Update README to reflect 94 datasets and new repository name

README.md

@@ -13,18 +13,18 @@ tags:
 - sequence-modeling
 - state-space-models
 - computational-complexity
-pretty_name: Permutation Groups Composition Dataset
+pretty_name: Group Theory Collection
 size_categories:
 - 10M<n<100M
 ---
 
-# Permutation Groups Composition Dataset
+# Group Theory Collection
 
 A comprehensive collection of permutation composition datasets for various mathematical groups, organized by computational complexity classes. This dataset is designed for studying the "Illusion of State" phenomenon in state-space models and transformer architectures.
 
 ## Overview
 
-This dataset provides 59 individual permutation group datasets spanning 10 different group families, systematically organized to facilitate research on the computational boundaries between solvable and non-solvable groups. The organization reflects the fundamental distinction between TC⁰-computable (solvable groups) and NC¹-complete (non-solvable groups) problems.
+This dataset provides 94 individual permutation group datasets spanning 10 different group families, systematically organized to facilitate research on the computational boundaries between solvable and non-solvable groups. The organization reflects the fundamental distinction between TC⁰-computable (solvable groups) and NC¹-complete (non-solvable groups) problems.
 
 ### Research Motivation
 
@@ -57,12 +57,12 @@ Contains 14 non-solvable groups requiring logarithmic-depth circuits for computa
 from datasets import load_dataset
 
 # Load specific group datasets
-s5_data = load_dataset("BeeGass/permutation-groups", data_dir="data/s5")
-a4_data = load_dataset("BeeGass/permutation-groups", data_dir="data/a4")
+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 from complexity-organized directories
-tc0_cyclic = load_dataset("BeeGass/permutation-groups", data_dir="TC0/c10")
-nc1_symmetric = load_dataset("BeeGass/permutation-groups", data_dir="NC1/s7")
+tc0_cyclic = load_dataset("BeeGass/Group-Theory-Collection", data_dir="TC0/c10")
+nc1_symmetric = load_dataset("BeeGass/Group-Theory-Collection", data_dir="NC1/s7")
 
 # Access train/test splits
 train_data = s5_data["train"]
@@ -75,15 +75,16 @@ Each example contains the following fields:
 
 ```python
 {
-    'input_sequence': [123, 456, 789],  # Permutation IDs to compose
-    'target': 234,                       # Result of composition
-    '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!)
+    '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
 }
 ```
 
-Note: Each dataset contains sequences of varying lengths. The 'length' field indicates how many permutations are in that particular example's input sequence (ranging from 3 to 1024).
+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).
 
 ### Filtering by Sequence Length
 
@@ -91,36 +92,37 @@ Since each dataset contains sequences of all lengths from 3 to 1024, researchers
 
 ```python
 # Load full dataset
-dataset = load_dataset("BeeGass/permutation-groups", data_dir="data/s5")
+dataset = load_dataset("BeeGass/Group-Theory-Collection", data_dir="data/s5")
 
 # Filter for sequences of specific lengths
-short_sequences = dataset.filter(lambda x: x['length'] <= 32)
-medium_sequences = dataset.filter(lambda x: 32 < x['length'] <= 128)
-length_16_only = dataset.filter(lambda x: x['length'] == 16)
+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)
 ```
 
 ## Group Inventory
 
-### TC⁰ Groups (Solvable) - 43 Groups
+### TC⁰ Groups (Solvable) - 75 Groups
 
 | Group Family | Groups | Orders | Mathematical Properties |
 |--------------|--------|--------|------------------------|
 | Symmetric | S3, S4 | 6, 24 | Solvable for n ≤ 4 |
 | Alternating | A3, A4 | 3, 12 | Solvable for n ≤ 4 |
-| Cyclic | C3, C4, C5, C6, C7, C8, C9, C10, C12, C15, C20, C25, C30 | 3-30 | Abelian groups |
-| Dihedral | D3, D4, D5, D6, D7, D8, D9, D10, D12, D15, D20 | 6-40 | Symmetries of regular polygons |
+| 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 |
 | Quaternion | Q8, Q16, Q32 | 8, 16, 32 | Non-abelian 2-groups |
-| Elementary Abelian | Z2², Z2³, Z2⁴, Z2⁵, Z3¹, Z3², Z3³, Z5¹, Z5² | Various | Direct products of cyclic 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 |
 
-### NC¹ Groups (Non-Solvable) - 14 Groups
+### NC¹ Groups (Non-Solvable) - 19 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) | 60, 168 | Simple groups |
+| Projective Special Linear | PSL(2,5), PSL(2,7), PSL(2,11), PSL(3,2), PSL(3,3), PSL(3,5) | Various | Simple groups |
 | Mathieu | M11, M12 | 7,920, 95,040 | Sporadic simple groups |
 
 ## Technical Specifications
@@ -143,7 +145,7 @@ For an input sequence [p₁, p₂, p₃], the target is computed as:
 
 ## Dataset Generation
 
-The code used to generate this dataset is available at [https://github.com/BeeGass/permutation-groups](https://github.com/BeeGass/permutation-groups). The repository includes:
+The code used to generate this dataset is available at [https://github.com/BeeGass/Group-Dataset-Generator](https://github.com/BeeGass/Group-Dataset-Generator). The repository includes:
 
 - Complete implementation of all permutation groups
 - Dataset generation scripts with configurable parameters
@@ -168,18 +170,18 @@ When using this dataset in academic work, please cite:
 ```bibtex
 @dataset{gass2024permutation,
   author = {Gass, Bryan},
-  title = {Permutation Groups Composition Dataset},
+  title = {Group Theory Collection},
   year = {2024},
   publisher = {Hugging Face},
-  url = {https://huggingface.co/datasets/BeeGass/permutation-groups},
+  url = {https://huggingface.co/datasets/BeeGass/Group-Theory-Collection},
   note = {Organized by computational complexity classes (TC⁰/NC¹)}
 }
 
 @software{gass2024generator,
   author = {Gass, Bryan},
-  title = {Permutation Groups Dataset Generator},
+  title = {Group Dataset Generator},
   year = {2024},
-  url = {https://github.com/BeeGass/permutation-groups}
+  url = {https://github.com/BeeGass/Group-Dataset-Generator}
 }
 
 @article{merrill2024illusion,