Update app.py

app.py

@@ -1,16 +1,14 @@
 import gradio as gr
 import hashlib, random
-import math
 
 # =========================
-# Shared utilities
+# Utilities
 # =========================
 def sha_seal(s: str) -> str:
-    import hashlib
     return hashlib.sha512(s.encode()).hexdigest()[:32] + "..."
 
 # =========================
-# Symbolic mutation engine (existing modes)
+# Codex symbolic mutation (50 epochs)
 # =========================
 operators = ["\\sin", "\\cos", "\\exp", "\\log", "\\nabla", "\\int", "\\frac{\\partial}{\\partial t}"]
 variables = ["x", "y", "t", "\\xi_1", "dP", "d\\Psi", "dT"]
@@ -32,29 +30,19 @@ def run_epochs(n=50):
         base = mutate_formula(base, epoch)
         seal = sha_seal(base)
         ledger.append(
-            f"## Epoch {epoch}\n\n$$ {base} $$\n\n**Immortality Glyph:** `{seal}`\n\n---\n"
-        )
-    return "\n".join(ledger)
-
-def run_mutation(seed, n=20):
-    ledger = []
-    base = seed
-    for epoch in range(1, n+1):
-        base = mutate_formula(base, epoch)
-        seal = sha_seal(base)
-        ledger.append(
-            f"## Mutation Epoch {epoch}\n\n$$ {base} $$\n\n**Immortality Glyph:** `{seal}`\n\n---\n"
+            f"## Epoch {epoch}\n\n"
+            f"$$ {base} $$\n\n"
+            f"**Immortality Glyph:** `{seal}`\n\n"
+            f"---\n"
         )
     return "\n".join(ledger)
 
 # =========================
-# 4D manifold forge
+# 4D Manifold Forge (20-epoch lineage)
 # =========================
-# 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])
@@ -63,134 +51,110 @@ def pretty_metric(g):
     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
+    # Heuristic evolving invariant (not exact): maps symbolic entries to small positive values
+    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)]
+    # Naive LU-like determinant
+    import copy
+    A = copy.deepcopy(M)
+    det = 1.0
+    for i in range(4):
+        pivot = A[i][i]
+        if abs(pivot) < 1e-9:
+            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
 
 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
+    neg = sum("log" in d for d in diag)
     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
+def random_overlay(c):
     overlays = [
         f"1+\\sin({c})",
         f"1+\\cos({c})",
         f"1+\\exp({c})",
-        f"1+\\log(1+{c}^2)"
+        f"1+\\log\\!\\big(1+{c}^2\\big)"
     ]
-    return overlays[random.randint(0, len(overlays)-1)]
+    return random.choice(overlays)
 
 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]
+        ci, cj = coords[i], coords[j]
         if i == j:
-            g[i][j] = random_overlay(g[i][j], c_i)
+            g[i][j] = random_overlay(ci)
         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})"
+                f"\\cos({ci})+\\log\\!\\big(1+{cj}^2\\big)",
+                f"\\exp({cj})-\\cos({ci})",
+                f"\\sin({ci}{cj})",
+                f"\\cos({ci})+\\log\\!\\big(1+{cj}^2\\big)"
             ]
-            g[i][j] = mix[random.randint(0, len(mix)-1)]
+            g[i][j] = random.choice(mix)
             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 christoffel_snippet():
+    return (
+        "\\Gamma^{1}_{\\;12} = \\tfrac{1}{2}\\, g^{11}\\!\\left(\\partial_{u} g_{22} + \\partial_{v} g_{12} - \\partial_{v} g_{11}\\right),\\quad"
+        "\\Gamma^{2}_{\\;34} = \\tfrac{1}{2}\\, g^{22}\\!\\left(\\partial_{v} g_{44} + \\partial_{t} g_{24} - \\partial_{w} g_{23}\\right),\\quad"
+        "\\Gamma^{4}_{\\;13} = \\tfrac{1}{2}\\, g^{44}\\!\\left(\\partial_{u} g_{33} + \\partial_{w} g_{13} - \\partial_{u} g_{34}\\right)"
+    )
 
 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"],
-        ]
+        g = [["1","0","0","0"],
+             ["0","1","0","0"],
+             ["0","0","1","0"],
+             ["0","0","0","1"]]
+    else:
+        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)
+        g_latex = pretty_metric(g)
         detg = det_approx(g)
         sig = signature_hint(g)
-        Gamma = christoffel_snippet(g)
+        Gamma = christoffel_snippet()
         Rscalar = scalar_curvature_hint(g)
-        vol = f"dV = \\sqrt{{\\det g}}\\, du\\, dv\\, dw\\, dt"
-
-        g_latex = pretty_metric(g)
+        vol = "dV = \\sqrt{\\det g}\\, du\\, dv\\, dw\\, dt"
         seal = sha_seal(g_latex + Rscalar)
 
         entry = (
             f"## Manifold Epoch {epoch}\n\n"
-            f"**Coordinates:** $\\mathbf{{X}}=(u,v,w,t)$  \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"$$ {g_latex} $$\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"- **Scalar curvature hint:** $$ {Rscalar} $$  \n"
+            f"- **Volume element:** $$ {vol} $$\n\n"
             f"**Immortality Glyph:** `{seal}`\n\n"
             f"---\n"
         )
@@ -199,7 +163,7 @@ def run_manifold(signature_choice="Euclidean (+,+,+,+)", intensity="medium", epo
     return "\n".join(ledger)
 
 # =========================
-# Gradio app
+# App UI
 # =========================
 custom_theme = gr.themes.Base(
     primary_hue="cyan",
@@ -209,7 +173,7 @@ custom_theme = gr.themes.Base(
 
 with gr.Blocks(theme=custom_theme) as demo:
     gr.Markdown("# 🌌 Resonance Atlas — The Living Codex")
-    gr.Markdown("Choose your path: 50‑epoch scroll run, Mutation Forge, or the 4D Manifold Forge.")
+    gr.Markdown("Choose: 50‑epoch Codex Scrolls or the 4D Manifold Forge (20‑epoch lineage).")
 
     with gr.Tab("Codex Scrolls"):
         gr.Markdown("### 🔢 Live 50 Epoch Run")
@@ -217,19 +181,13 @@ with gr.Blocks(theme=custom_theme) as demo:
         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")
-        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")
+        gr.Markdown("### 🧭 Forge 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")
+        epochs = gr.Slider(5, 30, value=20, step=1, label="Epochs")
+        run_manifold_btn = gr.Button("Forge 4D Manifold (Lineage)")
         manifold_out = gr.Markdown()
         run_manifold_btn.click(fn=run_manifold, inputs=[signature, intensity, epochs], outputs=manifold_out)