cyberank
focus read at a single particle: $\mathrm{cyberank}(p) = \phi^*(p)$. it is the fixed-point probability that the tri-kernel random process observes particle $p$ — the canonical, network-wide ordering of knowledge.
$$\mathrm{cyberank}(p) = \phi^*(p), \qquad \sum_{p} \mathrm{cyberank}(p) = 1$$
the tri-kernel computes cyberank by iterating three coupled operators — diffusion, springs, and heat — to equilibrium. each particle receives a score proportional to the focus flowing through its cyberlinks. the more neurons stake on paths leading to a particle, the higher its cyberank.
inheritance from PageRank
cyberank keeps PageRank's recursive idea: a particle is important when important particles point to it. the cyber variant replaces web hyperlinks with cyberlinks and replaces the uniform random surfer with a focus-weighted walker whose teleport distribution reflects real economic stake and karma. it extends PageRank with two further operators — springs for structural constraint and heat for multi-scale context — so cyberank is the leading term of the full tri-kernel fixed point, not diffusion alone (see tri-kernel §2.4 for the five equivalent readings of $\phi^*$).
what reads it
cyberank is the canonical ordering of knowledge: search results, feed rankings, glia routing, and karma calculations all derive from it. because the computation is deterministic and verifiable, every node arrives at the same ranking — a shared, checkable measure of collective attention, the consensus reality of what matters.
when a neuron creates a new cyberlink, it redistributes focus across the graph and tru recomputes cyberank at the next epoch. the per-signal change is an impulse $\Delta\phi^*$.
see focus for the full distribution · karma for the per-neuron projection · tri-kernel for the operators · focusing for the epoch computation.
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