- second operator of the tri-kernel
- graph Laplacian
L = D - A, screening μ > 0, reference x₀
(L + μI)x* = μx₀- answers: “what satisfies structural constraints?”
- encodes hierarchy — keeps connected nodes at consistent levels
- deviation from structural equilibrium is detectable via residual
- the screened Green’s function
(L+μI)⁻¹ has exponential decay, ensuring locality
- positive semi-definite, null space = constant vectors
- locality: exponential decay via screening parameter μ
- the structure force — an elastic lattice that holds things in place
- universal pattern
- physics: elastic lattice, tensegrity
- biology: skeleton, connective tissue
- ecology: food webs, symbioses
- economics: institutions, contracts, norms
- together with diffusion and heat kernel forms the tri-kernel that computes cyberank
- see tri-kernel for completeness proof
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