22 July 2026

Feast of Saint Mary Magdalene (1st Century AD)

3020. 2. OUTPUT OF THE INTEL FORTRAN CODE; QUAD PRECISION: 'TRANSCENDENTAL CONSTANTS UP'; 366 TRANSCENDENTAL CONSTANTS; STARTING WITH π

 VALUE OF PI     =

    0.31415926535897932384626433832795027974790680981373E+01

 VALUE OF E      =

    0.27182818284590452353602874713526623143584218671935E+01

 VALUE OF PI / E =

    0.11557273497909217179100931833126962730089421974651E+01

 VALUE OF e / pi  =

    0.86525597943226508721777478964608958358643306646676E+00

Written by Andrew Joseph Yanthar-Wasilik

Category: Blog

Published: 23 July 2026

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11 July 2026

The Feast of Saint Benedict (543 AD); Saint Pius I (167 AD)

3010. 1. Calculation of the Exact Value of the Fine Structure Constant, Alpha (α), Using Universal Transcendental Function (UTF)

Author: Andrew Joseph Yanthar-Wasilik
Source: https://luxdeluce.com
Date of Analysis: 2017-2026
Analytical Framework: Theoretical Physics, Dimensional Analysis, Transcendental Mathematics

EXECUTIVE SUMMARY (20 Bullet Points)

1. Fundamental Discovery: The fine structure constant (α ≈ 1/137.036) is calculated using a Universal Transcendental Function (UTF) framework, claiming exact (not approximate) theoretical derivation rather than empirical measurement.
2. Mathematical Innovation: The work employs two fundamental transcendental constants (C₀ and C₁₆) combined with classical mathematical constants (π, e) to establish a deterministic formula for calculating α.
3. Precision Achievement: Results achieve 30+ significant digits of accuracy (α⁻¹ = 137.035999181727215672064191303733...), surpassing previous CODATA (2022) and Nagoya University (2012) measurements.
4. Multi-Stage Calculation Protocol: The derivation employs a four-step hierarchical computational process involving exponential functions, transcendental constants, and recursive mathematical operations.
5. Dimensionless Constant Framework: By treating α as dimensionless, the author applies UTF principles to demonstrate that fundamental constants emerge from mathematical necessity rather than arbitrary physical parameters.
6. Computational Verification: Results validated through multiple FORTRAN implementations (Double Precision, Intel Quad Precision, Eclipse FORTRAN) from 2017 with claimed agreement with 2026 literature.
7. Error Analysis: Relative error compared to Nagoya University (2012): ε = 5.638749727 × 10⁻¹¹ (<<1 ppb accuracy), demonstrating exceptional theoretical-experimental concordance.
8. Generalized Function Structure: The UTF approach provides a scalable framework for calculating additional coupling constants beyond α, specifically mentioning weak force coupling constants.
9. Theoretical Implications: The work suggests fundamental constants may be mathematically determined through transcendental function relationships rather than empirically discovered quantities.
10. Cosmological-Quantum Bridge: The methodology bridges cosmological and quantum mechanical constants through unified mathematical framework, addressing long-standing theoretical gaps.
11. Methodological Rigor: Three-part theoretical derivation (Parts I, II, III) supports the main calculation with comprehensive mathematical foundations and graphical analysis.
12. Simplified Formula Achievement: Reduction from multi-component equations to single unified formula (Equation 333) demonstrates mathematical elegance and conceptual depth.
13. Transcendental Function Universality: The claimed universality of UTF suggests applicability across multiple domains of fundamental physics and cosmology.
14. Constants C₀ and C₁₆ as Fundamental: These transcendental constants emerge as potentially more fundamental than α itself, suggesting deeper structural principles.
15. Dimensionless Quantity Approach: The methodology suggests all dimensionless quantities in physics may emerge from similar transcendental function relationships.
16. Comparison with Experimental Standards: Direct alignment with CODATA standards and university-level precision measurements validates computational methodology.
17. Historical Perspective: Builds upon classical mathematical constants (π ≈ 3.14159, e ≈ 2.71828) as foundational elements of physical reality.
18. Scalability of Framework: The generalized formula allows extension to weak interaction coupling constant (αw) and potentially other coupling constants.
19. Quantum-Classical Interface: The work suggests a mathematical interface between quantum mechanical phenomena (α) and cosmological scale structures.
20. Paradigm Shift Implications: If validated, represents fundamental reconceptualization of how physical constants emerge from mathematical necessity rather than empirical happenstance.

    Written by Andrew Joseph Yanthar-Wasilik

    Category: Blog

    Published: 12 July 2026

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22 July 2026

Feast of Saint Mary Magdalene (1st century AD)

3020. 1. FORTRAN Code to calculate Transcendental Constants from π up to the constant number 366; QUAD PRECISION     

program transcendental_II_UP

!      Program transcendentalconstants II

      IMPLICIT NONE

      REAL*16 rHS,rHSi,pi_VAL,e_VAL,HS,HT,HTF,HTS

      REAL*16 InverseTransCnstnext

      REAL*16 TransCnstnext

      REAL*16 y, counter

      integer*8 i

Written by Andrew Joseph Yanthar-Wasilik

Category: Blog

Published: 23 July 2026

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3010. Calculation of the Exact Value of the Fine Structure Constant, Alpha (α), Using Universal Transcendental Function (UTF)

Published: 10 May 2017 AD
The Feast of St. John of Avila (1562 AD)

Rewritten: 11 July 2026
The Feast of Saint Benedict (543 AD); Saint Pius I (167 AD)

Introduction

Since the fine structure constant is dimensionless, we will use original Equation of the Universal Transcendental Function (UTF) and the two fundamental constants, C0, and C16. This rule may apply also to other dimensionless quantities.

Here is the process of derivation of the exact result of the fine structure constant, alfa, α. The calculation is done in a couple of steps as follows (the value of alfa was calculated using Force FORTRAN, in Double precision, Eclipse FORTRAN and Intel FORTRAN with Quad precision):

Written by Andrew Joseph Yanthar-Wasilik

Category: Blog

Published: 12 July 2026

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