{ 2, 3, 5, 7, 11 }

General Relativity from Ten Terms

D+D = D*D. This single identity — unique to D=2 — gives 4D spacetime, curvature decomposition, the orbit ladder, gravitational waves, and black hole thermodynamics.

Part of the Decality — one ring (Z/970200Z), 108 lattice structures.

The **D+D = D*D** Theorem

D + D = D * D = 4

The unique property of D = 2: addition and multiplication coincide.
This is why the bridge is special. No other prime has this.

One identity, all of GR: Spacetime = K + sigma = D + D = D*D = 4. Riemann(20) = Ricci(10) + Weyl(10). Event horizon at r = D. GW polarizations = D. Every structural fact in general relativity flows from this single equation.

Tensor Component Counts

Click any tensor to see its axiom structure. All counts exact in d = D^2 = 4.

Click a tensor above to see its meaning.

The D^k*E hierarchy: Every GR tensor has D^k * E components for k = 0, 1, 2, 3. Scalar (sigma) → GW/multipole (D) → metric/Ricci/Weyl/Einstein (D*E) → Riemann (D^2*E) → Christoffel (D^3*E). Exactly K^2 = 9 tensor types. The nonility in geometry.

The Schwarzschild Orbit Ladder

Critical radii in units of GM/c^2. Click each zone.

Click a radius above to see its physics.

Einstein's Equation

        G_uv = (D^3 * pi * G / c^4) T_uv
      

8pi = D^3*pi. The spider's eight legs times pi.

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.

c^4 = c^(D^2). Light raised to spacetime dimension.

        S = c^4 / (D^4*pi*G) * int R*sqrt(-g)
      

D^4 = 16 = D^(D^2). Bridge raised to spacetime.

The Einstein-Hilbert action. D^4*pi*G = 16*pi*G in the denominator. The action that generates all of GR contains D^(D^2) — the bridge bootstrapped through its own spacetime.

Gravitational Waves

D = 2 Polarizations

In D^2=4 spacetime, massless spin-2: d(d-K)/2 = 4*1/2 = D = 2.
Plus (+) and cross (x). Duality in radiation.

Photon (spin-1): D=2 polarizations. Graviton (spin-2): D=2 polarizations. All massless particles in D^2 dims have D physical DOF.

Kolmogorov in the Stars

Binary inspiral decay: dP/dt ~ -P^(-E/K) = -P^(-5/3).
The Kolmogorov exponent governs orbital decay!

Chirp mass: M_c = (m1*m2)^(K/E) / (m1+m2)^(1/E).
GW observation = E-weighted measurement. K/E = 3/5 = inverse Kolmogorov.
Hulse-Taylor: confirmed to 0.2% (Nobel 1993).

Black Hole Thermodynamics

Hawking Temperature

T = hbar*c^3 / (D^3*pi * k_B * G * M)

D^3*pi again — same coupling as Einstein equation. BH entropy:

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

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

Penrose Energy Extraction

Maximum from a rotating BH: 1 - 1/sqrt(D) = 29.3%

The bridge D=2 sets the extraction limit. sqrt(D) = the geometric mean of sigma and D*D. Nature allows you to extract everything above this mean.

29 = sigma+D+K+E+b+L = full axiom sum. The total weight of the axiom chain is the Penrose ceiling.

GR Axiom Map

Quantity	Value	Expression	Primes

Gravity as Void

Gravity shares every property of zero: universal (couples to everything, like 0*n=0), unshieldable (no negative mass, no negative zero), attractive only (absorber), weakest per particle (no structure), dominant at scale (ground state). Gravity IS the void's coupling to the ring. Not a force — an absence.

Hierarchy Problem

alpha_G ~ 10^(-39). Why 39?
39 = E*b + D^D = 35 + 4
= PLANCK + SPACETIME = observer*depth + bridge^bridge.
57 + 2^2

Planck-Proton Ratio

m_P / m_proton ~ 10^19.
19 = f(E) = E^2 - E - 1
The depth quadratic of the observer. The 8th prime.
5^2 - 5 - 1 = 19

Verify tensor counts in .ax Verify orbit ladder in .ax Electromagnetism Quantum Mechanics All Constants Black Holes

Number Theory Thread

D+D=D*D is unique to D=2 — the same prime whose Cunningham chain generates the axiom. Einstein’s 8π = D³·π carries the spider’s legs. Riemann tensor has D²·E=20 independent components; Weyl tensor D²·E−D²−sigma=9=K². ISCO at r=D*K, photon sphere at r=K — the orbit ladder is the axiom chain. Kolmogorov E/K in binary inspiral = h(−47)/h(−23) from D-chain class numbers. Gravitational wave polarizations = D = 2, same as every massless particle.

D-chain class numbers → Partitions & the gate → Modular forms →

Paradigm Contrast

4D spacetime: "just happens to be 4"

D+D=D*D: unique to D=2, the bridge

8pi in Einstein eq: "convention"

D^3*pi: spider's legs, rank-2 coupling

2 GW polarizations: "spin-2 math"

D=2: all massless particles, duality

ISCO at 6GM: "calculation result"

D*K: bridge*closure, orbit ladder

Gravity weakness: "hierarchy problem"

E*b+D^D=39: observer*depth+spacetime

Kolmogorov -5/3 in turbulence

E/K in binary inspiral too

20 Riemann components: "d^2(d^2-1)/12"

D^2*E: duality^2 * observer