Improve scientific documentation and code quality

[Devanik21]

This maintenance update enhances the repository's scientific professionalism and code quality through several targeted improvements:

1. Mathematical Standardization: Updated docs/hrf_titan26_monograph.md to use bold vector notation ($\mathbf{x}$, $\mathbf{p}_i$) and scaled LaTeX delimiters ($\left| ... \right|$), ensuring consistency with the main README.md and research papers.
2. Code Cleanliness: Removed redundant duplicate assignments for dists and frequency variables in the _wave_potential method within 1/harmonic_resonance_fields_hrf (1).py.
3. Syntax Warning Fix: Resolved a SyntaxWarning: invalid escape sequence in 1/harmonic_resonance_fields_hrf (1).py by converting the multi-line documentation string containing LaTeX formulas into a raw string (r""").
4. Versioning Context: Integrated "Maintainer's Notes" into the headers of HRF Codes/hrf_final_v16_hrf.py and 1/harmonic_resonance_fields_hrf (1).py, providing clear guidance on the use of v15.x (Stable) versus v16.x (Experimental Beta) versions.
5. Quality Assurance: Verified that all modified scripts pass compilation checks and adhere to environment hygiene standards.

These discipline-led edits strengthen the project's scientific clarity while preserving the original research intent.

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[gemini-code-assist]

Summary of Changes

Hello, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request focuses on enhancing the repository's scientific documentation and overall code quality. It introduces clearer mathematical notation in key documentation, refines Python code by removing redundancies and fixing syntax warnings, and provides crucial versioning context within the code files. The changes collectively aim to improve the project's clarity, maintainability, and scientific rigor without altering the core research intent.

Highlights

• Mathematical Standardization: Standardized LaTeX notation in docs/hrf_titan26_monograph.md to use bold vector notation and scaled delimiters, enhancing scientific consistency with research papers.
• Code Cleanliness: Removed redundant duplicate assignments for dists and frequency variables within the _wave_potential method in 1/harmonic_resonance_fields_hrf (1).py.
• Syntax Warning Fix: Resolved a SyntaxWarning: invalid escape sequence in 1/harmonic_resonance_fields_hrf (1).py by converting a multi-line documentation string containing LaTeX formulas into a raw string.
• Versioning Context: Integrated 'Maintainer's Notes' into the headers of HRF Codes/hrf_final_v16_hrf.py and 1/harmonic_resonance_fields_hrf (1).py, providing clear guidance on v15.x (Stable) versus v16.x (Experimental Beta) versions.
• Quality Assurance: Verified that all modified scripts pass compilation checks and adhere to environment hygiene standards.

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[gemini-code-assist]

Code Review

This pull request introduces a set of improvements that enhance code quality and documentation. The changes include removing redundant code assignments and fixing a syntax warning in 1/harmonic_resonance_fields_hrf (1).py, which cleans up the script. The mathematical notation in docs/hrf_titan26_monograph.md has been standardized for better scientific professionalism. Furthermore, contextual notes about versioning have been added to the headers of two Python files, which is helpful for developers. Overall, these are positive changes that improve the repository's clarity and maintainability. I have found no issues of medium or higher severity in these modifications.