gap45
plain-language theorem explainer
The constant gap forty-five is introduced as the natural number forty-five representing the body-plan ceiling in the Recognition Science inflation model. Cosmologists comparing RS predictions to CMB data would cite this value when computing the spectral index as one minus two over gap forty-five. The definition consists of a direct assignment without further computation or proof obligations.
Claim. Define the body-plan ceiling parameter by $g_{45} = 45$.
background
In the module on Inflation Spectral Index from J-Cost, the RS framework predicts the scalar spectral index via $n_s = 1 - 2/g$ where $g$ is a rung parameter on the phi-ladder. The module states that the RS prediction via gap-45 gives $n_s = 1 - 2/45$ approximately 0.956, lying in (0.955, 0.957) and compared to Planck 2018 observations of $n_s = 0.965$ with uncertainty 0.004. The J-cost function enters the underlying composition law, and the gap parameter enters the slow-roll approximation for the number of e-folds $N_e = g(3) +$ corrections with the ceiling fixed at forty-five.
proof idea
The definition is a direct constant assignment of the natural number forty-five.
why it matters
This definition supplies the specific numerical value for the gap parameter in the RS-Starobinsky inflation formula, allowing the derivation of $n_s = 1 - 2/g_{45}$. It connects to the eight-tick octave structure by fixing the effective number of e-folds near forty-five and enables the spectral index certificate to be checked against observational bounds, closing the loop from J-uniqueness to cosmological observables.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.