H_N_e_55
plain-language theorem explainer
H_N_e_55 encodes the hypothesis that 55 e-foldings driven by the J-cost potential produces spectral index 1 - 2/55. Cosmologists comparing Recognition Science inflation to CMB data would cite this numerical anchor. The definition directly instantiates the upstream spectral_index formula at N = 55.
Claim. The proposition asserts that the scalar spectral index after 55 e-foldings satisfies $n_s(55) = 1 - 2/55$, where $n_s(N) := 1 - 2/N$ is the standard slow-roll expression.
background
The module shows that the J-cost in logarithmic coordinates is the potential G(t) = cosh(t) - 1, whose curvature supplies the slow-roll parameters. The upstream definition states that the spectral index is given by spectral_index(N) := 1 - 2/N, the standard slow-roll result. This definition specializes that formula to the concrete value N = 55.
proof idea
One-line definition that substitutes 55 into the spectral_index expression and equates the result to the explicit rational 1 - 2/55.
why it matters
It supplies the numerical prediction for the N_e = 55 hypothesis inside the J-cost inflaton model, which the downstream theorem H_N_e_55_holds then discharges by reflexivity. The value 0.9636 lies inside the Planck 2018 band and connects the Recognition Composition Law to alpha-attractor cosmology via the phi-ladder and Fibonacci structure.
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