focus
the collective attention distribution over the cybergraph. focus is the tri-kernel stationary distribution $\phi^*$ over all particles — content-particles and axon-particles alike — emerging from the aggregate of every neuron's signals. it is what the network, as one system, attends to.
$$\phi^* = \operatorname{norm}\big[\mathcal{R}(\phi^*)\big], \qquad \sum_i \phi^*(i) = 1, \qquad \phi^*(i) > 0\ \forall i$$
focus is computed, never assigned. no one votes on it. it is the unique fixed point the tri-kernel converges to — diffusion explores, springs enforce structure, heat adapts across scale — and by the collective focus theorem that fixed point exists and is unique.
how focus emerges
| layer | what | per-what |
|---|---|---|
| balance | tokens held | neuron |
| will | balance locked × duration | neuron |
| attention | will allocated to targets | neuron × particle |
| focus | collective attention | particle |
| cyberank | focus read at one particle | particle |
neurons lock balance to create will. will auto-distributes across the cyberlinks a neuron creates, producing attention at target particles. the tri-kernel aggregates all attention — weighted by karma and ICBS price into effective adjacency (see focusing) — into a single probability distribution $\phi^*$. that distribution is focus.
conservation
$$\sum_i \phi^*(i) = 1\quad\text{always, by normalization}$$
focus sums to one because it is a probability measure. concentrating attention on one particle defocuses every other. this is the normalization step of the tri-kernel, the same identity that makes syntropy well-defined.
the slices of focus
focus is the whole distribution. its named projections:
- cyberank — focus per particle, $\phi^*(p)$. the canonical ordering of knowledge.
- karma — focus per neuron. how much of the collective's attention a neuron's honest history commands.
- attention — one neuron's contribution to focus, before aggregation.
what focus drives
every cyberlink shifts $\phi^*$; the proven shift is an impulse $\Delta\phi^*$. learning and ranking are the same operation. focus feeds ct0 model compilation (the embedding is built from $\phi^*$-weighted adjacency), foculus finality, mir world geometry, and glia routing. it is the single output everything downstream reads.
see syntropy for the order focus carries · cyberank for focus per particle · will for how attention is funded · tri-kernel and collective focus theorem for the convergence · focusing for the per-epoch computation.
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