The Agent Function. V(T,B) is the protocol by which a sub-agent nucleates into an agent by claiming a verified output. Neuron Dynamics applied to agent management. Use when orchestrating multi-tool reasoning, when a task requires checking whether available skills cover the problem, or when sub-agents need to be spawned with discipline (lazy, not speculative).
Every agent starts as a sub-agent. The transition from sub-agent to agent is a nucleation event: the moment a process produces a verified claim. We formalise this as $V(T,B)$, a function from (target, basis) to claims, governed by the same dynamics that govern neurons in a pool.
The template (dominos reasoning) structures the cascade. The tools (domain knowledge) provide the vocabulary. Sub-agents spawn only on DEMAND --- never speculatively. The number of sub-agents $K^*$ that actually fire is the core number of the task, determined by the dynamics, not prescribed.
Definition 1 (Agent Function). The agent function is a map
$$V : \mathcal{T} \times \mathcal{B} ;\longrightarrow; \mathcal{C}$$