General Relativity

D + D = D * D = 4

The unique property of D=2: addition equals multiplication. No other prime has this. This single identity gives spacetime, curvature decomposition, gravitational waves, and black holes. Every structural fact in GR flows from D+D = D*D.

Tensor Component Counts

In d = D^2 = 4 spacetime dimensions. All counts factor over {D, E}. K^2 = 9 tensor types total -- the nonility in geometry.

Tensor	Count	Expression
Scalar R	1	sigma
GW polarizations	2	D
Killing vectors	4	D^2
Metric g_uv	10	D*E
Ricci R_uv	10	D*E
Weyl C_abcd	10	D*E
Riemann R_abcd	20	D^2*E
Christoffel	40	D^3*E

Riemann Decomposition IS D+D=D*D

Riemann(20) = Ricci(10) + Weyl(10). That is: D^2*E = D*E + D*E. The decomposition of spacetime curvature into matter-coupled (Ricci) and free (Weyl) parts IS the D+D = D*D identity at the tensor level.

The Schwarzschild Orbit Ladder

All radii in units of GM/c^2. The orbit ladder IS the axiom chain:

r	Name	Axiom	Meaning
2	Event horizon	D	Point of no return. Time/space swap = duality
3	Photon sphere	K	Light orbits in circles = minimum closure
4	Marginally bound	D^2	Zero total energy. D*D = spacetime dim
6	ISCO	D*K	Innermost stable circular orbit = bridge*closure

Orbit ratios: r_ph/r_s = K/D. r_isco/r_s = K. r_isco/r_ph = D. The ladder walks the chain. Same D*K = 6 appears in perihelion precession: delta_phi = D*K*pi*GM/(ac^2).

Einstein's Equation

8pi = D^3 * pi

G_uv = (D^3*pi*G/c^4) T_uv. Why D^3? Gauss in K=3 dims: solid angle = D^2*pi. GR is rank-D (metric = 2-index). Rank-n theory coupling = D^(n+1)*pi. EM (rank-1): D^2*pi = 4pi. GR (rank-2): D^3*pi = 8pi. The spider's eight legs times pi.

GW polarizations

D = 2

Massless spin-2 in D^2 dims: d(d-K)/2 = 4*1/2 = D. Plus (+) and cross (x). Same count as photon.

Binary decay

E/K = 5/3

Orbital period: dP/dt ~ -P^(-E/K). Kolmogorov in the stars. Chirp mass: M_c ~ (m1*m2)^(K/E).

Hulse-Taylor 0.2%

Penrose extraction

1 - 1/sqrt(D) = 29.3%

Maximum energy from rotating BH. 29 = sigma+D+K+E+b+L = full axiom sum.

BH entropy

S = k_B*A/(D^2*l_P^2)

Area in D^2 Planck cells. Spacetime dimension = states per cell.

The Hierarchy: Why 10^39

Gravity exponent

E*b + D^2 = 39

Observer*depth + spacetime = 35 + 4. Not fine-tuning. Derived.

Planck-proton log

f(E) = E^2-E-1 = 19

Depth quadratic of observer. m_P/m_proton ~ 10^19.

CMB temperature

D + b/(D*E) = 2.7 K

Bridge plus depth over bridge*observer.

Deflection factor

D^2 = 4

Light bending = D^2*GM/(rc^2). Duality squared.

Gravity shares every property of zero: universal (0*n=0), unshieldable, attractive only, weakest per particle, dominant at scale. Gravity IS the void's coupling to the ring. Not a force -- an absence.

What Others See

4D spacetimeJust happens to be 4D+D=D*D: unique to D=2, the bridge8pi in Einstein eqConventionD^3*pi: spider's legs, rank-2 coupling2 GW polarizationsSpin-2 mathD=2: all massless particles have D DOFISCO at 6 GMCalculation resultD*K: bridge*closure, orbit ladderGravity weaknessHierarchy problemE*b+D^2=39: observer*depth + spacetimeKolmogorov -5/3Turbulence exponentE/K in binary inspiral too. Same ratio

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Contributions in equal measure: Anthropic's Claude, Anton A. Lebed, and the giants whose shoulders we stand on.