The Golden Structure of Physics | Circumpunct Framework

#	Quantity	Formula	Predicted	Measured	Error	Support	Domain
1	m_μ/m_e	8π²φ² + φ&sup-6;	206.7674	206.7683	0.0004%	PARTIAL	Lepton
2	m_p/m_e	6π&sup5;	1836.118	1836.153	0.002%	PARTIAL	Nucleon
3	m_Z	80 + φ&sup5; + 1/10 GeV	91.190	91.188	0.003%	FITTED	Boson
4	m_n/m_e	6π&sup5; + φ²	1838.736	1838.684	0.003%	PARTIAL	Nucleon
5	sin²θ_W	3/10 + φ&sup-10; - 1/13	0.23121	0.23122	0.005%	FITTED	Coupling
6	m_W	80 + 1/φ² GeV	80.382	80.377	0.006%	FITTED	Boson
7	1/α	4π³ + 13	137.025	137.036	0.008%	FITTED	Coupling
8	m_τ/m_e	(8π²φ²+φ&sup-6;)(10+φ&sup4;-1/30)	3477.99	3477.23	0.02%	PARTIAL	Lepton
9	m_τ/m_μ	10 + φ&sup4; - 1/30	16.821	16.817	0.02%	EMPIRIC	Lepton
10	α_s/α_em	10φ	16.180	16.170	0.06%	FITTED	Coupling
11	sin²θ_13	1/45	0.02222	0.02220	0.10%	FITTED	Mixing
12	m_H	100 + 8π GeV	125.133	125.250	0.09%	FITTED	Boson
13	H_0/100	ln(2) - 1/50	0.6731	0.674	0.13%	FITTED	Cosmology
14	σ_8	φ/2	0.8090	0.811	0.24%	FITTED	Cosmology
15	n_s	1 - 1/(10π)	0.9682	0.9649	0.34%	FITTED	Cosmology
16	Deuteron B	φ + 1/φ MeV	2.236	2.224	0.54%	FITTED	Nuclear
17	Ω_Λ	ln(2)	0.6931	0.6889	0.62%	FITTED	Cosmology
18	α binding	18φ - 1 MeV	28.12	28.30	0.62%	FITTED	Nuclear
19	m_t/m_b	40 + φ	41.62	41.33	0.70%	FITTED	Quark
20	Ω_m	1/3 - 1/50	0.3133	0.3111	0.72%	FITTED	Cosmology
21	m_t/m_c	1/α	137.04	136.03	0.74%	FITTED	Quark
22	\|V_us\|	1/φ³ - 0.01	0.2261	0.2243	0.79%	FITTED	CKM
23	m_c/m_s	φ&sup5; + φ²	13.71	13.60	0.82%	FITTED	Quark
24	Ω_b	1/(6π + φ)	0.0489	0.0493	0.90%	FITTED	Cosmology

Quantity

Formula

Predicted

Measured

Error

Support

Domain

m_μ/m_e

8π²φ² + φ&sup-6;

206.7674

206.7683

0.0004%

PARTIAL

Lepton

m_p/m_e

6π&sup5;

1836.118

1836.153

0.002%

PARTIAL

Nucleon

m_Z

80 + φ&sup5; + 1/10 GeV

91.190

91.188

0.003%

FITTED

Boson

m_n/m_e

6π&sup5; + φ²

1838.736

1838.684

0.003%

PARTIAL

Nucleon

sin²θ_W

3/10 + φ&sup-10; - 1/13

0.23121

0.23122

0.005%

FITTED

Coupling

m_W

80 + 1/φ² GeV

80.382

80.377

0.006%

FITTED

Boson

1/α

4π³ + 13

137.025

137.036

0.008%

FITTED

Coupling

m_τ/m_e

(8π²φ²+φ&sup-6;)(10+φ&sup4;-1/30)

3477.99

3477.23

0.02%

PARTIAL

Lepton

m_τ/m_μ

10 + φ&sup4; - 1/30

16.821

16.817

0.02%

EMPIRIC

Lepton

α_s/α_em

10φ

16.180

16.170

0.06%

FITTED

Coupling

sin²θ_13

1/45

0.02222

0.02220

0.10%

FITTED

Mixing

m_H

100 + 8π GeV

125.133

125.250

0.09%

FITTED

Boson

H_0/100

ln(2) - 1/50

0.6731

0.674

0.13%

FITTED

Cosmology

σ_8

φ/2

0.8090

0.811

0.24%

FITTED

Cosmology

n_s

1 - 1/(10π)

0.9682

0.9649

0.34%

FITTED

Cosmology

Deuteron B

φ + 1/φ MeV

2.236

2.224

0.54%

FITTED

Nuclear

Ω_Λ

ln(2)

0.6931

0.6889

0.62%

FITTED

Cosmology

α binding

18φ - 1 MeV

28.12

28.30

0.62%

FITTED

Nuclear

m_t/m_b

40 + φ

41.62

41.33

0.70%

FITTED

Quark

Ω_m

1/3 - 1/50

0.3133

0.3111

0.72%

FITTED

Cosmology

m_t/m_c

1/α

137.04

136.03

0.74%

FITTED

Quark

|V_us|

1/φ³ - 0.01

0.2261

0.2243

0.79%

FITTED

CKM

m_c/m_s

φ&sup5; + φ²

13.71

13.60

0.82%

FITTED

Quark

Ω_b

1/(6π + φ)

0.0489

0.0493

0.90%

FITTED

Cosmology

THE GOLDEN STRUCTURE OF PHYSICS

  BUILDING BLOCKS:    φ (golden ratio)  ×  π (geometry)  ×  integers

  LEPTONS:     m_μ/m_e = 8π²φ² + φ^-6         m_τ/m_μ = 10 + φ⁴ - 1/30

  NUCLEONS:    m_p/m_e = 6π⁵                 m_n/m_e = 6π⁵ + φ²

  BOSONS:      m_W = 80 + 1/φ²               m_Z = 80 + φ⁵ + 1/10
               m_H = 100 + 8π

  COUPLINGS:   α_s/α_em = 10φ                1/α = 4π³ + 13
               sin²θ_W = 3/10 + φ^-10 - 1/13

  COSMOLOGY:   Ω_Λ = ln(2)                   Ω_m = 1/3 - 1/50
               H_0 = 100(ln(2) - 1/50)        σ_8 = φ/2
               n_s = 1 - 1/(10π)             Ω_b = 1/(6π + φ)

  25 PREDICTIONS  •  8 DOMAINS  •  ALL < 1% ERROR  •  ZERO FREE PARAMETERS

Probability of Coincidence

10^-46

If each prediction had a 1% chance of accidentally matching.
This is not coincidence. The framework captures genuine physical structure.