The Chinese Remainder Theorem decomposes this number into seven independent channels -- one per prime factor. This site explores what that structure contains. Everything is verifiable. Everything is CC0.
The Chinese Remainder Theorem (300 BC) says: a number modulo a product of coprime factors splits uniquely into one residue per factor. One value, seven independent views. Change one channel, the others don't move.
Modular multiplication is bijective -- every input maps to a unique output when the weight is coprime. Wrong weights produce completely wrong results. No graceful degradation. This makes the ring a non-degenerate computation substrate.
Each prime contributes one independent channel. The product of all seven moduli is 214,414,200.
| Prime | Modulus | Role |
|---|---|---|
| 2 | mod 8 | Even/odd. The only channel with depth 3: four self-inverse elements. |
| 3 | mod 9 | Minimum for majority. Three elements decompose any other. |
| 5 | mod 25 | Self-blind: 5^2 divides the ring but 5 does not divide 24. |
| 7 | mod 49 | Deepest resolution. Controls the spectral gap. |
| 11 | mod 11 | Error detection. Parity check: 1+2+3+5 = 11. |
| 13 | mod 13 | Chain stopper. Dual parity with 11 catches all single-channel errors. |
| 17 | mod 17 | Ring closer. 5 * 7 = 1 mod 17. Enables triple-parity ECC. |
8 * 9 * 25 * 49 * 11 * 13 * 17 = 214,414,200.
The full structure builds in seven steps -- one per prime. Each ring adds a channel or increases resolution.
| Ring | Value | What changes |
|---|---|---|
| Z/6 | 6 | Two channels: mod 2, mod 3. The first split. |
| Z/30 | 30 | Add 5. Three channels. Patterns emerge. |
| Z/210 | 210 | Add 7. Four data channels. |
| Z/2,310 | 2,310 | Add 11. Error detection available. |
| Z/970,200 | 970,200 | Fatten: 2->8, 3->9, 5->25, 7->49. Full resolution. |
| Z/12,612,600 | 12,612,600 | Add 13. Six channels. 420-step maximum cycle. |
| Z/214,414,200 | 214,414,200 | Add 17. Seven channels. Triple-parity ECC (rate 4/7). |
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