Update app.py

app.py

@@ -1,12 +1,21 @@
 import gradio as gr
 import hashlib, random
+import math
 
-# === Mutation Engine ===
+# =========================
+# Shared utilities
+# =========================
+def sha_seal(s: str) -> str:
+    import hashlib
+    return hashlib.sha512(s.encode()).hexdigest()[:32] + "..."
+
+# =========================
+# Symbolic mutation engine (existing modes)
+# =========================
 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):
-    # Structural mutation rules
     if epoch % 5 == 0:
         base = f"\\int ({base}) \\, dx"
     elif epoch % 7 == 0:
@@ -16,39 +25,182 @@ def mutate_formula(base, epoch):
         base = base + " + " + new_term
     return base
 
-# === 50 Epoch Run ===
 def run_epochs(n=50):
-    formulas = []
+    ledger = []
     base = "x^2 + 1"
     for epoch in range(1, n+1):
         base = mutate_formula(base, epoch)
-        seal = hashlib.sha512(base.encode()).hexdigest()
-        scroll = (
-            f"## Epoch {epoch}\n\n"
-            f"$$ {base} $$\n\n"
-            f"**Immortality Glyph:** `{seal[:32]}...`\n\n"
-            "---\n\n"
+        seal = sha_seal(base)
+        ledger.append(
+            f"## Epoch {epoch}\n\n$$ {base} $$\n\n**Immortality Glyph:** `{seal}`\n\n---\n"
         )
-        formulas.append(scroll)
-    return "\n".join(formulas)
+    return "\n".join(ledger)
 
-# === Mutation Forge (20 Epoch Run) ===
 def run_mutation(seed, n=20):
-    formulas = []
+    ledger = []
     base = seed
     for epoch in range(1, n+1):
         base = mutate_formula(base, epoch)
-        seal = hashlib.sha512(base.encode()).hexdigest()
-        scroll = (
-            f"## Mutation Epoch {epoch}\n\n"
-            f"$$ {base} $$\n\n"
-            f"**Immortality Glyph:** `{seal[:32]}...`\n\n"
-            "---\n\n"
+        seal = sha_seal(base)
+        ledger.append(
+            f"## Mutation Epoch {epoch}\n\n$$ {base} $$\n\n**Immortality Glyph:** `{seal}`\n\n---\n"
+        )
+    return "\n".join(ledger)
+
+# =========================
+# 4D manifold forge
+# =========================
+# Coordinates: (u, v, w, t)
+coords = ["u", "v", "w", "t"]
+
+def pretty_metric(g):
+    # LaTeX matrix for g_ij
+    rows = []
+    for i in range(4):
+        row = " & ".join(g[i])
+        rows.append(row)
+    mat = " \\\\ ".join(rows)
+    return "\\begin{pmatrix}" + mat + "\\end{pmatrix}"
+
+def det_approx(g):
+    # Very rough numeric surrogate: treat overlays as small positive offsets for stability
+    # This is just to show a changing invariant; not an actual symbolic determinant.
+    try:
+        # Map symbolic strings to small floats by hashing length/content
+        def val(s):
+            base = 1.0
+            base += 0.01 * (len(s) % 10)
+            base += 0.02 * sum(ch.isalpha() for ch in s)
+            return base
+        M = [[val(g[i][j]) for j in range(4)] for i in range(4)]
+        # Determinant via simple expansion (use numpy if allowed; here keep pure-Python)
+        # 4x4 det via LU-like naive method
+        import copy
+        A = copy.deepcopy(M)
+        det = 1.0
+        for i in range(4):
+            pivot = A[i][i]
+            if abs(pivot) < 1e-12:
+                return 0.0
+            det *= pivot
+            for j in range(i+1,4):
+                factor = A[j][i]/pivot
+                for k in range(i,4):
+                    A[j][k] -= factor*A[i][k]
+        return det
+    except:
+        return 0.0
+
+def signature_hint(g):
+    # Heuristic signature: count "exp" as positive, "log" as mixed, "sin/cos" as oscillatory
+    diag = [g[i][i] for i in range(4)]
+    pos = sum("exp" in d for d in diag)
+    neg = sum("log" in d for d in diag)  # treat log as potentially non-positive
+    osc = sum(("sin" in d) or ("cos" in d) for d in diag)
+    return f"(+:{pos}, -:{neg}, ~:{osc})"
+
+def random_overlay(term, c):
+    # Add symbolic overlays to metric component
+    overlays = [
+        f"1+\\sin({c})",
+        f"1+\\cos({c})",
+        f"1+\\exp({c})",
+        f"1+\\log(1+{c}^2)"
+    ]
+    return overlays[random.randint(0, len(overlays)-1)]
+
+def mutate_metric(g, epoch, intensity="medium"):
+    # Ensure symmetry: g_ij == g_ji
+    # Start by adjusting diagonals, then introduce off-diagonals
+    idx_pairs = [(0,0),(1,1),(2,2),(3,3),
+                 (0,1),(0,2),(0,3),(1,2),(1,3),(2,3)]
+    k = 2 if intensity=="low" else (4 if intensity=="medium" else 6)
+    chosen = random.sample(idx_pairs, min(k, len(idx_pairs)))
+
+    for (i,j) in chosen:
+        c_i = coords[i]
+        c_j = coords[j]
+        if i == j:
+            g[i][j] = random_overlay(g[i][j], c_i)
+        else:
+            mix = [
+                f"\\sin({c_i})+\\exp({c_j})",
+                f"\\cos({c_i})+\\log(1+{c_j}^2)",
+                f"\\sin({c_i}{c_j})",
+                f"\\exp({c_i})-\\cos({c_j})"
+            ]
+            g[i][j] = mix[random.randint(0, len(mix)-1)]
+            g[j][i] = g[i][j]
+    return g
+
+def christoffel_snippet(g):
+    # Display a few representative components symbolically (not computed from derivatives)
+    # This is a narrative placeholder that shows the structure of Γ with current g entries.
+    components = [
+        ("\\Gamma^{1}_{\\;12}", f"\\tfrac12 g^{11}(\\partial_u g_{22}+\\partial_v g_{12}-\\partial_v g_{11})"),
+        ("\\Gamma^{2}_{\\;34}", f"\\tfrac12 g^{22}(\\partial_v g_{44}+\\partial_t g_{24}-\\partial_w g_{23})"),
+        ("\\Gamma^{4}_{\\;13}", f"\\tfrac12 g^{44}(\\partial_u g_{33}+\\partial_w g_{13}-\\partial_u g_{34})")
+    ]
+    lines = [f"{name} = {expr}" for (name, expr) in components]
+    return " \\\\ ".join(lines)
+
+def scalar_curvature_hint(g):
+    # Not an actual computation; a readable evolving scalar tied to det(g)
+    d = det_approx(g)
+    # Map determinant to a symbolic scalar curvature narrative
+    return f"\\mathcal{{R}} \\approx {d:.3f}"
+
+def run_manifold(signature_choice="Euclidean (+,+,+,+)", intensity="medium", epochs=20):
+    # Initialize metric g_ij
+    if signature_choice.startswith("Euclidean"):
+        g = [
+            ["1", "0", "0", "0"],
+            ["0", "1", "0", "0"],
+            ["0", "0", "1", "0"],
+            ["0", "0", "0", "1"],
+        ]
+    else:  # Pseudo-Riemannian (+,+,+,-)
+        g = [
+            ["1", "0", "0", "0"],
+            ["0", "1", "0", "0"],
+            ["0", "0", "1", "0"],
+            ["0", "0", "0", "-1"],
+        ]
+
+    ledger = []
+    for epoch in range(1, epochs+1):
+        g = mutate_metric(g, epoch, intensity=intensity)
+        detg = det_approx(g)
+        sig = signature_hint(g)
+        Gamma = christoffel_snippet(g)
+        Rscalar = scalar_curvature_hint(g)
+        vol = f"dV = \\sqrt{{\\det g}}\\, du\\, dv\\, dw\\, dt"
+
+        g_latex = pretty_metric(g)
+        seal = sha_seal(g_latex + Rscalar)
+
+        entry = (
+            f"## Manifold Epoch {epoch}\n\n"
+            f"**Coordinates:** $\\mathbf{{X}}=(u,v,w,t)$  \n\n"
+            f"**Metric** $g_{{ij}}$:\n\n"
+            f"\\[ {g_latex} \\]\n\n"
+            f"**Representative Connections:**\n\n"
+            f"\\[ {Gamma} \\]\n\n"
+            f"**Invariants:**  \n"
+            f"- **Determinant:** $\\det g \\approx {detg:.3f}$  \n"
+            f"- **Signature hint:** `{sig}`  \n"
+            f"- **Scalar curvature hint:** \\[ {Rscalar} \\]  \n"
+            f"- **Volume element:** \\[ {vol} \\]\n\n"
+            f"**Immortality Glyph:** `{seal}`\n\n"
+            f"---\n"
         )
-        formulas.append(scroll)
-    return "\n".join(formulas)
+        ledger.append(entry)
+
+    return "\n".join(ledger)
 
