https://github.com/selfapplied/zetadiffusion
Numerical Lab for Proving RH via Bundle Dynamics, RG Flow, and Topological Energy Harvesting
https://github.com/selfapplied/zetadiffusion
Last synced: 22 days ago
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Numerical Lab for Proving RH via Bundle Dynamics, RG Flow, and Topological Energy Harvesting
- Host: GitHub
- URL: https://github.com/selfapplied/zetadiffusion
- Owner: selfapplied
- Created: 2025-12-01T17:48:09.000Z (6 months ago)
- Default Branch: main
- Last Pushed: 2025-12-02T09:09:31.000Z (6 months ago)
- Last Synced: 2025-12-04T11:55:23.418Z (6 months ago)
- Language: Python
- Size: 293 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# ZetaDiffusion
**Numerical Lab for Proving RH via Bundle Dynamics, RG Flow, and Topological Energy Harvesting.**
Version: 0.3.0
## Overview
ZetaDiffusion v0.3 implements the complete **Field Equationist Generator (FEG-0.3)** architecture. It unifies the analytic study of the Riemann Zeta function with dynamical systems theory and thermodynamic information extraction.
## Architecture
### 1. Spectral Line Probe (`zetadiffusion.field`)
- Samples the Riemann field $\xi(1/2 + it)$.
- Detects zeros as topological defects in the complex phase.
### 2. Bundle Dynamics (`zetadiffusion.dynamics`)
- Maps spectral data to circle maps on $X \times S^1$.
- Generates rotation number spectra ("Devil's Staircase") using type-safe modular arithmetic (`Radians`/`Turns`).
### 3. Local RG Operator (`zetadiffusion.renorm`)
- Applies the Feigenbaum renormalization operator to local field potentials.
- Estimates the scaling dimension $\delta$ of the underlying universality class.
### 4. Topological Harvester (`zetadiffusion.energy`)
- **The Negentropic Engine**.
- Models the extraction of work from geometric shock waves.
- Implements the Hamiltonian $H_{extract} = -\eta \cdot \dot{\chi} \cdot \Phi$.
- Simulates the "Loading -> Shock -> Harvest -> Reset" anti-fragile cycle.
## Usage
Run the lab demonstration to see the full pipeline:
```bash
python3 demo.py
```
Run the energy harvesting simulation directly:
```bash
python3 zetadiffusion/energy.py
```
## Theoretical Basis
The system treats the Riemann Critical Line not as a static object, but as the **attractor** of a dynamical system. The zeros are the discrete points where the system achieves perfect phase locking (rational rotation numbers). The Energy Harvester demonstrates how a cognitive system can extract "insight" (computational work) by surfing the shock waves generated near these critical points.
## Documentation
### Status & Results
- **VALIDATION_STATUS.md** - Current validation results, issues, and next steps
- **PROJECT_STATUS.md** - Project overview and quick start guide
- **RESEARCH_FINDINGS.md** - Detailed diagnostic analysis and root causes
### Guides
- **FEG-0.4_Field_Manual.md** - Operator theory and implementation details
- **NOTION_SETUP.md** - Notion integration setup guide
- **SCRIPT_STANDARDS.md** - Code standards and conventions
- **NEXT_STEPS.md** - Historical roadmap and future directions