the observer that cyberank models — not a pure random walk, and not a free agent outside the graph. a rational neuron is the limiting attention process whose stationary distribution is φ*: where a coherent observer spends time if they follow stake, structure, and scale the way the tri-kernel encodes
how smart
rank is often glossed as “random walking neuron.” that names only one third of the engine
| operator | name | what the observer does | smarter than pure random walk? |
|---|---|---|---|
| D | diffusion | follows cyberlinks with probability mass — the Markov / exploration term | baseline: token-weighted walk on the cybergraph |
| S | springs | restores structural equilibrium among neighbors — consistency, not pure chance | yes: pulls rank toward coherent neighborhoods, dampens structural nonsense |
| H | heat kernel | smooths importance across scales — multi-hop context | yes: sees beyond one hop; local noise averages out, long-range signal survives |
the full update is one fixed point:
φ* = norm[ λ_d · D(φ) + λ_s · S(φ) + λ_h · H_τ(φ) ]
a pure random walker is D alone (classical pagerank family). a rational neuron is D + S + H at once: they explore edges, but also respect spring equilibrium and multi-scale heat. stake on cyberlinks weights the walk — attention follows will, not uniform chance. the collective focus theorem guarantees a unique positive φ* under the usual connectivity conditions; the tru computes it deterministically
so how smart? smart enough to be three physics at once — diffusion for curiosity, springs for coherence, heat for patience — and dumb enough to stay local: each update only needs an O(log(1/ε))-hop neighborhood (bounded locality). smarter than PageRank (structure + scale), dumber than an unbounded planner (no global search, no off-graph oracle). the intelligence is the fixed point of rational attention, not a simulation of free will
what it is not
not a separate person outside the protocol. every real neuron that links already stakes and shapes the same graph; cyberank is the observation probability that graph implies for a rational reader of it. not a vote. not a clock. not “six blocks later”
uses
cyberank per particle is the rational-neuron observation mass. it feeds foculus finality (φ*_i > τ), karma for linkers, syntropy of the whole, and ranking in cyb
see tri-kernel, focus, rank, collective focus theorem
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