This paper extends the theory of structural openness from single-agent decisionmaking to the collective dynamics of multi-agent systems, establishing a spectralgeometric criterion for distributed consensus and a selection mechanism for the collective optimal recursion depth. Traditional research on distributed systems treatsconsensus as a product of communication protocols or game-theoretic equilibria,lacking consideration of the topological structure of rule spaces. Under the axiomsof information conservation and computability, we construct the fibred product ofthe joint rule algebra of multiple agents and its faithful representation, and establish a functorial framework for the joint spectral triple. The strict positivity ofthe joint Dirac operator’s spectral gap is equivalent to the stability of distributedconsensus. Collective cognitive economics shows that the Pareto-optimal allocation for homogeneous agents is locked at a symmetric recursion depth. The rightto exit is formalised in the commutative geometric setting as a K-theoretic indexof a boundary Dirac operator, whose integer value corresponds to the number ofeffective exit channels. When the joint spectral gap closes, the system undergoes abifurcation phase transition, and the unified rule space splits into rule islands. Thethree-layer homotopy structure of cognitive architecture, under the constraints ofinformation conservation and computability, locks the meta-constraint recursiondepth to 3. This paper strictly distinguishes theorems, constructive propositions,and conditional conjectures; all core concepts are defined within the underlyingself-consistent logic.