Sum u ' 1 = u 1 2 + u 2 2 implying usual 4D and supergravity 11D

a 00

137

u 1 = 4 ; u 2 = 11

Third term of Combinatorial Hierarchy ( 2 2 1 ) + ( 2 3 1 ) + ( 2 7 1 )

a 00

137

[7]

Electric coupling constant ( α 1 ) = c / v 1 ( 1 + 1 / p t )

a

137.035999084 (21)

0.15 ppb

Opt. ser. with p W 2 = 3511 = p 495 28 , the Wieferich prime 137 + 1 / 28 + 1 / p W 2

a 0

137035999104

p W 2 = 3511 = p 495 28

Electron Excess Magnetic moment d e ( a 136 ) 9 / 2 d e 2 137 n t β 2 / p t H

d e

1.00115965218128

0.15 ppb

Atiyah constant Γ = γ a / π ( p t / p W ) 2 a / 2 e d e 3 a s ( d e n t / p t β 2 ) 2 3 × 137 / 44 π g 1 2 β 4

Γ

25.17809724196

π / γ ( g 2 / g 1 2 ) n t p W / p H

Opt. scalar boson/Electron mass ratio; 495 g 1 g 2 g 3 H / ( H p t )

H ( 0 )

4952 = 245025

H m e s ( 0 ) : 245000 (250)

Opt. charged weak boson/Electron mass ratio; W ( 8 π / 3 ) a 2

W

157,340.1093

[5] W m e s : 157297 (24)

Opt. neutral weak boson/Electron mass ratio; Z ( 70 p p b ) ( 2 R ƛ e e ( 1 + v 1 / c ) / l P 2 ) 1 / 16

Z

178,451.7524

[5] Z m e s : 178450 (4)

Opt. Weak ratio W / Z 495 q 2 a / β 1 / 4 ln P sin θ ( ( 2 q ) 3 H β / p t ) 1 / 2 2 π ( F 3 / a W Z 2 ) 2

cos θ

0.88169557

0.1 ppm

Opt. U(1) Gauge coupling Z sin θ / H ( 0 ) ( γ / y ) ( n t / 1837 ) p W 2 / H f ( 2 ) ( K 0 / Π ± 2 ) 1 / 4

g 1

0.3436256

1 / g 1 a s ( a 136 ) / 3

A-dimens. El. charge q 3 / π 2 ( 3 / 10 ) 6 F / 1836 ( 6 2 / β d e ) 1 / 3 ( 6 μ / 137 g 0 Γ ) 2

q

0.30297311

6 2 137 / 53 (Indian music)

Opt. SU(2) coupling W / H ( 0 ) g 1 + g 2 ( 139 / 140 ) 2

g 2

0.6421390

g 2 y / Φ 2 π g 1 / y

Gravitational Coupling p t p G / 2 a 3 = g 0 ( 1 g 1 ) ( p W / H ) 8 ( 2 π / ( g 0 + g 1 + g 2 + g 3 ) ) 4 n t / 8 π 2

g 0

0.6534149985

1 ppb, this work

Opt. SU(3) Gauge coupling g 3 = g 0 g 2 / g 1 Φ a 7 / 137 4 p E d 2

g 3

1.2210476

0.1 ppm, this work

Opt. charged Pion/Electron mass ratio Π ± 2 H p G / p t ( 3 g 3 ) 2 Π ± Π 0 3 × 139 × 419 g 2 2 n t / p W

Π +

273.1328373

Π + m e s : 273.13288 (47)

Opt. neutral Pion/Electron mass ratio Π 0 3 g 2 r H / ƛ e 419 / ( 3 × 139 ) F 5 / P a 3

Π 0

264.143971

Π 0 m e s : 264.14341 (97)

Opt. eta Meson/Electron mass ratio 4 ( Π 0 Π + ) 1 / 2 ( 137 / a ) 8

η

1072.147344

η m e s : 1072.139 (33)

Opt. “Squared Effective ( m Z ) Weak-mixing angle” e / 32 sin θ ( cos θ ) 2

( sin θ 1 ) 2

0.2315965

( sin θ 1 ) m e s 2 : 0.23153 (4)

DNA Adenine-Thymine couple main mass/mH o 1 μ g 0 / g 1 g 2 o 2 μ / Π 0 g 2 g 3 o 2 4 g 2 g 3 / π

o 1

612.312280

[36]

DNA Guanine-Cytosine couple main mass/mH o 2 p t / 3 g 1 a s Π 0 g 0 g 3 / g 1

o 2

613.299802

[36]

Opt. Muon/Electron mass ratio m 419 π 2 / 20 g 1 5 2 ( p 1 ) 7

μ

206.7682869

μ m e s : 206.7682830

Opt. Koide Tau ratio τ 120 / 61 g 1 7 , with p K = ( 1 + μ + τ ) / 2 = ( 1 + μ + τ ) 2 / 3 [35]

τ

3477.441701

τ m e s : 3477(2)

Koide constant p K β τ ln ( 2 + 3 + 5 + 7 ) / ln ( 2 × 3 × 5 × 7 )

p K

1842.604994

bases 2; 3; 5; 7

Fermi mass ratio: a w ( 4 π / 3 ) ( ln P ) 3 ( y Π + / 2 d e q ) 2 ( p t / n t ) ( 137 a a s ) 2 / 4 π τ [5]

F

573,007.3652

F m e s : 573,007.362

Eta-Tau mass ratios product with Kaons K 0 973.78 and K ± 966.12

η τ

3.728 × 106

3 K 0 K ± p K 2 / a 3

Product of the Wieferich primes 1093 × 3511

p W 1 p W 2

3.837 × 106

p W 1 / η ( p W 2 β / τ ) 2

Third Primary Economic Number e 3

e e e

3814 × 106

e 3 / e 2 a H

Opt. Gravitational (inverse) coupling constant R / 2 e = P 2 / p H

a G

1.691936467 × 1038

ppb [5]

Opt. Electroweak (inverse) coupling constant ( 2 Γ × 137 ) 3 ( 6 ( ƛ C M B / ƛ e ) 3 ) 2 / 5

a w

3.283374406 × 1011

ppb [5]

Opt. Strong (inverse) coupling constant a w / 2 π ( p H ) 3 / 2 ( π H 3 / 2 / τ ) 1 / 2 ( H / 8 a ) 2

a s

8.434502906

[5] a s g 1 2 ( p t / H ) 8