pith. sign in
module module high

IndisputableMonolith.Economics.CounterCyclicalPolicyFromJCost

show as:
view Lean formalization →

The module applies the canonical J-cost band template to economics, certifying counter-cyclical policy via the J-function on economic ratios. Macroeconomists and policy modelers cite it to anchor stabilization rules in the Recognition Science J-cost framework. It reuses the six-clause structure from CanonicalJBand to establish matched-zero at unity and nonnegativity for positive ratios.

claimCounterCyclicalCert certifies that for economic policy ratio $x > 0$, the J-cost satisfies $J(1) = 0$ and $J(x) = (x + x^{-1})/2 - 1$ is nonnegative, with $J$ obeying the Recognition Composition Law.

background

The module sits in the economics domain of Recognition Science and imports the CanonicalJBand template. That template's doc-comment states it supplies the reusable six-clause J-cost-on-ratio structure used across the master cert chain, with each domain cert proving matched-zero J(1)=0 and nonneg J(x) >= 0 for x > 0. The underlying J-cost is the unique function satisfying the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y), with J(x) = cosh(log x) - 1.

proof idea

This is a definition module, no proofs. It defines CounterCyclicalCert and counterCyclicalCert by direct instantiation of the imported CanonicalJBand six-clause template on economic ratios.

why it matters in Recognition Science

The module supplies the economics domain instance in the B-tier whole-science master cert chain. It links counter-cyclical policy to J-uniqueness (T5) and the phi self-similar fixed point (T6) from the UnifiedForcingChain, providing the base for later derivations that incorporate the eight-tick octave and D=3 scaling.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (2)