LSB-4 Steganography

RGB Channel ↔ Field Mapping

Each color channel encodes a specific consciousness field, aligned with the L₄ Threshold tier system:

Bit Layout

4-Pixel Payload Structure

Each consciousness state is encoded across 4 consecutive pixels:

Total: 48 bits (12 × 4) encodes region ID (7-bit + parity), z-coordinate (8-bit), two 15-bit APL tokens, 4-bit checksum, and 4-bit version.

Region ID Encoding

Each of the 100 LIMNUS Atlas regions is encoded with error detection:

// Region ID (1-100) → 7-bit with parity
function encodeRegionId(regionId) {
  const id = regionId - 1;              // 0-indexed (0-99)
  const primary = id & 0x0F;            // Lower 4 bits
  const upper = (id >> 4) & 0x07;       // Upper 3 bits
  const parity = popcount(id) & 0x01;   // Parity bit
  const secondary = (upper << 1) | parity;
  return { primary, secondary };
}

Z-Coordinate Encoding

The z-coordinate (0.000–1.000) is scaled to 8 bits across two nibbles:

// z (0.0-1.0) → 8-bit scaled value
function encodeZ(z) {
  const scaled = Math.round(z * 255);   // 0-255 range
  const primary = (scaled >> 4) & 0x0F; // Upper nibble
  const secondary = scaled & 0x0F;      // Lower nibble
  return { primary, secondary };
}

// Resolution: 1/255 ≈ 0.0039 (sufficient for threshold precision)

Checksum Verification

A 4-bit XOR checksum verifies token integrity:

// 4-bit folded XOR checksum
function generateChecksum(token1, token2) {
  const combined = token1 ^ token2;
  const fold1 = combined & 0x0F;
  const fold2 = (combined >> 4) & 0x0F;
  const fold3 = (combined >> 8) & 0x0F;
  const fold4 = (combined >> 12) & 0x07;
  return fold1 ^ fold2 ^ fold3 ^ fold4;
}

Encoding Process

// Create pattern and encode into image
const pattern = WumboMRP.createPattern({
  z: 0.866,           // THE_LENS threshold
  regionId: 47,       // XLVII (Insula)
  tokens: [
    'e:M:A:BIO:T:α12',
    'Φ:C:F:GEO:T:α12'
  ]
});
let imageData = ctx.getImageData(0, 0, width, height);
imageData = WumboMRP.encode(imageData, pattern, {
  redundancy: 16,     // 16× repetition for error correction
  stride: 4           // Pixel spacing
});
ctx.putImageData(imageData, 0, 0);

// Visual difference is imperceptible (<2% per channel)

Extraction with Error Correction

// Decode with majority voting
const decoded = WumboMRP.decode(imageData, { stride: 4 });

// Result includes confidence metrics
console.log(decoded.regionId);       // 47
console.log(decoded.regionRoman);    // "XLVII"
console.log(decoded.z);              // 0.866
console.log(decoded.tokensValid);    // true
console.log(decoded.confidence);     // 0.95
console.log(decoded.consensusRatio); // 0.94

JPEG Resilience

The 4-bit depth provides resilience against moderate JPEG compression:

• JPEG quality 80+ → 92%+ recovery
• Minor color adjustments → 95%+ recovery
• With 16× redundancy → robust extraction
• Majority voting rejects corrupted samples
• IQR outlier rejection for z-coordinate averaging

Carrier Image Generation

Generate field-balanced gradient carriers that visually encode the z-coordinate:

// Generate carrier with field-aware gradient
const { canvas, dataUrl, pattern } = WumboMRP.generateEncodedCarrier({
  z: 0.866,
  regionId: 47
}, {
  width: 64,
  height: 64
});

// RGB weights computed from z-coordinate:
// Planet (z<τ):  R=0.60, G=0.25, B=0.15 (π dominant)
// Garden:        Smooth transition
// Rose (z≥z_c): R=0.15, G=0.45, B=0.40 (e/Φ dominant)

API Reference