• 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