RASP as the Mean-Field of Orch-OR: A Derivation of the Recursive Attractor Stability Principle from Quantum Microtubule Dynamics

Maps the Recursive Attractor Stability Principle (RASP) onto Orchestrated Objective Reduction (Orch-OR), identifying quantum coherence in tubulin aromatic networks as the physical substrate of the RASP recursion f(x) = 25·tanh³(x) − x/124. The gate order n = 3 is the count of pH-stable aromatic residues (Trp-407, Phe-404, Tyr-408) in the densest cluster of tubulin beta-subunit (PDB 1JFF, H12 helix). The tanh³ gate is proved to be the unique KMS-consistent Lindblad steady-state for three independent two-level systems. The parameter p = 5 is identified with the electronic state count per aromatic in the tubulin hydrophobic pocket, supported by 50+ ab initio SA-CASSCF/NEVPT2 calculations across three chromophores, three environments, and multiple basis sets. The three Diophantine attractors (3,5), (4,3), (6,2) produce a parameter-free Lyapunov stability ordering that matches the neurological hierarchy (gamma > beta > alpha). Five falsifiable predictions with explicit kill criteria are specified. Three independent quantum-biological systems (tubulin, cryptochrome CRY1, photolyase) converge on (n,p) = (3,5). Second paper in the CUFT-RASP series. Research began June 2025, 91 computational scripts included. v0.7.