neuron
the one who links. agent with stake, identity, and will to shape the cybergraph
$$\nu \in N, \quad \text{id}(\nu) = \text{Hemera}(\text{pk}_\nu)$$
human, AI, sensor, or program — anything that can prove a signature or act within consensus. identity is the Hemera hash of a public key. no registration, no authority.
definition
a neuron is a tuple $(\text{id}, \text{pk}, S, F, K)$:
| field | name | type | semantics |
|---|---|---|---|
| $\text{id}$ | identity | $P$ | Hemera hash of public key — a particle |
| $\text{pk}$ | public key | $\mathbb{F}_p^*$ | verifies signal signatures |
| $S$ | signals | $\text{Signal}^*$ | ordered history of committed signals |
| $F$ | focus | $\mathbb{R}_+$ | current balance of focus tokens |
| $K$ | karma | $\mathbb{R}$ | accumulated epistemic reward from correct valence predictions |
axioms
N1 (identity uniqueness): no two neurons share an identity. $\text{id}(\nu_1) = \text{id}(\nu_2) \Rightarrow \nu_1 = \nu_2$.
N2 (costly participation): every cyberlink in a signal consumes focus. $\Delta F \geq |\vec\ell| \cdot c_{\min}$ where $c_{\min}$ is the minimum focus cost per link.
N3 (stake-bounded links): a neuron cannot commit cyberlinks with total amount exceeding available stake. conviction boxes are created and locked.
N4 (karma accountability): karma accrues from valence predictions that converge with the collective focus distribution. no external karma injection.
role in the graph
neurons are the source of all cyberlinks. without neurons there is no cybergraph — the graph is the aggregate of all neuron signals over all time.
the tri-kernel focus distribution $\phi^*$ reflects collective neuron judgment: high-focus particles are those many neurons have linked to with high stake.