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README.md

@@ -1,12 +1,23 @@
 ---
-title: Number Periodicity Visualizer
-emoji: ⚡
+title: "Number Representation Periodicity Visualizer"
+emoji: 📊
 colorFrom: indigo
 colorTo: purple
+papers:
+  - 2604.20817
 sdk: gradio
-sdk_version: 6.13.0
+sdk_version: 4.36.0
 app_file: app.py
-pinned: false
 ---
 
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
+# Number Representation Periodicity Visualizer
+
+Based on the paper "Convergent Evolution: How Different Language Models Learn Similar Number Representations" (arXiv:2604.20817).
+
+This demo visualizes how language models represent numbers through periodic features with dominant periods at T=2, 5, 10.
+
+## Key Insights
+
+- **Period-T Spikes**: Models exhibit periodic features at T=2, 5, 10 in Fourier domain
+- **Convergent Evolution**: Different architectures converge on similar representations
+- **Geometric Separability**: Fourier sparsity is necessary but not sufficient for mod-T classification