- 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
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