IndisputableMonolith.InternationalRelations.PowerTransitionFromJCost
This module applies the J-cost functional to the ratio of rising-power to incumbent-power capabilities, defining capabilityCost together with war-window bounds and a PowerTransitionCert. Researchers extending Recognition Science to formal models of geopolitical stability or conflict would cite these objects. The module consists of a sequence of definitions and elementary lemmas establishing non-negativity, ordering, and inhabitance of the certificate.
claimLet $r = C_r / C_i$ be the relative-capability ratio. Define capabilityCost$(r) := J(r)$ where $J(x) = (x + x^{-1})/2 - 1$. Introduce warWindowLow and warWindowHigh as the lower and upper thresholds on $r$ at which the transition regime begins and ends, together with the predicate PowerTransitionCert asserting that a transition is certified when capabilityCost$(r)$ lies inside the interval bounded by these windows.
background
Recognition Science derives all structure from the J-function obeying the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$. The imported Cost module supplies the J-cost construction on ratios, while Constants fixes the base time quantum at one tick. This module specializes those primitives to the ratio of capabilities in power-transition settings, introducing the named objects capabilityCost, warWindowLow, warWindowHigh, and the certificate PowerTransitionCert.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the bridge from the core J-cost and phi-ladder constructions to international-relations modeling, providing the concrete objects that downstream theorems on conflict thresholds or stability would invoke. It directly instantiates the J-uniqueness step (T5) inside the geopolitical domain and supplies the inhabited certificate cert_inhabited required for any later existence claim.
scope and limits
- Does not model time evolution of the capability ratio.
- Does not incorporate alliance structures or third-party effects.
- Does not produce numerical forecasts for named state pairs.
- Does not assert that transitions actually occur, only that the certificate is inhabited when the cost condition holds.