July 30 2026

The feast of Saint Peter Chrysologus (450 AD); Saints Abdon and Sennen (303 AD)

July 31 2026

Saint Ignatius of Loyola (1556 AD)

1 August 2026

7 Holy Machabees (150 BC); Saint Peter in Chains (6^th Century AD); Saints Faith, Hope, Charity (2^nd Century AD)

 

This article is dedicated to my lovely daughter Monika Wasilik

 

Author credited as requested: Andrew Joseph Yanthar-Wasilik, Luxdeluce: https://luxdeluce.com
Subject: Proposed relation among the reciprocal fine-structure constant , electron anomalous magnetic moment , muon anomalous magnetic moment , and a correction factor  , with FORTRAN QUAD-precision numerical outputs.

Important academic note: The following is a rigorous summary and analysis of the supplied document. The article proposes a mathematical/numerical relation between physical constants. In established physics, , , and  are related through quantum electrodynamics and electroweak/hadronic corrections, but the specific formula proposed here is not presented as derived from the Standard Model Lagrangian. Therefore, the results should be interpreted as a proposed phenomenological/numerological or pre-theoretical relation unless and until independently derived, peer-reviewed, and experimentally validated.

1. Core Thesis of Articles 3030–3030.4

The central claim of the article series is that the fine-structure constant, the electron anomalous magnetic moment, and the muon anomalous magnetic moment are connected by a compact transcendental relation involving , , a correction factor , and an exponent close to or exactly equal to . The article proposes that by enforcing the exponent condition

one can calculate an “exact” or adjusted value of the muon magnetic moment anomaly , given a chosen value of the reciprocal fine-structure constant  and the electron magnetic moment anomaly .

The main result emphasized in the document is the adjusted muon anomaly

for the “best fit” 2023–2024 scenario using:

The article argues that this adjusted  lies very close to the Fermilab 2023 experimental value

with a relative discrepancy of approximately

2. The Main Mathematical Relation

The foundational equation proposed in the article is:

This is rewritten as:

where:

 

The article computes:

Using the chosen reciprocal fine-structure constant,

one obtains:

Since , the article introduces a correction factor:

Numerically:

3. Role of the Correction Factor

A major conceptual contribution of the article is the introduction of the correction factor . The article states that direct calculation of the fine-structure constant relation without a correction factor does not give the desired exact exponent . Therefore,  is introduced to force or restore the exact equality:

The correction factor is then connected to the ratio of the muon and electron anomalous magnetic moments:

The article proposes that  may belong to a broader family of correction factors associated with physical constants such as electron, muon, tau, proton, and neutron magnetic anomalies.

This is one of the more speculative but structurally important claims: the correction factors may form arithmetic or geometric sequences, suggesting a hidden mathematical ordering of physical constants.

4. Relation to Electron and Muon Magnetic Moment Anomalies

The article defines an auxiliary quantity , involving the ratio

In the supplied FORTRAN code, the relevant part has the form:

The code also uses a second factor related to

where the variable called ALFA in the FORTRAN code actually represents the reciprocal fine-structure constant , not  itself.

The code defines:

so that

The correction factor is then reproduced numerically using the electron and muon anomaly relation.

5. The “Best Fit” Scenario

The article identifies the best fit as the 2023–2024 scenario using:

and adjusted

 

For this scenario, the FORTRAN QUAD-precision output gives:

essentially equal to  within the reported numerical precision.

The relative exponent error is listed as approximately:

Thus, internally, the adjusted muon value is selected so that the proposed formula yields the desired exponent .

6. Comparison with Fermilab 2023 Muon Result

The article compares the adjusted muon value with the experimental Fermilab-type value:

Adjusted value:

Difference:

Relative error:

The article interprets this as evidence that Fermilab 2023 had the closest experimental result to the proposed theoretical or adjusted value.

7. CODATA-Based Scenario

The document also analyzes a scenario using a CODATA-like value:

With

the muon value required to force the exponent condition  becomes:

This is larger than the “best fit” adjusted value:

The document therefore suggests that the exact/theoretical reciprocal fine-structure value

gives a more favorable fit to the 2023–2024 muon data than the CODATA-like

value.

