eContinuedFraction
plain-language theorem explainer
eContinuedFraction supplies the finite prefix of Euler's number continued fraction as the list of natural numbers [2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8]. Researchers examining Recognition Science connections between e and phi via continued fractions would cite this explicit sequence. The entry is supplied directly as a constant list with no computation or proof steps.
Claim. The continued fraction expansion of $e$ begins with the terms $2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8$.
background
The Mathematics.Euler module targets derivation of Euler's number from phi-related summations. Euler's number is defined as the base of the natural logarithm, the limit of $(1 + 1/n)^n$, and the series sum $1/n!$. Recognition Science links e to J-cost exponential decay, phi-continued fractions, and 8-tick probability normalization.
proof idea
This is a direct constant definition that assigns the finite list of natural numbers.
why it matters
The definition supports the module target of deriving e from phi-summation by exhibiting the explicit continued fraction pattern. It connects to Recognition Science landmarks including phi-forcing and the eight-tick octave. The entry leaves open the question of proving the infinite extension equals e or establishing a rigorous link to the J-function.
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