Update README with complete group inventory (94 groups: 58 TC^0, 36 NC^1)

README.md

@@ -606,13 +606,13 @@ Recent theoretical work demonstrates that TC⁰ models, including Transformers a
 The dataset is organized in three complementary ways to support different research approaches:
 
 ### 1. Flat Organization (data/)
-All 59 individual group datasets are available for direct access in a flat structure, facilitating straightforward loading and comparison across groups.
+All 94 individual group datasets are available for direct access in a flat structure, facilitating straightforward loading and comparison across groups.
 
 ### 2. TC⁰ Complexity Class (TC0/)
-Contains 43 solvable groups that can theoretically be computed by constant-depth threshold circuits. These groups serve as positive controls where current neural architectures should succeed.
+Contains 58 solvable groups that can theoretically be computed by constant-depth threshold circuits. These groups serve as positive controls where current neural architectures should succeed.
 
 ### 3. NC¹ Complexity Class (NC1/)
-Contains 14 non-solvable groups requiring logarithmic-depth circuits for computation. These groups represent problems that are provably beyond the computational capacity of TC⁰ models.
+Contains 36 non-solvable groups requiring logarithmic-depth circuits for computation. These groups represent problems that are provably beyond the computational capacity of TC⁰ models.
 
 ## Usage
 
@@ -621,11 +621,13 @@ Contains 14 non-solvable groups requiring logarithmic-depth circuits for computa
 ```python
 from datasets import load_dataset
 
-# Load specific group datasets
-s5_data = load_dataset("BeeGass/Group-Theory-Collection", data_dir="data/s5")
-a4_data = load_dataset("BeeGass/Group-Theory-Collection", data_dir="data/a4")
+# Load specific group datasets using config names
+s5_data = load_dataset("BeeGass/Group-Theory-Collection", name="s5")
+a4_data = load_dataset("BeeGass/Group-Theory-Collection", name="a4")
+m11_data = load_dataset("BeeGass/Group-Theory-Collection", name="m11")
 
-# Load from complexity-organized directories
+# Alternative: Load from data directories
+s5_data = load_dataset("BeeGass/Group-Theory-Collection", data_dir="data/s5")
 tc0_cyclic = load_dataset("BeeGass/Group-Theory-Collection", data_dir="TC0/c10")
 nc1_symmetric = load_dataset("BeeGass/Group-Theory-Collection", data_dir="NC1/s7")
 
@@ -640,34 +642,40 @@ Each example contains the following fields:
 
 ```python
 {
-    'input_sequence': "123 456 789",     # Space-separated permutation IDs to compose
-    'target': "234",                      # Result of composition as string
-    'sequence_length': 3,                 # Number of permutations in this sequence
-    'group_degree': 7,                    # Degree of the permutation group (e.g., S7 acts on 7 elements)
-    'group_order': 5040,                  # Order (size) of the group (e.g., |S7| = 7!)
-    'group_type': "symmetric"             # Type of the group
+    'input_sequence': "123 456 789 ... (1024 IDs)",  # Space-separated permutation IDs (fixed length 1024)
+    'target': "234",                                  # Result of composition as string
+    'sequence_length': 1024,                          # Always 1024 (fixed length sequences)
+    'group_degree': 7,                                # Degree of the permutation group (e.g., S7 acts on 7 elements)
+    'group_order': 5040,                              # Order (size) of the group (e.g., |S7| = 7!)
+    'group_type': "symmetric"                         # Type of the group
 }
 ```
 
-Note: Each dataset contains sequences of varying lengths. The 'sequence_length' field indicates how many permutations are in that particular example's input sequence (ranging from 3 to 1024).
+Note: All sequences contain exactly 1024 permutation IDs. The provided target is the composition of all 1024 permutations. Researchers who need shorter sequences can take a subset of the permutation IDs and recompute the composition target for that subset.
 
-### Filtering by Sequence Length
+### Working with Different Sequence Lengths
 
-Since each dataset contains sequences of all lengths from 3 to 1024, researchers often need to filter for specific length ranges:
+To work with sequences shorter than 1024, take a subset of permutation IDs and compute their composition:
 
 ```python
 # Load full dataset
-dataset = load_dataset("BeeGass/Group-Theory-Collection", data_dir="data/s5")
+dataset = load_dataset("BeeGass/Group-Theory-Collection", name="s5")
+
+# Example: Work with sequences of length 32
+example = dataset['train'][0]
+all_ids = example['input_sequence'].split()  # All 1024 permutation IDs
+
+# Take first 32 permutation IDs
+subset_ids = all_ids[:32]
 
-# Filter for sequences of specific lengths
-short_sequences = dataset.filter(lambda x: x['sequence_length'] <= 32)
-medium_sequences = dataset.filter(lambda x: 32 < x['sequence_length'] <= 128)
-length_16_only = dataset.filter(lambda x: x['sequence_length'] == 16)
+# You would need to recompute the target for this subset
+# The new target would be the composition of these 32 permutations
+# (Implementation depends on your permutation representation)
 ```
 
 ## Group Inventory
 
-### TC⁰ Groups (Solvable) - 75 Groups
+### TC⁰ Groups (Solvable) - 58 Groups
 
 | Group Family | Groups | Orders | Mathematical Properties |
 |--------------|--------|--------|------------------------|
@@ -675,19 +683,19 @@ length_16_only = dataset.filter(lambda x: x['sequence_length'] == 16)
 | Alternating | A3, A4 | 3, 12 | Solvable for n ≤ 4 |
 | Cyclic | C2-C30 (all) | 2-30 | Abelian groups |
 | Dihedral | D3-D20 (all) | 6-40 | Symmetries of regular polygons |
-| Klein | V4 | 4 | Smallest non-cyclic abelian group |
+| Klein | V4 | 4 | Smallest non-cyclic abelian group (isomorphic to Z₂²) |
 | Quaternion | Q8, Q16, Q32 | 8, 16, 32 | Non-abelian 2-groups |
 | Elementary Abelian | Z2^[1-5], Z3^[1-4], Z5^[1-4] | Various | Direct products of cyclic groups |
 | Frobenius | F20, F21 | 20, 21 | Transitive permutation groups |
-| Projective Special Linear | PSL(2,2), PSL(2,3), PSL(2,4), PSL(2,8), PSL(2,9), PSL(3,4) | Various | Some solvable PSL groups |
+| Projective Special Linear | PSL(2,2), PSL(2,3) | 6, 12 | Solvable PSL groups |
 
-### NC¹ Groups (Non-Solvable) - 19 Groups
+### NC¹ Groups (Non-Solvable) - 36 Groups
 
 | Group Family | Groups | Orders | Mathematical Properties |
 |--------------|--------|--------|------------------------|
 | Symmetric | S5, S6, S7, S8, S9 | 120-362,880 | Non-solvable for n ≥ 5 |
 | Alternating | A5, A6, A7, A8, A9 | 60-181,440 | Simple groups for n ≥ 5 |
-| Projective Special Linear | PSL(2,5), PSL(2,7), PSL(2,11), PSL(3,2), PSL(3,3), PSL(3,5) | Various | Simple groups |
+| Projective Special Linear | PSL(2,4), PSL(2,5), PSL(2,7), PSL(2,8), PSL(2,9), PSL(2,11), PSL(3,2), PSL(3,3), PSL(3,4), PSL(3,5) | Various | Simple groups (PSL(2,4) ≅ A5) |
 | Mathieu | M11, M12 | 7,920, 95,040 | Sporadic simple groups |
 
 ## Technical Specifications