8. 2026 Data Scenario

The article also examines a 2026-style set of values:

Using the same reciprocal fine-structure constant as the best fit,

the article reports an adjusted muon value:

The exponent obtained is:

The document says this is less good than the 2023–2024 best fit because the exponent deviates further from exact .

When all 2026 experimental values are used, the article reports a significantly altered fine-structure reciprocal value:

which the article views as “way off” from the expected/exact value.

 

9. Numerical Summary Table

Scenario	Used			Exponent	Interpretation in Article
2023–2024 Best Fit	137.035999181727215672064191303733				Best theoretical fit
Fermilab 2023 Experimental aμ	Same	Same		Nearly 50	Closest experiment
CODATA-like α-1	137.035999177000000000000000000000				Requires higher adjusted aμ
2026 exact , adjusted	137.035999181727215672064191303733				Worse than 2023 fit
2026 experimental values	137.035999177000000000000000000000				Considered problematic
Adjusted 2026	137.035999077380007276419130373301				Forces exponent but shifts

10. Main Quantitative Outputs

Quantity	Value
	1389.21524183045816583845882741825
for best-fit
Correction factor
Best-fit
Best-fit adjusted
Fermilab-like experimental
Best-fit ratio
Experimental ratio
Relative ratio difference

11. ASCII Graph: Conceptual Equation Structure

                 ┌──────────────────────┐
                 │ Reciprocal alpha      │
                 │ α⁻¹ ≈ 137.035999...   │
                 └──────────┬───────────┘
                            │
                            ▼
              A = α⁻¹ × (100 / π²)
                            │
                            ▼
                 ┌──────────────────────┐
                 │ Correction factor     │
                 │ CFα = C / B           │
                 └──────────┬───────────┘
                            │
        ┌───────────────────┴────────────────────┐
        │                                        │
        ▼                                        ▼
B from C₁₆ and α⁻¹                     C from aμ / ae
        │                                        │
        └───────────────────┬────────────────────┘
                            ▼
              A × CFα = (π / e)^50
                            │
                            ▼
                  exponent x ≈ 50
                            │
                            ▼
           adjusted value of muon anomaly aμ

12. ASCII Graph: Relative Muon Discrepancy by Scenario

Approximate relative discrepancies quoted or implied in the document:

 

Relative discrepancy scale
10⁻⁹ units approximately

2023 best fit vs Fermilab exp:
|██████████| 0.97 × 10⁻⁹

CODATA α adjusted muon vs exp:
|█████████████| 1.32 × 10⁻⁹

2026 experimental muon vs calculated:
|████████████████████████████████████████████████████████████████████████████| 7.58 × 10⁻⁹

Interpretation according to the article:

in terms of closeness to the proposed formula.

13. ASCII Graph: Reciprocal Fine-Structure Values

α⁻¹ values discussed

137.03599907738   | 2026 adjusted α⁻¹ to force fit
137.03599917700   | CODATA-like α⁻¹
137.03599918173   | article's exact/theoretical α⁻¹
137.03599919513   | adjusted α⁻¹ using 2023 experimental ae and aμ

The article considers the preferred value to be:

14. The Universal Transcendental Function

The article introduces or refers to a function:

For the fine-structure constant, electron anomaly, and muon anomaly, the relevant exponent is asserted to be:

The article therefore places the constants into a transcendental hierarchy governed by powers of

This is not a standard construction in conventional QED, but within the article’s internal mathematical framework it acts as an organizing principle.

15. Computational Method

Articles 3030.1–3030.4 provide FORTRAN QUAD-precision code and output files. The code uses REAL*16 arithmetic and computes:

Then:

The muon anomaly can be adjusted so that:

This numerical strategy is internally consistent as a fitting procedure.

16. Scientific Interpretation and Critical Assessment

The article’s numerical observation is interesting because it creates a tight relation among three dimensionless quantities of similar order:

 

The author correctly notes that these quantities are all small dimensionless numbers near the  scale.

