Amundson Mathematics

Rigorous analytic number theory and approximation theory for the Amundson sequence

$$ G(n) = \frac{n^{n+1}}{(n+1)^n} = n \left( \frac{n}{n+1} \right)^n $$

and the associated constant

$$ A_G = \sum_{n=1}^\infty \frac{G(n)}{n!} = \sum_{n=1}^\infty \frac{1}{(n-1)!} \left( \frac{n}{n+1} \right)^n \approx 1.244331783986725\ldots $$

Core Results

• Hausdorff moment representation of the sequence $q_n = (n/(n+1))^n$
• Explicit compound-Poisson / Lévy representation with jump density $$ k(x) = \int_0^1 t e^{-tx}, dt = \frac{1-(1+x)e^{-x}}{x^2} $$
• Power-tilt closure and exact logarithmic cumulants of the tilted measure
• Fibre Gram matrices and the Family-D orbit identity
• Theorem C0: Endpoint Christoffel growth $$ K_d^\nu(0,0) \asymp d^2 (\log d)^2 $$

Repository Structure

• section6/ — Frozen §6 (Moving-Power Hausdorff Measure)
• theorem-c0/ — Theorem C0 + corollaries on endpoint Christoffel asymptotics
• open-problems/ — Problems A–F and the research queue
• notes/ — Technical notes, prettier formulations, and priority discipline

Status

§6 is frozen.
Theorem C0 is proved modulo the standard doubling-weight Christoffel theorem (priority of the concrete application under audit).

Priority Discipline

• Classical inputs (Hausdorff theorem, compound-Poisson transforms, doubling Christoffel estimates) are clearly tagged.
• No novelty claims are made for statements whose prior status has not been independently audited.
• Rationality/irrationality of $A_G$ remains open.

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BlackRoad OS / Amundson Mathematical Framework — rigorous core only.