OpenAI reports cyclic-length chromatic fixed-point loss

For every prime p, finite p-group G, subgroup H and height n≥0, the optimal chromatic fixed-point loss from H to G equals the shortest subnormal-chain length from H to G with cyclic quotients.

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Understanding the problem

Read the background

For every prime p, finite p-group G, subgroup H and height n≥0, the optimal chromatic fixed-point loss from H to G equals the shortest subnormal-chain length from H to G with cyclic quotients.

Why it matters

If correct, resolves the Kuhn–Lloyd equality and makes the optimal loss independent of chromatic height.

What counts as progress

Is cyclic subnormal-chain length the exact chromatic fixed-point loss for p-groups?

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