Address review comments: fix attribution, notebook-verbatim Möbius sum, add Fourier convention

Co-authored-by: blackboxprogramming <118287761+blackboxprogramming@users.noreply.github.com>
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copilot-swe-agent[bot]
2026-02-27 21:18:14 +00:00
parent c07e622c6c
commit 78dd0f08f2

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@@ -1,7 +1,7 @@
# Notebook Page 1 — Transcription
> Source: `→ halting problem.pdf`, page 1 of 24.
> Transcribed by Alexa Louise Amundson.
> Author: Alexa Louise Amundson. Markdown transcription by repository maintainers.
---
@@ -102,7 +102,7 @@ M(x) = Σ_{n ≤ x} μ(n)
```
Σ_{n=1}^{∞} μ(n)/n = 0
Σ_{n=1}^{∞} (μ(n) ln n)/n = 1
Σ_{n=1}^{∞} μ(n)/n² = 6/π² = 1/ζ(2)
Σ_{n=1}^{∞} μ(n)/n² = 15/π² [as written in notebook; correct value is 6/π² = 1/ζ(2)]
```
> **Historical note:** Gauss considered the Möbius function over 30 years before Möbius,
@@ -132,6 +132,11 @@ f(x) = a · e^((xb)² / 2c²)
### Fourier Transform Proofs
Convention used (unitary, angular frequency):
```
F{ f(x) }(ω) = ∫_{−∞}^{∞} f(x) e^{iωx} dx
```
**Transform of a Gaussian:**
```
F{ a · e^(bx²) } = (a / √(2b)) · e^(−ω² / 4b)