app.py

import gradio as gr
import hashlib, random

# =========================
# Utilities
# =========================
def sha_seal(s: str) -> str:
    return hashlib.sha512(s.encode()).hexdigest()[:32] + "..."

# =========================
# 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"]

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

def run_epochs(n=50):
    ledger = []
    base = "x^2 + 1"
    for epoch in range(1, n+1):
        base = mutate_formula(base, epoch)
        seal = sha_seal(base)
        ledger.append(
            f"## Epoch {epoch}\n\n"
            f"$$ {base} $$\n\n"
            f"**Immortality Glyph:** `{seal}`\n\n"
            f"---\n"
        )
    return "\n".join(ledger)

# =========================
# 4D Manifold Forge (20-epoch lineage)
# =========================
coords = ["u", "v", "w", "t"]

def pretty_metric(g):
    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):
    # 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):
    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)
    osc = sum(("sin" in d) or ("cos" in d) for d in diag)
    return f"(+:{pos}, -:{neg}, ~:{osc})"

def random_overlay(c):
    overlays = [
        f"1+\\sin({c})",
        f"1+\\cos({c})",
        f"1+\\exp({c})",
        f"1+\\log\\!\\big(1+{c}^2\\big)"
    ]
    return random.choice(overlays)

def mutate_metric(g, epoch, intensity="medium"):
    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:
        ci, cj = coords[i], coords[j]
        if i == j:
            g[i][j] = random_overlay(ci)
        else:
            mix = [
                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] = random.choice(mix)
            g[j][i] = g[i][j]
    return g

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):
    d = det_approx(g)
    return f"\\mathcal{{R}} \\approx {d:.3f}"

def run_manifold(signature_choice="Euclidean (+,+,+,+)", intensity="medium", epochs=20):
    if signature_choice.startswith("Euclidean"):
        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()
        Rscalar = scalar_curvature_hint(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"**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"
        )
        ledger.append(entry)

    return "\n".join(ledger)

# =========================
# App UI
# =========================
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")
    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")
        run_button = gr.Button("Run 50 Epochs")
        output = gr.Markdown()
        run_button.click(fn=run_epochs, inputs=None, outputs=output)

    with gr.Tab("4D Manifold Forge"):
        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(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)

demo.launch()