- first operator of the tri-kernel
- transition matrix
P = AD⁻¹ governs probability flow across the cybergraph
π^(t+1) = α P^T π^(t) + (1-α)u
- α = teleport parameter
- u = prior (stake-weighted)
- answers: “where does probability flow?”
- the exploration component of the cyberank. the full cyberank is the fixed point of all three tri-kernel operators blended together
- row-stochastic, preserves probability mass
- powers remain local. converges to unique stationary distribution under ergodicity
- locality: geometric decay via teleport parameter α
- the exploration force — a gas wandering, sampling connections
- universal pattern
- physics: gas wandering, sampling
- biology: synaptic chatter, neural noise
- ecology: species dispersal, seed rain
- economics: trade, migration, meme flow
- together with springs and heat kernel forms the tri-kernel
- see tri-kernel for completeness proof
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