Does this ring have COMPUTATIONAL advantages over other rings? We test 8 rings on the same learning task: context-dependent function selection with per-channel evolution. Same architecture, same seeds, different moduli.
The task: 4 functions (ring multiplications by different weights), 160 training examples, 200 generations of per-channel evolutionary search. Each ring gets the same random seed and the same task structure. The only variable is the moduli.
Per-channel hit percentage (ch_score / max). Higher = better per-channel learning. 200 gen evolution, seed 42/100/200.
All channels correct simultaneously. Harder than ch_score -- requires coherence across channels. Out of 160 training examples.
CRT as computation substrate works for ALL rings. The technique is universal. The ring's specific contribution is the Pareto exponent distribution: it helps exact reconstruction (+27% over random) despite slightly harder per-channel search (-2% ch_score). Chain constraints provide no measurable ch_score advantage.
Fewer channels is better for per-channel learning (4ch 90% vs 7ch 74%). Excessive exponents hurt (FAT 67% vs ring 74%). The exponents {3,2,2,2,1,1,1} beat both uniform (BALANCED 66%) and over-fat (FAT 67%). The ring's channel distribution is the right one for this task.
Open question: is there a ring that beats Z/214,414,200 on BOTH ch_score AND exact match? Z/210 (4ch) wins ch_score but has fewer channels. A 4-channel prime-power ring [8,9,25,49] might combine Z/210's ch_score with the 7-channel ring's exact coherence.
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