IndisputableMonolith.Mathematics.GameTheoryDepthFromRS
The module derives core game theory objects from Recognition Science by defining solution concepts for strategic interactions and certifying their structural depth. It introduces SolutionConcept to capture stable strategy profiles and GameTheoryDepthCert to assign a phi-ladder depth value consistent with the forcing chain. The module consists entirely of definitions that translate RS-native units into game-theoretic language without external axioms.
claimA solution concept on a game $G$ is a subset of strategy profiles satisfying the Recognition Composition Law. The depth certificate assigns to each such concept a value on the phi-ladder given by the J-cost of the interaction.
background
The module sits in the Mathematics domain and imports only Mathlib. It works inside the Recognition Science setting whose landmarks are the unified forcing chain T0-T8, the J-uniqueness formula, and the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y). The sibling definitions SolutionConcept and GameTheoryDepthCert supply the concrete objects: the former enumerates stable outcomes while the latter places them on the phi-ladder using the same rung arithmetic that yields D = 3 and the eight-tick octave.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the mathematical substrate that later Recognition Science results use to embed game theory inside the same functional equation that forces phi and the spatial dimensions. It therefore sits upstream of any application that certifies strategic depth in RS-native units.
scope and limits
- Does not prove existence of solution concepts for arbitrary games.
- Does not derive payoff functions from the J-cost functional equation.
- Does not connect depth certificates to physical constants such as alpha or G.