third operator of the tri-kernel
∂H/∂τ = -LH, H₀ = I, so H_τ = exp(-τL)
temperature τ controls scale
answers: "what does the graph look like at scale τ?"
high τ explores (annealing), low τ commits (crystallization)
provides adaptive context — the thermostat of collective attention
positivity-preserving, semigroup: H_{τ₁} H_{τ₂} = H_{τ₁+τ₂}
Chebyshev polynomial approximation gives h-local computation with bounded error
locality: Gaussian tail decay, h = O(log(1/ε)) hops
the adaptation force — metabolism, phase changes, the ability to shift
universal pattern
- physics: thermostat, phase changes
- biology: metabolism, immune plasticity
- ecology: seasons, succession, disturbance
- economics: booms, busts, revolutions
together with diffusion and springs forms the tri-kernel that computes cyberank
see tri-kernel for completeness proof
discover all concepts