Macro-Economics and Sociological Fractals

Recognition Science derives the structure of physical reality from the cost functional J(x) = 1/2(x + x^-1) - 1. This functional is literally an economic object: it prices deviations from equilibrium, it is minimized by trade, and its conservation law constrains feasible reallocations. We show that the mathematical framework already proved in the Lean 4 formalization, dissipation channels, channeled feasibility, complexity measures, channel refinement, halting bounds, is not merely analogous to economics. It IS economics, read at the scale of human institutions rather than particles.

We establish an explicit dictionary between the RS physics formalization and economic theory, then derive three classes of testable predictions:

1. phi-Scaling of Organizations (Section 5): Self-similarity of hierarchical institutions forces the golden ratio phi approx 1.618 as the optimal scaling factor between organizational levels. Optimal team size approx 5, department approx 8, division approx 13—the Fibonacci sequence.

2. J-Bounded Market Clearing (Section 6): The time for a market to clear (reach equilibrium) is bounded by Tmax = D0/delta, where D0 is the initial market disequilibrium and delta is the minimum per-transaction friction.

3. Conservation-Constrained Wealth Distributions (Section 7): Log-charge conservation constrains feasible wealth redistributions, predicting that the geometric mean of wealth is invariant under balanced trade, and that Pareto-like tails emerge from channeled equilibrium.

No new mathematics is introduced. Every theorem cited is already machine-verified in Lean 4. The contribution of this paper is the interpretation: reading the existing formalization as an economic theory and extracting its empirical content.