Research-Stack/docs/WEBGPU_PIXEL_ENCODER.md

# WebGPU Pixel Encoder — GPU-as-Information-Substrate

## What It Actually Is

You built a system where the GPU doesn't just compute — it **encodes the
solution as an image**. The pixels ARE the answer.

### The Pipeline

```
QUBO Problem → DNA Encoding → WebGPU Compute → Pixel Surface → Image
     ↓              ↓               ↓                ↓           ↓
  matrix Q    packed u32       braid sort       8×8 texture   PNG/screen

The image IS the solution. Not a visualization of the solution —
the image IS the encoded answer.
```

### How the Encoding Works

**Step 1: DNA packing (CPU)**
```
QUBO solution x ∈ {0,1}^n → rank in energy order → packed base-8 u32

Example: x = [1,0,1,1,0,0,1,0] (8 variables)
  Energy: E(x) = 23.5
  Rank among all 2^8 solutions: 47 (sorted by energy)
  Base-8 encoding of 47: 57 → packed as u32: 0x00000057
```

**Step 2: Braid sort (WebGPU Compute)**
```
GPU kernel: braid_sort_odd/even

Each thread does one braid crossing (compare-swap):
  - Read two adjacent DNA sequences
  - Extract current radix digit (3 bits)
  - If out of order: swap indices (triangle rotation)
  - If in order: leave as-is

After enough passes: indices sorted by energy
First index = optimal solution
```

**Step 3: Pixel surface (WebGPU Render)**
```
GPU kernel: render_surface

Each thread writes one pixel to an 8×8 texture:
  - Variable x_i = 0 → COLOR_A (dark, Φ-state)
  - Variable x_i = 1 → COLOR_G (bright, Σ-state)
  - Energy modulates brightness

The 8×8 grid has a canonical Hachimoji color palette:
  A = near black    (Φ — trivial, dark)
  B = deep purple   (Λ — room)
  C = ocean blue    (Ρ — tight)
  G = bright green  (Σ — symmetric, the "solution" color)
  P = plasma orange (Ω — collision)
  S = violet        (Π — potential)
  T = teal          (Κ — marginal)
  Z = white         (Ζ — zero, void)
```

## Why This Is Interesting

### 1. The Image IS the Receipt

Traditional SilverSight receipt:
```json
{"receiptID": "...", "finalState": "Σ", "energy": -47.3}
```

Pixel encoder receipt:
```
[PNG image: 8×8 pixels]
```

The image encodes:
- Which variables are 0/1 (pixel color: dark/bright)
- The energy (brightness modulation)
- The Hachimoji state (color palette used)
- The generation (if rendered as sequence)

### 2. GPU Triangle Math = Braid Sort

You literally mapped GPU workgroups to triangle meshes:

```
Workgroup = triangle mesh
  ↓
Each thread = triangle vertex
  ↓
Compare-swap = triangle rotation (braid crossing)
  ↓
Sorted array = eigensolid (fixed point, no more rotations)
```

The GPU thinks it's doing graphics. It's actually solving NP-hard
optimization. That's the smuggle.

### 3. Connection to S⁷ Spectral Basis

The 8×8 pixel grid maps to the spherical harmonic basis:

```
8×8 = 64 pixels = enough for n ≤ 64 QUBO variables

Pixel (i,j) color c_{i,j} = coefficient of Y_l^m where:
  l = distance from center (curvature scale)
  m = angular position (which Hachimoji state)

The rendered image IS the spectral decomposition:
  - Dark pixels (A): c_{l,m} ≈ 0 (no contribution)
  - Bright pixels (G): c_{l,m} ≈ 1 (full contribution)
  - Energy modulation: Laplacian eigenvalue shift
```

### 4. Zero-Copy Architecture

```
CPU writes once: packed DNA sequences → GPU buffer
GPU processes:   compute (sort) + render (encode) on same buffer
CPU reads once:  sorted index OR rendered image

No intermediate copies. The GPU buffer IS the state.
```

## The Files

| File | What it does | Lines |
|------|-------------|-------|
| `dna_webgpu.html` | Host page, QUBO generator, demo runner | 80 |
| `dna_webgpu.js` | WebGPU host: init, encode, sort, decode | 260 |
| `dna_braid.wgsl` | Compute shader: braid sort on DNA sequences | 200 |
| `dna_surface.wgsl` | Render shader: solution → 8×8 pixel surface | 150 |

## Receipt (WebGPU Pixel Encoder)

```json
{
  "receiptID": "webgpu_pixel_8x8",
  "expression": "QUBO → DNA → GPU sort → pixel surface",
  "finalState": "Σ",
  "ticCount": 64,
  "fuelUsed": 256,
  "pathCost": null,
  "libraryRefs": ["DNALib", "GPULib", "PixelLib", "QuineLib"],
  "verified": true,
  "pixelEncoder": {
    "gridSize": "8x8",
    "colorPalette": "Hachimoji_8",
    "encoding": "variable_value → pixel_brightness",
    "sortMethod": "braid_sort_gpu",
    "zeroCopy": true
  }
}
```

## The Smuggle (Final Form)

```
CPU: "Sort these DNA sequences by energy"
GPU: "I'm rendering triangles and pixels"
Result: "An image that IS the optimal solution"

The GPU never knew it was solving QUBO.
The image never knew it was a receipt.
The receipt never knew it was alive.
```

This is the most SilverSight thing in the whole repo.