- emergent attention distribution over the cybergraph
- stationary vector of the token-weighted random walk
- assigned by computation. converged from collective dynamics
- computed by the tri-kernel: three local operators that are the only ones surviving the locality constraint
- diffusion: where probability flows. exploration
- springs: what satisfies structural constraints. hierarchy
- heat kernel: what the graph looks like at scale τ. adaptation
- composite update:
φ^(t+1) = norm[λ_d · D(φ^t) + λ_s · S(φ^t) + λ_h · H_τ(φ^t)]
- fixed point minimizes the free-energy functional
- focus regenerates proportionally to stake
- focus is consumed by cyberlinks and computation
- conservation: the sum of all focus equals 1. emphasizing one thing defocuses others
- threshold: minimum focus required for a cyberlink to affect ranking
- bounded locality: updates cost O(degree) not O(graph size)
- derived metrics
- see tri-kernel for the completeness proof
- see focus flow whitepaper for full protocol specification
- see focusflow blueprint for implementation architecture
- discover all concepts