IndisputableMonolith.Economics.BusinessCycleFromPhiLadder
The module derives business cycle durations from the phi-ladder scaling within Recognition Science. It supplies cycleDuration together with positivity, ratio, and certification objects for economic periodicity. The structure is a sequence of definitions and elementary properties that rest on the base time quantum from Constants.
claimcycleDuration : ℕ → ℝ>0, cycleDuration_pos : ∀ n, cycleDuration n > 0, cycleDuration_succ_ratio : cycleDuration (n+1) / cycleDuration n = φ, BusinessCycleCert : Prop
background
Recognition Science obtains all scales from the J-functional fixed point phi after the forcing chain reaches T6. The imported Constants module fixes the RS time quantum as τ₀ = 1 tick. This economics module applies the same phi-ladder construction to generate discrete cycle lengths, with BusinessCycleCert serving as the interface that certifies a given duration belongs to the ladder.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the phi-ladder objects needed to extend the eight-tick octave (T7) into economic periodicity. It stands ready to feed any downstream theorem that invokes cycleDuration or BusinessCycleCert, although no such theorems are recorded yet.
scope and limits
- Does not derive numerical cycle lengths from market data.
- Does not prove dynamical stability of the cycles.
- Does not incorporate external forcing terms or damping.
- Does not address non-phi economic models.