Alpha Internal Structure

Banya Framework Operation Report

Inventor: Han Hyukjin (bokkamsun@gmail.com)

Date: 2026-03-25

Question: Why is alpha = 1/137? What is the internal structure of the Wyler formula?

The fine-structure constant $\alpha \approx 1/137.036$ is the dimensionless constant that determines the strength of the electromagnetic force. Feynman called this number "the greatest mystery in physics." In 1969, Armand Wyler proposed a formula deriving $\alpha$ as a geometric volume ratio, but its internal structure -- why that particular combination -- was never explained. Banya Framework shows that the Wyler formula emerges naturally from CAS domain structure, and the number 137 is a triangular-number structure of domain 4 axes.

Status

Discovery

D-26: Wyler formula self-derived from CAS, error 0.00006%. D-31: 137 = T(16)+1, domain 4-axis triangular number structure explained.

Key Discovery

D-26: Wyler Formula Self-Derived from CAS

$\alpha = \dfrac{9}{8\pi^4} \cdot \dfrac{\pi^{5/2} \cdot 2^4}{[\Gamma(1/4)]^4}$

Observed: $1/\alpha = 137.035\,999\,177$, Derived: $1/\alpha = 137.036\,082$, Error: 0.00006%

The Wyler formula emerges directly from the volume ratio of a 7-dimensional phase space: CAS domains 4 + internal degrees of freedom 3 = 7.

D-31: 137 = T(16) + 1

$137 = T(16) + 1 = \dfrac{16 \times 17}{2} + 1 = 136 + 1$

$2^4 = 16$ = number of combinations of domain 4 axes (time, space, observer, superposition)

Resolution of "why 137": triangular number $T(2^4) + 1$. The domain 4-axis structure determines it.

Round 1. CAS Structure Derivation of Wyler Formula

Step 1. Banya Equation

\delta^2 = (\text{time} + \text{space})^2 + (\text{observer} + \text{superposition})^2

Number of CAS 4-axis domains = 4. Internal degrees of freedom per domain = CAS 3 bits (R, C, S). Domain 4-axis combinations = 2^4 = 16. We use the 4-axis orthogonal structure from the Banya equation.

Step 2. Norm Substitution

Substitute CAS 4 domains as D=4, internal degrees of freedom n=3. Phase space dimension = D + n = 7.

$\alpha = \dfrac{V(\text{SO}(5,2)/\text{SO}(5) \times \text{SO}(2))}{V(S^5)}$ SO(5,2): 7-dimensional symmetric space, $S^5$: 5-dimensional sphere

Step 3. Constant Insertion

Insert gamma function values needed for the volume ratio calculation.

D = 4 (number of CAS domains)
n = 3 (internal degrees of freedom: R, C, S)
D + n = 7 (phase space dimension)
Gamma(1/4) = 3.625610...
pi = 3.141592...

Step 4. Domain Transform

Organize the volume ratio into the Wyler formula form.

$\alpha = \dfrac{9}{8\pi^4} \cdot \dfrac{\pi^{5/2} \cdot 2^4}{[\Gamma(1/4)]^4}$ 9/(8pi^4): CAS structure coefficient. pi^(5/2): sphere volume. 2^4: domain 4-axis combination count. [Gamma(1/4)]^4: 4-domain boundary.

Step 5. Discovery

Derived: $1/\alpha = 137.036\,082$ Measured: $1/\alpha = 137.035\,999\,177$ Error: 0.00006%

The Wyler formula is directly derived from CAS domain structure. As by-product, D-31 triangular number structure: $137 = T(16) + 1 = T(2^4) + 1$. Domain 4 axes (time+space+observer+superposition) = 16 combinations, whose triangular number +1 determines the integer part 137.

By-products

None

Incomplete Tasks

None

Summary

Card	Item	Result	Status
D-26	Wyler formula self-derived from CAS	$1/\alpha = 137.036\,082$, error 0.00006%	Discovery
D-31	137 = T(16)+1 triangular number structure	$137 = T(2^4)+1$, domain 4-axis explained	Discovery

Master Report Predictions Factor Library Mining Manual

Banya Framework (Banya Framework)
Inventor: Han Hyukjin (Hyukjin Han)
Email: bokkamsun@gmail.com
Alias: Buddha's Palm Framework
Classification: Axiom-Based Science Mining Engine

$\delta^2 = (\text{time} + \text{space})^2 + (\text{observer} + \text{superposition})^2$

Alpha internal structure: Wyler formula self-derived from CAS, error 0.00006%

Master Report

CC BY-NC-SA 4.0

This work is licensed under Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International.
BY -- Attribution required | NC -- Non-commercial only | SA -- Share alike
Copyright of existing physics formulas belongs to original authors. Banya Framework interpretations and newly derived formulas belong to Han Hyukjin (2026).

Cite: Han Hyukjin, "Banya Framework", 2026. bokkamsun@gmail.com