IndisputableMonolith.InternationalRelations.PowerTransitionFromJCost
This module applies the J-cost function to the ratio of rising-power to incumbent-power capabilities and introduces associated war-window bounds plus a PowerTransitionCert. International-relations modelers seeking RS-derived conflict thresholds would cite these objects. The module consists entirely of definitions and elementary lemmas establishing non-negativity, ordering, and boundary behavior.
claimLet $r = C_r / C_i > 0$ be the relative-capability ratio. Define capabilityCost$(r) := J(r)$ where $J$ obeys the Recognition Composition Law. The conflict-prone interval is bounded by warWindowLow $> 0$ and warWindowHigh $> 1$ with warWindowLow $<$ warWindowHigh. A PowerTransitionCert is an inhabited certificate witnessing the transition condition at the phi-boundary.
background
The module imports Constants, which fixes the RS-native time quantum $ au_0 = 1$ tick, and Cost, which supplies the J-cost function and its algebraic properties. It works in the setting where J-cost is evaluated on capability ratios exactly as the Recognition Composition Law prescribes for any positive real argument. The sibling definitions capabilityCost, warWindowLow, warWindowHigh, and PowerTransitionCert are introduced directly from this imported machinery.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module extends the Recognition Science chain (T5 J-uniqueness and the Recognition Composition Law) into the domain of power transitions by packaging J-cost into a PowerTransitionCert. No downstream theorems are listed, so the constructions remain available for later use in global-dynamics models that require an RS-native measure of capability imbalance.
scope and limits
- Does not incorporate alliance networks or third-party actors.
- Does not derive numerical values for real-world capability ratios.
- Does not address nuclear or economic deterrence mechanisms.
- Does not prove existence of equilibria beyond the supplied certificate.