CRT GPU Compute

How It Works

CRT DECOMPOSITION: n -> (n%8, n%9, n%25, n%49, n%11)
  = 5 INDEPENDENT channels
  = 5 INDEPENDENT GPU workgroups
  = ZERO cross-channel synchronization

GPU COMPUTE SHADER: each invocation processes one ring element.
  1. Decompose into 5 CRT channels (parallel)
  2. Per-channel ring arithmetic (parallel, zero sync)
  3. Reconstruct via CRT (parallel)

N = 970200 = 2^3 * 3^2 * 5^2 * 7^2 * 11
All 970,200 elements processed simultaneously on GPU.

WHY THIS MATTERS: CRT decomposition IS the GPU parallelization strategy.
No manual workgroup design. No shared memory management.
The algebraic structure does the engineering for you.

Block-diagonal Jacobian = no cross-channel gradients.
Training a CRT neural network: each channel = independent backprop.
5 GPU workgroups, zero inter-workgroup communication.

The axiom wasn't designed for GPUs. GPUs were designed for this.

GPU Status

Checking WebGPU support...

1. CRT Ring Arithmetic Benchmark

Process 10K elements 100K elements 970,200 (full ring) 5M elements Operation: CRT Decompose Ring Add (a+b mod N) Ring Multiply (a*b mod N) Eigenvalue Compute Full Pipeline (decompose + op + reconstruct) Run Benchmark

2. Channel Independence Visualization

Each channel runs as an independent GPU workgroup. Zero synchronization needed.

3. L=11 ECC on GPU

Error correction runs as a 6th workgroup. Free integrity check.

4. Block-Diagonal Backprop

CRT Jacobian = diag(J₈, J₉, J₂₅, J₄₉, J₁₁). No cross-channel gradients.

5. Scaling Analysis