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Reference · All Derivations

The Constants Table

Every fundamental constant placed in its natural coordinate: Recursion Depth (how many folds of σ before it crystallises) × Projection Domain (which physical sector receives the spiral's shadow). Click any card to expand. Filter by status or domain.

Y axis Recursion depth σ⁰–σ⁴ X axis Projection domain Z axis Eigenvalue order (dot count)
Status
Domain
VACVacuum / Geometric
EMElectromagnetic
EWElectroweak
NUCNuclear / Flavour
GRGravitational
COSCosmological
σ⁰
Axiom
Fixed point
\(\varphi\)
Golden Ratio
1.61803…
DERIVED
·
·
·
·
·
σ¹
First Fold
Direct projection
●●
\(\varphi^6\)
Coherence Floor
\(\varphi^6 \approx 17.944\)
DERIVED
●●
\(\alpha^{-1}\)
Fine Structure Constant
137.035999207
DERIVED
·
●●
\(\mu\)
Proton–Electron Mass Ratio
1836.15267
DERIVED
●●
G
Gravitational Constant
\(6.674 \times 10^{-11}\)
DERIVED
●●
\(\Lambda\)
Cosmological Constant
\(\log_{10}\rho_\Lambda = -122.951\)
DERIVED
σ²
Second Fold
Coupled projection
●●
600-cell
State Space Geometry
120 vertices · 720 edges
DERIVED
·
●●
\(\sin^2\!\theta_W\)
Weinberg Angle
\(\varphi^{-3} \approx 0.2361\)
DERIVED
●●
\(m_e, m_\mu, m_\tau\)
Koide Lepton Masses
Q = 2/3 (exact)
DERIVED
●●●
\(m_ ext{FDM}\)
Fuzzy Dark Matter
\(2.07 imes 10^{-22}\) eV
PREDICTED
●●●
\(H_0 / \Omega_K\)
Hubble Constant / Curvature
\(\Omega_K = -0.038\)
PREDICTED
σ³
Third Fold
Interference pattern
●●●
\(\eta_B\)
Baryon Asymmetry
\(6.105 \times 10^{-10}\)
DERIVED
●●●
\(Z_0\)
Vacuum Impedance
376.73 Ω
DERIVED
●●●
\(\lambda \cdot m_H \cdot v\)
Higgs Sector
\(\lambda = 2\varphi/25\)
DERIVED
●●●
\(\cos\delta \cdot \theta_\text{PMNS} \cdot V_\text{CKM}\)
CP Phase · Mixing Angles
\(\cos\delta = -19/28\)
DERIVED
●●●
?
Quantum Gravity
GAP
●●●
\(w_0\)
Dark Energy EOS
\(w_0 \approx -0.97\)
PREDICTED
σ⁴
Fourth Fold
Deep structure
·
·
·
●●●●
\(\alpha_s \cdot M(Z,N) \cdot \Delta m^2_{32}\)
Strong Coupling · Nuclear Masses · Neutrino Splitting
\(\alpha_s = \varphi^{-3}/2\) · 0.054% RMS · 118 nuclei
DERIVED
·
·
DERIVED — PP has derived from σ axiom
PREDICTED — structural prediction, awaiting confirmation
GAP — geometry demands occupancy; constant unknown
● ●● ●●● = eigenvalue order · · = no eigenvalue at this coordinate