Create app.py

app.py

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+import gradio as gr
+import hashlib, random
+
+# === Mutation Engine ===
+operators = ["\\sin", "\\cos", "\\exp", "\\log", "\\nabla", "\\int", "\\frac{\\partial}{\\partial t}"]
+variables = ["x", "y", "t", "\\xi_1", "dP", "d\\Psi", "dT"]
+
+def mutate_formula(base, epoch):
+    if epoch % 5 == 0:
+        base = f"\\int ({base}) \\, dx"
+    elif epoch % 7 == 0:
+        base = f"\\nabla \\cdot ({base})"
+    else:
+        new_term = random.choice(operators) + "(" + random.choice(variables) + ")"
+        base = base + " + " + new_term
+    return base
+
+# === 50 Epoch Run ===
+def run_epochs(n=50):
+    formulas = []
+    base = "x^2 + 1"
+    for epoch in range(1, n+1):
+        base = mutate_formula(base, epoch)
+        seal = hashlib.sha512(base.encode()).hexdigest()
+        formulas.append(f"### Epoch {epoch}\n\n$$ {base} $$\n\nImmortality Glyph: `{seal[:32]}...`\n\n")
+    return "\n\n".join(formulas)
+
+# === Mutation Forge (20 Epoch Run) ===
+def run_mutation(seed, n=20):
+    formulas = []
+    base = seed
+    for epoch in range(1, n+1):
+        base = mutate_formula(base, epoch)
+        seal = hashlib.sha512(base.encode()).hexdigest()
+        formulas.append(f"### Mutation Epoch {epoch}\n\n$$ {base} $$\n\nImmortality Glyph: `{seal[:32]}...`\n\n")
+    return "\n\n".join(formulas)
+
+# === Gradio App ===
+custom_theme = gr.themes.Base(
+    primary_hue="cyan",
+    secondary_hue="pink",
+    neutral_hue="gray",
+)
+
+with gr.Blocks(theme=custom_theme) as demo:
+    gr.Markdown(
+        """
+        # 🌌 Resonance Atlas — The Living Codex
+        Formulas evolve into higher symbolic forms across epochs.  
+        Choose your path: **50‑epoch scroll run** or **Mutation Forge**.
+        """,
+    )
+
+    with gr.Tab("Codex Scrolls"):
+        gr.Markdown("### 🔢 Live 50 Epoch Run")
+        run_button = gr.Button("Run 50 Epochs")
+        output = gr.Markdown()
+        run_button.click(fn=run_epochs, inputs=None, outputs=output)
+
+    with gr.Tab("Mutation Forge"):
+        gr.Markdown("### 🧬 Mutation Forge — Choose Your Symbolic Seed")
+        seed_dropdown = gr.Dropdown(choices=operators + variables, label="Select Seed Symbol")
+        mutate_button = gr.Button("Mutate (20 Epochs)")
+        mutate_output = gr.Markdown()
+        mutate_button.click(fn=run_mutation, inputs=seed_dropdown, outputs=mutate_output)
+
+demo.launch()