Causal Influence

Causal Influence is the effect a prior pulse state has on later states, carried through the connectivity of the substrate, by which recursive operations can refer to and build on what came before. It is written 𝒞(①₁), the historical state impact mediated by substrate connectivity. The book also uses the term at the other end of its range, the boundary where it stops: at a Null Well's event horizon, direct causal influence and pulse propagation cease. There the Causal Influence Boundary is ∂A/∂r|r=r_s = A₀/λ, with A the pulse amplitude [∅], r the radial coordinate [𝕃], r_s the Schwarzschild radius [𝕃], A₀ the amplitude in the active substrate far outside the horizon [∅] and λ the decay length [𝕃], giving [𝕃⁻¹]; and the Information Flow Rate reaches zero, I⥂(r_s) = 0. Beyond that surface local pulse states collapse exponentially toward the central Null Well. It connects to The Prime Recursion, Memory Encoding, Referential Continuity, Null Well and Null Well Boundary.