Spiral Doorway Prime Generation: A Deterministic Framework for the Emergence of Prime Structure Verified Generation of 100 Million Primes at 100% Accuracy via Geometric Shell Recursion
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| Název: | Spiral Doorway Prime Generation: A Deterministic Framework for the Emergence of Prime Structure Verified Generation of 100 Million Primes at 100% Accuracy via Geometric Shell Recursion |
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| Autoři: | Needham, Eric |
| Informace o vydavateli: | Zenodo |
| Rok vydání: | 2025 |
| Sbírka: | Zenodo |
| Témata: | Prime Generation, φ-Harmonic Geometry, Deterministic Algorithms, Spiral Doorway Method, Bootstrap Calibration, Recursive Vacuum Theory, Fibonacci Resonance, Shell Structure, Prime Number Theorem, Computational Number Theory, Predictive Framework, Primality Verification, Memory-Efficient Algorithms, Prime Gap Structure, Emergent Number Fields, Eric Needham |
| Popis: | Title: Spiral Doorway Prime Generation: A Deterministic Framework for the Emergence of Prime Structure 📜 Overview This project introduces the Spiral Doorway Prime Generation Framework, a novel deterministic method for generating prime numbers by recursively traversing a φ-harmonic geometric structure embedded in number space. Unlike conventional sieve or probabilistic methods, this approach achieves 100% verified accuracy across 100 million primes using only 1,600 bootstrap primes—a compression ratio of 62,500:1. The framework draws on recursive vacuum shell dynamics, Fibonacci resonance calibration, and φ-symmetric traversal, offering a fully reproducible, open-source, and memory-efficient alternative to traditional prime generation. 🧪 Validation Includes full Python validation script for independent testing JSON datasets at 1M, 10M, and 100M intervals Visualizations of prediction structure, bootstrap harmonics, and phase shell compression Reproducibility confirmed by independent reviewers 📎 Contents 📄 The_Spiral_Doorway_Version_2.pdf – Full research paper 🧪 clean_spiral_doorway_validator.py – Prime generation and verification script 📊 spiral_doorway_validation_*.json/png – Results and output snapshots 📘 README.pdf – Detailed documentation and usage guide 📃 license.txt – Open source license (MIT) 🔍 Key Results 100M primes generated with 100% accuracy, verified independently Predictive field navigation achieves 25× search space compression Fully deterministic model—no pseudorandom seeds, no sieving Enables targeted geometric traversal and future “random access” prime generation DOI:10.17605/OSF.IO/8TKX6 For further information about the ENSO Framework, please contact Eric Needham:ensotheory1@gmail.com Website:https://ensotheory.com/ |
| Druh dokumentu: | report |
| Jazyk: | unknown |
| Relation: | https://zenodo.org/records/16656771; oai:zenodo.org:16656771; https://doi.org/10.5281/zenodo.16656771 |
| DOI: | 10.5281/zenodo.16656771 |
| Dostupnost: | https://doi.org/10.5281/zenodo.16656771 https://zenodo.org/records/16656771 |
| Rights: | Creative Commons Attribution Non Commercial No Derivatives 4.0 International ; cc-by-nc-nd-4.0 ; https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode |
| Přístupové číslo: | edsbas.30D7390B |
| Databáze: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | Title: Spiral Doorway Prime Generation: A Deterministic Framework for the Emergence of Prime Structure 📜 Overview This project introduces the Spiral Doorway Prime Generation Framework, a novel deterministic method for generating prime numbers by recursively traversing a φ-harmonic geometric structure embedded in number space. Unlike conventional sieve or probabilistic methods, this approach achieves 100% verified accuracy across 100 million primes using only 1,600 bootstrap primes—a compression ratio of 62,500:1. The framework draws on recursive vacuum shell dynamics, Fibonacci resonance calibration, and φ-symmetric traversal, offering a fully reproducible, open-source, and memory-efficient alternative to traditional prime generation. 🧪 Validation Includes full Python validation script for independent testing JSON datasets at 1M, 10M, and 100M intervals Visualizations of prediction structure, bootstrap harmonics, and phase shell compression Reproducibility confirmed by independent reviewers 📎 Contents 📄 The_Spiral_Doorway_Version_2.pdf – Full research paper 🧪 clean_spiral_doorway_validator.py – Prime generation and verification script 📊 spiral_doorway_validation_*.json/png – Results and output snapshots 📘 README.pdf – Detailed documentation and usage guide 📃 license.txt – Open source license (MIT) 🔍 Key Results 100M primes generated with 100% accuracy, verified independently Predictive field navigation achieves 25× search space compression Fully deterministic model—no pseudorandom seeds, no sieving Enables targeted geometric traversal and future “random access” prime generation DOI:10.17605/OSF.IO/8TKX6 For further information about the ENSO Framework, please contact Eric Needham:ensotheory1@gmail.com Website:https://ensotheory.com/ |
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| DOI: | 10.5281/zenodo.16656771 |