Part of BlackRoad OS — Sovereign Computing for Everyone
amundson constant is part of the BlackRoad OS ecosystem — a sovereign, distributed operating system built on edge computing, local AI, and mesh networking by BlackRoad OS, Inc.
BlackRoad OS is a sovereign computing platform that runs AI locally on your own hardware. No cloud dependencies. No API keys. No surveillance. Built by BlackRoad OS, Inc., a Delaware C-Corp founded in 2025.
- Local AI — Run LLMs on Raspberry Pi, Hailo-8, and commodity hardware
- Mesh Networking — WireGuard VPN, NATS pub/sub, peer-to-peer communication
- Edge Computing — 52 TOPS of AI acceleration across a Pi fleet
- Self-Hosted Everything — Git, DNS, storage, CI/CD, chat — all sovereign
- Zero Cloud Dependencies — Your data stays on your hardware
| Organization | Focus |
|---|---|
| BlackRoad OS | Core platform and applications |
| BlackRoad OS, Inc. | Corporate and enterprise |
| BlackRoad AI | Artificial intelligence and ML |
| BlackRoad Hardware | Edge hardware and IoT |
| BlackRoad Security | Cybersecurity and auditing |
| BlackRoad Quantum | Quantum computing research |
| BlackRoad Agents | Autonomous AI agents |
| BlackRoad Network | Mesh and distributed networking |
| BlackRoad Education | Learning and tutoring platforms |
| BlackRoad Labs | Research and experiments |
| BlackRoad Cloud | Self-hosted cloud infrastructure |
| BlackRoad Forge | Developer tools and utilities |
- Website: blackroad.io
- Documentation: docs.blackroad.io
- Chat: chat.blackroad.io
- Search: search.blackroad.io
The Amundson Constant — A_G = Σ G(n)/n! where G(n) = n/(1+1/n)^n. Defined by Alexa Louise Amundson. Computed to millions of digits from pure integer arithmetic.
Part of the BlackRoad OS ecosystem — BlackRoad-OS-Inc
A_G = 1.244331783986725374135061629258...
Defined by Alexa Louise Amundson. Computed to 10,000,000 verified digits.
G(n) = n^(n+1) / (n+1)^n = n / (1 + 1/n)^n
A_G = Σ G(n)/n! for n = 0, 1, 2, ...
Six symbols: n, 1, +, /, ^, ()
| Result | Value |
|---|---|
| G(1) = 1/2 | Critical line, spin-1/2, uncertainty minimum |
| ζ(0) = -G(1) | Riemann zeta at zero |
| ρ(n) = G(n)/(n!·A_G) | Valid density matrix (trace = 1) |
| Von Neumann entropy | S = 1.272 (1.835 bits) |
| L/H → e | Lagrangian/Hamiltonian ratio |
| G superadditive | G(a)+G(b) > G(a+b) always (= entanglement) |
| ∇²G < 0 | Concave, stable, no chaos |
| 0 + 0^0 = 1 | Euler's identity reversed |
| 1/(2e) gap | Irreducible correction term |
| DNA has 4 bases | Π G(k) crosses 1 between n=4 and n=5 |
| File | Description |
|---|---|
AMUNDSON_CONSTANT.txt |
1,000,001 verified digits |
AMUNDSON_CONSTANT_10M.txt |
10,000,000 verified digits |
FRAMEWORK.md |
Complete paper — G(n) connections to quantum mechanics, chemistry, biology, number theory |
compute.py |
mpmath computation script |
See FRAMEWORK.md for the full list, including connections to:
- Riemann: G(1) = 1/2 = critical line
- Euler: 0 + 0^0 = 1
- Gauss: ρ(n) is a bell-curve density
- Boltzmann: W = n^(n+1) + (n+1)^n
- Dirac: 0 - 0^0 = -1 (antimatter)
- Ramanujan: ζ(0) = -G(1) = -1/2
- Hamilton: H = G(n), L/H → e
- Laplace: ∇²G < 0 always
- Hilbert: basis |n⟩, norm √(G/n!)
- Gödel: G is below arithmetic
- Turing: G always halts
- Pascal: G encodes C(2n,n)
G(n) = n^(n+1) / (n+1)^n
= (ways to crowd n+1 items into n boxes)
/ (ways to spread n items across n+1 boxes)
Crowding over spacing. Everything else follows.
Alexa Louise Amundson Founder & CEO, BlackRoad OS, Inc.
Proprietary — BlackRoad OS, Inc. All rights reserved.