Update README.md

README.md

@@ -1,15 +1,21 @@
 ---
-title: NanoGenzen GUI
-emoji: 📚
-colorFrom: gray
-colorTo: green
-sdk: gradio
-sdk_version: 6.25.0
-python_version: '3.12'
-app_file: app.py
+title: "nanoGentzen Neurosymbolic Studio"
+emoji: "🧠"
+colorFrom: "indigo"
+colorTo: "purple"
+sdk: "gradio"
+sdk_version: "6.25.0"
+app_file: "app.py"
 pinned: false
-license: mit
-short_description: Test nanoGenzen in app
+license: "mit"
 ---
 
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
+# 🧠 nanoGentzen Neurosymbolic Studio
+
+Interactive AI studio coupling Neural LLMs with a deterministic, mathematically certified **Gentzen Sequent Calculus Engine (LI & LK)**.
+
+## Capabilities
+
+* **Dual-Process Reasoning**: System 1 (LLM) generates transparent `<think>` steps while System 2 (nanoGentzen) certifies deductive soundness in < 25 ms.
+* **Dual-Mode Prover**: Verifies constructive proofs in Intuitionistic Logic ($LI$) and classical tautologies in Classical Logic ($LK$ via Glivenko's Theorem).
+* **Fallacy Detection**: Detects and flags formal fallacies (*Affirming the Consequent*, *Denying the Antecedent*, circular arguments).