reginafield 1.0.0

Toolkit for analyzing, scoring, and visualizing structural features of the Regina Field prime distribution model.

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

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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.

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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)

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Input Format

The input CSV must contain a column named:

Candidate

Each row should contain an integer value.

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Usage

python extract_sequence_features.py --input known_primes.csv --output enriched_output.csv

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Output

The output CSV will include:

Candidate, MotifSum, Entropy, Curvature, ...

This output is compatible with downstream Regina Field analysis pipelines.

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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.

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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.

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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.

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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

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License

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Contact

[e-mail]