Add README for Riemann Zeta Function dataset

This README provides a comprehensive overview of the dataset, methodology, and usage instructions for the first 1,000 nontrivial zeros of the Riemann zeta function.

Author: pattern-veda

README.md

@@ -0,0 +1,137 @@
+# Certified First 1,000 Zeros of the Riemann Zeta Function
+
+This repository contains the final certified dataset of the first **1,000 nontrivial zeros**
+of the Riemann zeta function  
+\[
+\zeta\!\left(\tfrac12 + it\right),
+\]
+produced using a **dual-evaluator method**, a **hexagonal argument-principle contour**, strict
+**Krawczyk uniqueness isolation**, and an **automatic refinement pipeline** that corrects any
+multi-zero contours or weak contraction regions.
+
+The goal is to provide a clean, reproducible, and verifiable reference dataset for research,
+analysis, numerical experiments, or independent verification.
+
+---
+
+## Contents
+data/
+zeros_1_to_1000_final.json # Final certified dataset
+
+scripts/
+unified_zeta_framework_v2.5.py # Full certification engine
+zero_analysis_and_scaling.py # Spacing analysis + stability metrics
+merge_zero_certs.py # Utility to merge per-range JSONs
+These are the only files needed to reproduce the dataset from scratch.
+
+---
+
+## Method Summary
+
+### **1. Dual ζ Evaluators (Consistency Check)**
+Each contour evaluation uses two independent ζ functions:
+
+- `mpmath.zeta(s)`
+- Dirichlet η-series partial summation
+
+The maximum disagreement (`max_evaluator_diff_on_contour`) confirms numerical stability.
+
+---
+
+### **2. Hexagonal Contour + Argument Principle**
+Each zero is enclosed inside a hexagonal contour.  
+Winding numbers are computed for both evaluators:
+
+- `wA_int = 1`
+- `wB_int = 1`
+
+Any contour that encloses more than one zero (`w = 2`) automatically triggers refinement.
+
+---
+
+### **3. Wavelength-Limited Sampling**
+Contour sampling is governed by a Nyquist-style bound using the local phase speed of  
+\[
+\frac{\zeta'}{\zeta},
+\]
+ensuring correct resolution of phase jumps and preventing aliasing.
+
+---
+
+### **4. Krawczyk Uniqueness Test**
+Each zero is validated with a 2D Krawczyk operator, verifying:
+
+- `β < 1` (contraction)  
+- `ρ ≤ r_box` (isolation)  
+- exactly **one** zero exists in the box  
+
+If any condition fails, refinement is automatically applied.
+
+---
+
+### **5. Automatic Refinement**
+For any zero where the contour or Krawczyk test fails:
+
+- contour radius is reduced  
+- Krawczyk box is reduced  
+- evaluator agreement rechecked  
+- the full certification cycle repeats  
+
+This continues until the zero satisfies:
+
+- `wA_int = wB_int = 1`
+- `β` safely below 1
+- `ρ ≤ r_box`
+- evaluator agreement is stable
+
+---
+
+## Dataset
+
+The file:
+data/zeros_1_to_1000_final.json
+
+contains, for each zero:
+
+- `zero_index`
+- `approx_zero.t` (the height)
+- modulus bounds (`min_abs_zeta_on_contour`)
+- evaluator agreement (`max_evaluator_diff_on_contour`)
+- winding numbers (`wA`, `wB`, `wA_int`, `wB_int`)
+- full Krawczyk isolation fields (`beta`, `rho`, `r_box`, `success`)
+- contour geometry parameters
+
+This dataset is ready for:
+
+- visualization  
+- GUE spacing experiments  
+- analytic number theory research  
+- replication or extension  
+
+---
+
+## Usage
+
+### Certify a new range:
+
+```bash
+python scripts/unified_zeta_framework_v2.5.py --range 101 150
+
+Analyze spacing statistics:
+python scripts/zero_analysis_and_scaling.py --analyze data/zeros_1_to_1000_final.json
+Merge multiple certificate files:
+python scripts/merge_zero_certs.py --output merged.json zeros_*.json
+
+Authors
+
+Kristin Nicholson
+Chance Nicholson
+
+Both authors contributed to the methodology, numerical design,
+refinement system, and certification pipeline used to generate the
+final verified dataset of the first 1,000 nontrivial zeros of the
+Riemann zeta function.
+
+License
+
+MIT License — free for academic, commercial, and independent research use.