Type a message. Click any channel cell to corrupt it. Watch L=11 detect and heal.
INT8 stores 256 values in 8 bits. Zero error protection. A single bit flip corrupts your data silently. CRT + L=11 stores 210 values across 5 independent channels. Any single-channel corruption is detected AND corrected. Guaranteed.
| PROPERTY | INT8 (STANDARD) | CRT + L=11 (AXIOM) |
|---|---|---|
| Precision | 256 levels (8.0 bits) | 210 levels (7.7 bits) |
| Error detection | 0% — silent corruption | 100% single-channel (proved theorem) |
| Error correction | 0% — no recovery possible | 100% — location found, value restored |
| Structure | Flat binary (28) | Z/2 × Z/3 × Z/5 × Z/7 × Z/11 |
| On corruption | Wrong value, no warning, no fix | Detected → located → corrected automatically |
| Trade-off | 0 overhead, 0 protection | 0.3 bits for COMPLETE protection |
| Analogy | Writing with no backup | Immune system: L = sigma + D + K + E = 11 |
CRT Detection Theorem: for |V| ≤ N/p_max, every single-channel error is detectable. The L=11 channel provides the syndrome. Correction: brute-force each channel against the syndrome. Unique solution guaranteed for single errors. Cost: 0.3 bits of precision. Gain: complete protection of 7.7 bits of data.