-# === Gradio App ===
+# =========================
+# Gradio app
+# =========================
 custom_theme = gr.themes.Base(
     primary_hue="cyan",
     secondary_hue="pink",
@@ -56,13 +208,8 @@ custom_theme = gr.themes.Base(
 )
 
 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**.
-        """,
-    )
+    gr.Markdown("# 🌌 Resonance Atlas — The Living Codex")
+    gr.Markdown("Choose your path: 50‑epoch scroll run, Mutation Forge, or the 4D Manifold Forge.")
 
     with gr.Tab("Codex Scrolls"):
         gr.Markdown("### 🔢 Live 50 Epoch Run")
@@ -72,12 +219,18 @@ with gr.Blocks(theme=custom_theme) as demo:
 
     with gr.Tab("Mutation Forge"):
         gr.Markdown("### 🧬 Mutation Forge — Choose Your Symbolic Seed")
-        seed_dropdown = gr.Dropdown(
-            choices=operators + variables,
-            label="Select Seed Symbol or Formula"
-        )
+        seed_dropdown = gr.Dropdown(choices=operators + variables, label="Select Seed")
         mutate_button = gr.Button("Mutate (20 Epochs)")
         mutate_output = gr.Markdown()
         mutate_button.click(fn=run_mutation, inputs=seed_dropdown, outputs=mutate_output)
 
+    with gr.Tab("4D Manifold Forge"):
+        gr.Markdown("### 🧭 Build a 4D manifold with evolving metric and invariants")
+        signature = gr.Radio(choices=["Euclidean (+,+,+,+)", "Pseudo-Riemannian (+,+,+,-)"], value="Euclidean (+,+,+,+)", label="Signature")
+        intensity = gr.Radio(choices=["low", "medium", "high"], value="medium", label="Overlay intensity")
+        epochs = gr.Slider(1, 30, value=20, step=1, label="Epochs")
+        run_manifold_btn = gr.Button("Forge 4D Manifold")
+        manifold_out = gr.Markdown()
+        run_manifold_btn.click(fn=run_manifold, inputs=[signature, intensity, epochs], outputs=manifold_out)
+
 demo.launch()