fib_10
plain-language theorem explainer
This definition sets the tenth Fibonacci number to 55. Modelers of inflation in the Recognition Science framework cite it to anchor the e-folding count in the J-cost potential. The definition consists of a direct constant assignment.
Claim. Let $F_{10}$ denote the tenth Fibonacci number. Then $F_{10} = 55$.
background
The JCostInflaton module proves that the Recognition Composition Law forces the inflaton potential to take the form $G(t) = cosh(t) - 1$ in log coordinates. This yields the slow-roll parameters from the curvature at the minimum, with $G(0) = 0$ and $G''(0) = 1$. The definition supplies the integer 55 for conjectures on the number of e-foldings.
proof idea
The definition is a direct assignment of the value 55 to the tenth Fibonacci number.
why it matters
The definition anchors the hypothesis that the number of inflationary e-foldings equals 55, the tenth Fibonacci number. This identification connects to the phi-ladder, where 55 factors as 5 times 11 and 11 approximates phi to the fifth power. It contributes to closing the master certificate for inflation derived from the J-cost in the Recognition framework.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.