Harmonic Zeta Sieve

Modular harmonic sieve for detecting nontrivial Riemann zeta zeros through phase-locked resonance analysis. This project provides code and data for independent verification of the harmonic sieve described in the paper:

Sadie A. Sherratt (2025).Phase-Locked Modular Resonance and the Structure of Zeta Zeros.

📄 Overview

This repository includes the full data bundle for the harmonic sieve model, designed to detect nontrivial Riemann zeta zeros using a phase-locked modular resonance approach. This approach leverages the interplay between base-3 and base-π logarithmic spirals to identify resonance points where zeta zeros align, without relying on statistical approximations.

Key Features:

• Fast, scalable zero detection using modular harmonic resonance.

• Precomputed datasets for efficient verification without full recalculation.

• Structured for direct use in numerical experiments and algorithm development.

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📄 Contents

• /data/ — Numpy arrays and parameter sets used in the sieve
• /results/ — Sieve validation and false positive report
• /zeros/ — Archive of known zeta zeros used for validation
• README.md — This documentation file
• LICENSE.txt — License for academic use

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📈 Purpose

This bundle provides the datasets necessary to reproduce the harmonic sieve validation described in the paper:

• Modular drift between base-3 and base-(\pi) logarithmic spirals.
• Dynamic harmonic envelope structure isolating resonance points.
• Modular sieve construction confirming alignment with known zeta zeros up to high (t).

The datasets allow independent verification of the modular geometric model without requiring full recalculation.

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📋 File Types

• .npy — Numpy array files storing drift, envelope, or symbolic modular quantities.
• .txt — Documentation or symbolic tables describing the dataset structure.
• .txt — List of known nontrivial zeta zeros used for empirical validation.

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⚙️ Requirements

• Python 3.8+ recommended
• Library:
  • numpy

No special or proprietary packages are needed to load or use the data.

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Quickstart:

To load the included data files:

import numpy as np

# Load the primary sieve data
sieve_data = np.load('data/sieve_parameters.txt')
zeros = np.load('zeros/zeros1.gz')

data_band = np.load('data/within_band_mask.npy')

print(f"Loaded {len(zeros)} known zeros.")

This snippet demonstrates loading the core sieve data and known zero files for quick inspection. For more detailed usage, refer to the accompanying paper.

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📜 License

This bundle is released for non-commercial research and educational purposes only.
Please cite the associated paper if used in derived works.

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📬 Contact

For questions, updates, or related inquiries:

Sadie A. Sherratt
Website: https://sherrattmath.org
Email: sadie@sherrattmath.org

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