All Standard Model observables from three axioms · No free parameters ·
Click any card for detail · A Philosophy of Time, Space and Gravity
Gauge Sector
Gauge Group
Isom(\(S^3\!\times\!\mathbb{CP}^2\))
\(\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)\)
exact
Fermion Generations
\(\chi(\mathbb{CP}^2, \mathbf{3})\) — Atiyah-Singer index
3
observed: 3
exact
Koide Value \(K_\mathrm{eg}\)
Hodge\((\mathbb{CP}^2)\)
2/3
6 ppm from observed
6 ppm
Unified Coupling \(\alpha_U\)
instanton / Chern-Simons
1/42
consistent
✓
Weak Coupling \(1/\alpha_2(M_Z)\)
\(42 \times 5/7\)
30
observed: 30.00
exact
Strong Coupling \(1/\alpha_s(M_Z)\)
\(42/5\)
8.40
observed: 8.48
0.96%
Hypercharge \(1/\alpha_1(M_Z)\)
prime self-reference
59
observed: 59.00
exact
Fine Structure \(1/\alpha_\mathrm{em}\)
bilateral spin variables · \(\pi(p)=33\)
137
observed: 137.036
0.026%
Weinberg Angle \(\sin^2\theta_W\)
bilateral fixed point
0.23122
observed: 0.23122
0.0001%
Neutrino Sector
Neutrino Mass \(m_3\)
\(\tau_0\) massless — inverted ordering
0 exact
<0.45 eV
✓
Neutrino Mass Ordering JUNO ~2027
Mirror Koide \(K_\nu = \mathrm{Vol}(\mathbb{CP}^2)/\pi^2\)
Inverted, \(m_3=0\)
binary test
Neutrino Koide \(K_\nu\)
\(\mathrm{Vol}(\mathbb{CP}^2)/\pi^2\)
1/2
observed: 0.500007
0.001%
Neutrino Mass Sum \(\Sigma m_i\)
\(m_1 + m_2\) (IO, \(m_3=0\))
99.9 meV
<120 meV (Planck)
✓
PMNS \(\theta_{12}\)
\(\pi/3 - \arctan(1/2)\)
33.43°
33.41°
0.06%
PMNS \(\theta_{13}\)
\(\arcsin(1/\sqrt{42})\)
8.88°
8.58°
3.5%
PMNS \(\theta_{23}\)
\(\arctan(7/6)\) (IO)
49.40°
49.5°
0.2%
PMNS CP Phase \(\delta_\mathrm{CP}\)
phase of \(\tau_0\)
270°
282°±28°
0.5σ
Quark Mixing (CKM)
CKM \(\theta_{12}\)
\(\arcsin(2/9)\)
12.84°
13.04°
1.5%
CKM \(\theta_{13}\)
\(\theta_{13}^\mathrm{PMNS}\cdot\alpha_U\)
0.204°
0.201°
1.5%
CKM \(\theta_{23}\)
\(\arctan(1/24)\)
2.386°
2.380°
0.25%
CKM CP Phase \(\delta_\mathrm{CKM}\)
\(\arctan(13/6)\)
65.22°
65.55°
0.5%
Fermion Masses & QCD
Tau Mass \(m_\tau\)
\(\tfrac{3}{2}e^{-(5-4\alpha/3)}v/\sqrt{2}\)
1776.858 MeV
1776.860 MeV
0.0001%
Muon Mass \(m_\mu\)
\(\tfrac{2}{3}e^{-7}v/\sqrt{2}\)
105.841 MeV
105.660 MeV
0.17%
Electron Mass \(m_e\)
Koide\((m_\tau, m_\mu)\)
0.5106 MeV
0.5110 MeV
0.08%
Top Quark Mass \(m_t\)
\((v/\sqrt{2})\,e^{-(8\sqrt{5}-17)/12}\)
161.7 GeV
162.5 GeV
0.5%
QCD Scale \(\Lambda_\mathrm{QCD}\)
\(\sqrt{M_Z \times m_e}\)
0.216 GeV
0.217 GeV
0.5%
Strange Quark \(m_s\)
two-ladder geometric mean
94.6 MeV
93.4 MeV
1.3%
Pion Decay Constant \(f_\pi\)
bilateral completeness
0.09197 GeV
0.09210 GeV
0.14%
Higgs Sector
Higgs VEV \(v\)
two-loop bilateral
246.21 GeV
246.22 GeV
0.003%
Higgs Mass \(m_H\)
Born rule + gauge correction
125.249 GeV
125.25 GeV
0.0007%
Charge Quantisation
Proton / Electron Charges
\(\mathrm{Re}(e^{i\cdot0})\), \(\mathrm{Re}(e^{i\pi})\)
+1, −1
+1, −1
exact
Quark Charges
Koide egress fraction \(K_\mathrm{eg}=2/3\)
+2/3, −1/3
+2/3, −1/3
exact
Gravity & Cosmology
Einstein Field Equations
A1+A2+A3+Lovelock uniqueness
\(G_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi G T_{\mu\nu}\)
confirmed
Newton's Constant \(G_N\)
\(e^{-2p_{12}}/(36(v/\sqrt{2})^2)\)
\(6.673\times10^{-39}\)
\(6.674\times10^{-39}\)
0.02%
Cosmological Constant \(\Lambda\)
\((H_0/M_\mathrm{Pl})^2\)
\(1.5\times10^{-122}\)
\(2.9\times10^{-122}\)
order
Force Hierarchy
ladder dominance by prime index
QCD / EW / EM / grav
confirmed
Mathematical Structure
\(\pi\) as angular invariant
Weyl equidistribution on zeros/primes/gaps
\(\pi\)
exact
RGE Beta Coefficients
\(b_0^{SU(3)} = p_4 = 7\), \(b_0^{SU(2)} = p_2 = 3\)
7, 3
7, 3
exact
Yang-Mills Mass Gap
\(\Delta = t_1 / 2\pi\)
2.249
open problem
conjecture
Dark Prime Proximity
nearest prime to \(\exp(t_n/\sqrt{2\pi})\)
\(\epsilon_n \ll\) Cramér
10 orders, \(R_n\geq4\)
conjecture
Dynamical Framework
Born Rule
bilateral crossing product
\(|\psi|^2\)
confirmed
Spin-Statistics
crossing closure (Möbius twist)
fermions / bosons
confirmed
Second Law of Thermodynamics
τ-monotonicity (A3)
entropy increases
confirmed
Least Action Principle
return to \(\infty_0\): \(\delta S = 0\)
Euler-Lagrange equations
derived