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This paper explores the Regulated Trinary Reduction Theory framework to derive fundamental constants from electron mass and five integers.

May 12, 2026Open Access

GRE Foundry / Regulated Trinary Reduction Theory: Foundational Constants, SU(3) Routing Algebra, Yang–Mills Mass Gap ,Prime Universe, Gravity Quantization, Alpha Derivation, C as Nyquist Limit, and Planck from Electron Mass.

Key Points

This paper explores the Regulated Trinary Reduction Theory framework to derive fundamental constants from electron mass and five integers.
Derived constants using electron mass and integers {2, 3, 4, 5, 7}.
Provided six papers detailing different aspects and implications of RTRT.
Used precise metrics to evaluate fundamental constants over twelve magnitudes.
Successfully derived the Planck constant as ħ = 1 in TITO units with 80-digit precision.
Reported Yang-Mills mass-gap value of Δ = 1.676 GeV, demonstrating a close relationship with lattice QCD values (3.1% deviation).
Established the speed of light and its relation to Nyquist limits and particle classification.

Abstract

# RTRT Publication Set — May 2026 **Author: ** Garret R. J. Krampe **Affiliation: ** GRE Foundry, Daram, Samar, Philippines **Concept DOI: ** 10. 5281/zenodo. 17431815 (https: //doi. org/10. 5281/zenodo. 17431815) **License: ** CC BY-NC-ND 4. 0 ## Overview Regulated Trinary Reduction Theory (RTRT) is a discrete integer-only theoretical physics framework. From one measured input (the electron mass) and five structural integers 2, 3, 4, 5, 7, it derives fundamental constants spanning twelve orders of magnitude in precision. This upload contains six papers and supporting materials. ## Papers ### 1. The Planck Constant as a Projection Coefficient (8 pages) Shows that ħ = 1 in TITO natural units (algebraically exact, verified to 80-digit precision). Derives eight fundamental constants from one measurement. Proposes single-anchor metrology replacing Planck units. ### 2. Yang–Mills Mass Gap: Clay Prize Formulation (14 pages) Formal RTRT routing-lattice derivation of the Yang–Mills mass-gap value: Δ = 3⁸ × E₀ = 1. 676 GeV (3. 1% from lattice QCD, 0. 7σ). Includes boundary operator ∂RGB, physical projection, five-layer formal wrapper, Route B bridge to Osterwalder–Schrader reconstruction, TITO natural units, interpolation bound, and glueball excitation spectrum. ### 3. Yang–Mills Mass Gap: Zenodo Summary (8 pages) Compact version of the mass gap derivation with Route B bridge. Suitable for first reading. ### 4. Route B Bridge Note (3 pages) Technical note formulating the path from Wilson action reflection positivity to RTRT physical projection. Reduces the Clay wrapper to one specialist question. ### 5. The Nyquist Ceiling (12 pages) Derives the speed of light as c = SPAN/ROT = 5/4 (Nyquist sampling limit), the Lorentz factor from the Pythagorean triple 3² + 4² = 5², Cherenkov radiation as aliasing above the sampling ceiling, and Wang superluminal envelope as sub-Nyquist group velocity. ### 6. The PD2 Prime Universe (9 pages) Particle classification from integer TITO addresses. Two-level system: PD2Target (energy scale, prime = stability) and PD2Type (gap = particle type). Covers electron, proton, neutron, pion, positronium. ## Supporting Materials - **RTRTcitations. bib** — BibTeX entries for all papers - **LICENSE. txt** — CC BY-NC-ND 4. 0 - **README. md** — This file ## Precision Table | Constant | Formula | Precision | |----------|---------|-----------| | α⁻¹ | 137 + 9/250 − 1/1, 198, 750 | ~7×10⁻¹² | | a₀ | (λTITO/AP) × α⁻¹ | 2. 2×10⁻¹⁰ | | ħ | ETITO × τTITO | Exact (0. 0) | | G | 1/NG | −0. 133 ppm | | mₚ | 3672 × ETITO | ~0. 01% | | mₙ | 3677 × ETITO | ~0. 01% | | Q_β | 49 × OGᵤnit | 0. 017% | | ΔYM | 3⁸ × ETITO | 3. 1% | One measurement (mₑ). Five integers 2, 3, 4, 5, 7. Zero free parameters. ## File Formats Each paper is provided in four formats: - **. pdf** — Typeset document (pdfLaTeX) - **. tex** — LaTeX source - **. docx** — Word document (pandoc conversion) - **. md** — Markdown (pandoc conversion) ## Contact Garret R. J. Krampe GRE Foundry Daram Island, Samar, Philippines DOI: 10. 5281/zenodo. 17431815 ## How to Cite ```bibtex @misckrampe2026ᵣtrt, author = {Krampe, Garret R. J. , title = RTRT Publication Set -- May 2026, year = 2026, publisher = Zenodo, doi = 10. 5281/zenodo. 17431815, url = https: //doi. org/10. 5281/zenodo. 17431815 } ```

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