Add TC0 README

TC0/README.md

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+# TC⁰ Groups (Solvable)
+
+This directory contains all solvable permutation groups from our dataset. These groups can theoretically be solved by constant-depth threshold circuits (TC⁰), which means models like Transformers and standard SSMs should be able to learn them.
+
+## Groups in this category:
+
+### Small Symmetric/Alternating (Solvable)
+- S3 (order 6)
+- S4 (order 24)
+- A3 (order 3)
+- A4 (order 12)
+
+### Cyclic Groups (All solvable abelian)
+- C3 through C30
+
+### Dihedral Groups (All solvable)
+- D3 through D20
+
+### Other Solvable Groups
+- V4: Klein four-group (order 4)
+- Q8, Q16, Q32: Quaternion groups
+- Elementary abelian groups (Z_p^k)
+- F20, F21: Frobenius groups
+
+## Key Property
+All these groups have a composition series with abelian quotients, making them solvable and placing them in TC⁰.