kondratieff_in_classical_band
plain-language theorem explainer
The declaration shows that the Kondratieff long-wave period of 45 years lies inside the classical empirical band of 44 to 60 years. Macroeconomists modeling technology-paradigm cycles from the gap-45 lattice would cite this containment when assembling certified period records. The proof is a one-line term that unfolds the constant definition and applies numerical bounds.
Claim. $44 ≤ T_K ≤ 60$, where $T_K = 45$ is the bare gap-45 lattice period applied to technology-replacement cycles.
background
The module derives business-cycle periods from the Recognition Science 8-tick cadence and the consciousnessGap 3 = 45 σ-budget on the inter-firm credit graph. The Kondratieff long wave is defined as the bare gap-45 lattice period T_K = 45 applied to technology-replacement on the wider economy, while the Juglar cycle is 8 · φ. The upstream definition supplies the constant 45, which is then checked against the empirical band [44,60].
proof idea
The term proof unfolds the definition of kondratieff_period to the constant 45 and applies norm_num twice to confirm the lower and upper bounds.
why it matters
This bound is assembled into the BusinessCyclePeriodCert record, which certifies both Juglar and Kondratieff periods together with their Schumpeter ratio. It closes the classical-band containment step in the derivation of the 45-year long wave from the gap-45 lattice and the eight-tick octave.
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