themselves particles ranked by focus:

• the epistemic poles — TRUE, FALSE (see dialect)
• the emergent relations — is-a, causes, part-of, contradicts, follows, see-also
• the ~15 universal image schemas as primitive relations — PATH, CONTAINER, LINK, BALANCE, SOURCE-PATH-GOAL (see frontier)

new relation-words are not decreed; a word used in the relation slot across enough sentences accrues focus and enters the dialect.

reading a typed relation

axon_id(from, to) is deterministic and public (bbg::state::axon_id), and axons are exposed to inf as a relation. so "all X is-a Y" is an inf query: the axons whose to is is_a, joined back to the base pair each types.

see wire for the signal it rides, dialect for the expander, word for the relation-word, frontier for tension/curvature.