Every claim in this atlas has running code behind it. No trust required.
Five programs. 1490 lines of C. No libraries, no frameworks, no dependencies. Just arithmetic. A classifier that sees things it was never shown. Error correction that heals itself. Your DNA read as a ring. Numbers that literally sing. A complete map of the structure. All of it compiles with one command.
Train on 10%. Test on 90%. CRT sees everything — even what it has never been shown.
928 CRT parameters vs 76,230 standard. Five small softmax heads instead of one giant one. Each channel generalizes independently. Unseen combinations are predicted from seen values.
Interactive version →Corrupt any channel. The guardian (L=11) detects and corrects — for free.
210 CRT levels vs 256 INT8 levels. When a bit flips, INT8 drops 34.4 dB. CRT detects it, locates it, fixes it. Cost: 0.2 dB signal quality. The 5th channel (L=11) is free error correction.
Interactive version →The genetic code IS a CRT decomposition. Z/21 = Z/K x Z/b. Life chose the same mathematics.
64 codons map to 21 targets through Z/3 (reading frame) and Z/7 (codon class). Mutual information between channels: 2.0% (near-independent). Wobble position degeneracy = biological error correction.
Interactive version →Close your eyes and hear the eigenvalue. Five harmonics at prime frequencies. The ring sings.
The eigenvalue IS consonance. C sounds like a major chord. The void sounds like everything at once. Walking the Cayley graph is a melody. The overtone series IS the axiom chain.
Interactive version (with sound) →Walk the ring. See every element. Explore the whole structure with your own hands.
Terminal-based explorer. Eigenvalue histogram. Element inspector. Cayley walk. The complete ring in one program.
Interactive version (web) →← Chapter 7: Five Tricks Chapter 9: Millennium Problems →
The Interactive Atlas · Z/2310Z → Z/970200Z · Chapter 8 of 14