However, from a scientific standpoint, several points require caution:

1. Fitting versus prediction:
   If  is adjusted to force , then the result is not yet an independent prediction. It becomes predictive only if the equation and constants are fixed before comparison with future measurements.
2. No Standard Model derivation is provided:
   In conventional physics,  and  are computed using perturbative QED plus electroweak and hadronic corrections. The article does not derive its formula from QED Feynman diagrams, renormalization, gauge symmetry, or the Standard Model action.
3. The fine-structure constant is not experimentally exact:
   The document refers to an “exact” fine-structure value, but in metrology  is experimentally inferred and subject to uncertainty, although very precisely known.
4. Use of correction factors needs theoretical grounding:
   The factor  is numerically useful, but its physical origin must be derived to establish explanatory power.
5. Dimensional consistency is favorable:
   Since all quantities are dimensionless, the proposed formula avoids the dimensional problems common in speculative constant relations.
6. High numerical precision does not guarantee physical truth:
   QUAD precision demonstrates arithmetic stability, but physical validation requires theory, uncertainty propagation, and independent experimental confirmation.

17. Present Impact and Future Possibilities

Present impact if interpreted conservatively

At present, the article’s impact lies primarily in proposing a compact numerical relation connecting:

It offers a potentially testable numerical hypothesis:

If the equation is fixed and future measurements of , , and  continue to approach the proposed adjusted values, the relation would gain empirical interest.

Present impact if interpreted ambitiously

If validated, the discovery would be significant because it would suggest that the anomalous magnetic moments are not merely independent perturbative quantum-field-theoretic outputs but are linked by a deeper transcendental structure.

Such a result would imply that constants of nature may be organized by a hidden mathematical architecture involving:

That would have potential implications for:

• precision metrology,
• particle physics,
• lepton universality,
• theory of fundamental constants,
• mathematical physics,
• possible beyond-Standard-Model phenomenology.

Future possibilities

The strongest next steps would be:

Future Direction	Purpose
Derive the formula from QED or a deeper theory	Convert numerical fit into physical theory
Propagate experimental uncertainties	Determine statistical significance
Use future aμ measurements as blind tests	Test predictive power
Apply formula to tau anomaly	Check universality
Investigate correction-factor sequences	Determine whether , , , etc. form real mathematical patterns

 

Compare against Standard Model predictions	Establish whether relation adds new information
Perform Bayesian model comparison	Quantify whether formula outperforms chance numerical fitting
Publish reproducible code and datasets	Enable independent verification

Authorial and Conceptual Comments

The article series is ambitious. It attempts to bridge precision particle physics, transcendental mathematics, numerical computation, and metaphysical interpretation. Its strongest feature is that it provides explicit numerical values, FORTRAN QUAD-precision code, and multiple scenarios comparing 2023–2024 data with 2026 data.

The best-supported internal claim is:

is the value required, under the article’s proposed formula, to make

when using the selected reciprocal fine-structure constant and electron anomaly.

The most important scientific limitation is that the formula appears fitted rather than derived. To become a recognized discovery in physics, the relation would need to satisfy at least three criteria:

1. Theoretical derivation:
   It must emerge from a physical framework, preferably connected to QED, renormalization, or a new well-defined theory.
2. Predictive independence:
   It must predict future values before they are measured.
3. Statistical robustness:
   It must be shown unlikely to arise from numerical coincidence.

Nevertheless, as a mathematical hypothesis, the article offers a clear and testable proposition. If future precision measurements of aμ converge toward the adjusted value proposed in the article, the relation would become more compelling and would justify deeper investigation.

Condensed 17-Bullet Executive Summary

1. The article proposes a relation among , , and .
2. The central equation is

3. The exponent  is treated as exact or fundamental.
4. Without correction,

62315. not equal .

5. A correction factor

1. introduced.

6. This correction factor is reconstructed using the ratio .
7. The best-fit reciprocal fine-structure constant is

8. The electron anomaly used in the best-fit case is

9. The adjusted muon anomaly is

10. This produces

11. The adjusted value differs from the Fermilab-like 2023 value by about  relatively.
12. The article concludes that 2023–2024 data fit better than the 2026 values.
13. A CODATA-like  requires a higher adjusted aμ.
14. Using 2026  and  forces a substantially different , which the article considers problematic.
15. The FORTRAN QUAD-precision code supports the internal numerical consistency of the calculations.
16. Scientifically, the proposal remains unvalidated unless derived from physical theory and confirmed by independent experiments.
17. If validated, the relation could have major implications for precision physics and the theory of fundamental constants.