Regina-Field-Toolkit
Regina Field Toolkit (Sequence-Based Release)
This toolkit provides feature extraction and analysis utilities for studying structural properties of prime numbers using the Regina Field framework.
Legacy Version
For the previous digit-based feature extraction approach, see:
README_legacy.md
Overview
The toolkit computes structural features derived from prime step sequences, including:
- MotifSum — motif-based structural signal derived from step decomposition
- Entropy — distributional complexity of motif patterns
- Curvature — second-order structural variation across motifs
These features define an embedding of primes into a curvature–entropy feature space, which is used for structural analysis of prime distributions.
Feature Extraction
Script: extract_sequence_features.py
This script processes a CSV of candidate numbers and computes:
- MotifSum (sequence-based motif structure)
- Entropy (motif distribution)
- Curvature (structural variation)
Input Format
The input CSV must contain a column named:
Candidate
Each row should contain an integer value.
Usage
python extract_sequence_features.py --input known_primes.csv --output enriched_output.csv
Output
The output CSV will include:
Candidate, MotifSum, Entropy, Curvature, ...
This output is compatible with downstream Regina Field analysis pipelines.
Methodology Summary
The sequence-based approach differs from earlier versions by operating on prime step sequences rather than digit patterns.
Key aspects include:
- Prime gaps are converted into step sequences
- Gaps of 6 are decomposed into
[2,4]and[4,2]motifs - Motif frequencies are extracted over local windows
- Entropy is computed from motif distributions
- Curvature is derived from second-order variation in motif structure
This produces a structured representation of primes in feature space.
Important Note on Versions
This release introduces a sequence-based feature extraction method.
Previous versions of the toolkit used a digit-based approach.
Those versions are preserved for transparency but are not used in current analyses.
Relation to Regina Field Paper
The results presented in:
The Regina Field: Discrete Entropy-State Structure in Prime Distributions and Its Relationship to Prime Counting Error
were generated using this version of the toolkit.
Changelog
v2.0-sequence-regime
- Replaced digit-based feature extraction with sequence-based motif analysis
- Introduced step-sequence motif decomposition (including
6 → [2,4]and[4,2]) - Updated definitions of:
- MotifSum
- Entropy
- Curvature
- Aligns with results presented in the Regina Field paper
v1.x (legacy)
- Digit-based feature extraction
- Retained for historical reference only
License
Contact
middlebrookstech@gmail.com