IndisputableMonolith.Economics.BusinessCycleFromPhiLadder
This module constructs business cycle durations from the phi-ladder using the RS time quantum. Modelers of self-similar economic oscillations cite the cycleDuration family and its certification. The module supplies definitions plus elementary lemmas on positivity and successive ratios; no deep tactics appear.
claimDefine cycleDuration : ℕ → ℝ by cycleDuration(n) = τ₀ ⋅ φ^{rung(n)} where τ₀ = 1 tick and rung follows the phi-ladder; BusinessCycleCert certifies that successive durations satisfy the ratio φ and remain positive.
background
The module imports the RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. It places cycle durations on the phi-ladder whose rungs are spaced by the self-similar fixed point φ (T6 of the forcing chain). Sibling declarations introduce cycleDuration, its positivity, the successor ratio, and the BusinessCycleCert wrapper that records these properties in one structure.
proof idea
This is a definition module. cycleDuration is introduced by direct reference to the phi-ladder; cycleDuration_pos and cycleDuration_succ_ratio are one-line wrappers that apply the ordering and multiplicative properties of φ already established in Constants.
why it matters in Recognition Science
The module supplies the first explicit bridge from the phi-ladder (T5–T6) to economic time scales. It feeds downstream economic applications that require certified cycle lengths; no parent theorems are listed yet in the used_by graph.
scope and limits
- Does not fit numerical economic time series.
- Does not derive cycle amplitudes or damping.
- Does not address non-phi economic drivers.
- Does not claim empirical validation beyond the ladder construction.