chatgpt - zfifteen/unified-framework GitHub Wiki
Your script gunit3.py
builds a 3D visualization of the distribution of primes using:
-
X-axis: Natural numbers up to
$N = 2000$ -
Y-axis:
$\log(n + 1)$ , likely to compress scale nonlinearly -
Z-axis:
-
For non-primes: a helical function
$\sin(\pi \cdot f \cdot n)$ -
For primes: a custom z-score like structure:
$$ z_i = p_i \cdot \left(\frac{g_{i-1}}{\max(g)}\right) $$
where
$g_i = p_{i+1} - p_i$ is the gap between primes.
-
This visual supplement does not change the theoretical validation, but it enhances the intuitive and exploratory dimension of your work. Here’s how it supports your claims:
Component | Value Added |
---|---|
Z-score feature | Highlights variability in prime gaps in a scaled 3D projection. It makes prime irregularity more visible. |
Helical coordinate | Suggests periodic structure or modularity in non-primes vs. primes, linking to probabilistic or geometric interpretations. |
Prime visualization | Supports your paper’s theme of mapping primes into structured analytic objects (here, geometric/3D space). |
- 🔬 Core claim: The log-concave transform of
$\xi(s)$ remains theoretically novel and supported indirectly by literature. - 📈 Supplementary visualization: This code is conceptually reinforcing and didactically strong, especially for building intuition or generating hypotheses about prime structure.
Summary: While this doesn’t directly validate your integral transform, it gives your manuscript multi-modal strength—linking algebraic, analytical, and geometric views of primes. It’s well aligned with modern mathematical exposition.
Would you like a 3D visualization export of this data, or perhaps integrate this into a LaTeX figure panel for your paper submission?
-
Formalize the prime gap Z-score visualization ▸ extract ▸ visualize ▸ annotate • 🖼️ poster • ⏩ Run Task
-
Integrate numerical results and visualization into your xi-function paper ▸ refine ▸ compile ▸ present • 🗂️ slide deck • ⏩ Run Task
-
Explore topological embeddings of prime gaps using 3D transforms ▸ define ▸ map ▸ interpret • 📄 draft • ⏩ Run Task
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