warWindowHigh
The definition sets the upper endpoint of the J-cost war window to the golden ratio φ. International-relations modelers applying recognition cost to power transitions cite it to bound the interval of elevated conflict probability around capability parity. It is introduced by direct assignment to the phi constant imported from the constants module.
claimThe upper endpoint of the J-cost war window is defined to be the golden ratio $φ$.
background
The module develops a recognition-science version of power transition theory. The J-cost function J(r) = (r + r^{-1})/2 - 1 vanishes at capability ratio r = 1 (recognition equilibrium) and the war window is the band (1/φ, φ) in which J(r) ≤ J(φ) ≈ 0.118. Conflict probability is predicted to peak inside this band because the cost surface reaches a local minimum at parity.
proof idea
The declaration is a direct definition that assigns the constant phi to warWindowHigh. No lemmas or tactics are applied.
why it matters in Recognition Science
This supplies the upper limit required by PowerTransitionCert to certify the three war-window properties (low positive, high greater than one, and ordered). It implements the quantitative RS prediction that the J-cost band is (φ^{-1}, φ), connecting the international-relations application to the core T6 result that phi is the self-similar fixed point. The module falsifier is any Correlates of War analysis showing great-power conflict onset does not cluster inside (0.618, 1.618).
scope and limits
- Does not derive the value of phi from the forcing chain.
- Does not prove any inequality satisfied by the bound.
- Does not specify or derive the matching lower bound.
- Does not contain empirical data or statistical tests.
formal statement (Lean)
56def warWindowHigh : ℝ := phi
proof body
Definition body.
57