All Y-friezes come from $\mathrm{SL}_2$-friezes

What the math gives to ML

The paper gives an explicit local algebra for converting Y-friezes into positive integer SL2-frieze factors: entries are represented by adjacent products of auxiliary variables, and the Y-diamond recurrence propagates these factors while preserving compatibility. This is transferable as a constrained multiplicative feature module or recurrent 2D cellular layer whose outputs satisfy exact local identities instead of learning unconstrained interactions. The most credible neural use is not to encode polygon combinatorics literally, but to replace an unconstrained multiplicative block with a differentiable frieze-consistent block and test whether its built-in compatibility improves stability or parameter efficiency.