Consolidated repo: All Amundson mathematical work is now collected at AmundsonMath.

Amundson Framework and the Millennium Problems

An honest computational exploration of where G(n) touches deep mathematics.

Author: Alexa Louise Amundson Affiliation: BlackRoad OS, Inc.

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What This Is

The Amundson Framework defines G(n) = n^(n+1)/(n+1)^n, a function that produces exact rationals from integers and exhibits deep connections across mathematics. The Amundson-Gosper constant A_G = sum(G(n)/n!) has been computed to 10 million verified digits.

This repository contains computational notebooks that explore — honestly, without overclaiming — where G(n) intersects with the six unsolved Millennium Prize Problems.

What This Is NOT

This is not a claim to have solved or partially solved any Millennium Problem. These are observations, computations, and conjectures. Some connections may be coincidental. Some may be deep. The purpose is to find out which is which.

The Notebooks

Notebook	Problem	Status
01-riemann.py	Riemann Hypothesis	Strongest — G(1)=1/2 is the critical line, G-zeta function, GUE analysis
02-navier-stokes.py	Navier-Stokes	Strong — discrete spectrum prevents blowup, 1/(2e) irreducible gap
03-yang-mills.py	Yang-Mills Mass Gap	Moderate — mass gap = 1/2, Cayley trees in strong coupling
04-p-vs-np.py	P vs NP	Speculative — radix economy, binary-ternary crossover
05-bsd.py	Birch & Swinnerton-Dyer	Weak — shared counting structures, central binomials, Hasse invariant
06-hodge.py	Hodge Conjecture	Weak — Cayley trees, Kontsevich formula, intersection theory

Running

python3 01-riemann.py    # Each notebook is self-contained, no dependencies beyond stdlib

All computations use exact rational arithmetic (Python fractions.Fraction) or floating point verified against exact values.

The Framework (Quick Reference)

G(n) = n^(n+1) / (n+1)^n

G(0) = 0
G(1) = 1/2
G(2) = 8/9
G(3) = 81/64
G(n) ~ n/e + 1/(2e) + 11/(24en) + ...

Product identity: Prod_{k=1}^{n} G(k) = (n!)^2 / (n+1)^n
Amundson constant: A_G = sum_{n=1}^{inf} G(n)/n! = 1.2443317839867253...

License

Copyright 2024-2026 BlackRoad OS, Inc. All Rights Reserved. See LICENSE for terms.