IndisputableMonolith.Econ.MarketEquilibriumFromJCost
The module Econ.MarketEquilibriumFromJCost applies the J-cost function to normalized price ratios p/p* to define deviation measures and equilibrium certificates. It supplies the basic objects needed to link price stability to the Recognition Science cost structure. Economists working inside the RS framework would cite these definitions when deriving equilibrium conditions from J-uniqueness. The module consists entirely of definitions and elementary properties with no complex proofs.
claimThe deviation of a price ratio is given by $d = J(p/p^*)$ where $J(x) = (x + x^{-1})/2 - 1$. Equilibrium holds when $d = 0$, with associated non-negativity, threshold, and certification structures.
background
The Recognition Science framework supplies the J-cost via the functional equation $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$ together with the explicit form $J(x) = (x + x^{-1})/2 - 1$. The Constants module fixes the base time unit as the tick with τ₀ = 1. This module extends the Cost definitions to economic prices by treating the ratio p/p* as the argument of J, thereby producing a deviation function and related equilibrium objects.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the core objects (priceDeviation, MarketEquilibriumCert and their properties) that allow market equilibrium to be expressed directly in terms of J-cost. It thereby connects price dynamics to the J-uniqueness and self-similar fixed-point steps of the forcing chain. No downstream theorems are recorded yet, so the module functions as a foundational layer for subsequent economic derivations within Recognition Science.
scope and limits
- Does not derive time-dependent price trajectories.
- Does not incorporate stochastic shocks or external noise.
- Does not treat multi-commodity or general-equilibrium settings.
- Does not calibrate against empirical market data.