apply

the third verb: move each cyberlink's box into authenticated state.

apply(signal) → new root
  for each cyberlink: move the box (coin, amount) into state
    particle energy, axon weights, focus debit, box ownership
  extend A(x) / N(x) ; recompute the root

cybergraph routes the state mutation to bbg (insert, the mutator set). bbg holds the polynomial state and enforces the structural double-spend invariant ($N(n)=0$); cybergraph hands it the validated, ordered signal and takes back the new root.

mechanism, not decision: apply is deterministic — the same signal yields the same state move. it runs only after validate and order pass.

see order for the prior verb · expose for reads · box for what moves · bbg for the state.