"""
Quark-Arranged Skyrms Walker Personality Model
Five walkers. Ten bosons. Quark confinement. Settlement to Nash equilibrium.
A personality is not what you are. It is what you are not.
The void boundary -- the accumulated rejections across five dimensions
of irreversible choice -- IS the person.
Hot off Lean 4. Zero sorry.
"""
import gradio as gr
import numpy as np
import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
from dataclasses import dataclass, field
import json
# ─── AeonOS Dark Theme ──────────────────────────────────────────────────────
DARK_RC = {
"figure.facecolor": "#09090b", "axes.facecolor": "#111114",
"axes.edgecolor": "#1f1f23", "axes.labelcolor": "#a1a1aa",
"text.color": "#fafafa", "xtick.color": "#71717a", "ytick.color": "#71717a",
"grid.color": "#1f1f23", "grid.alpha": 0.3, "figure.dpi": 100,
"savefig.facecolor": "#09090b", "font.family": "sans-serif",
}
WALKER_NAMES = ["Try", "Choose", "Commit", "LetGo", "Learn"]
WALKER_COLORS = ["#3b82f6", "#22c55e", "#a855f7", "#ef4444", "#f59e0b"]
PRIMITIVES = ["Fork", "Race", "Fold", "Vent", "Interfere"]
PARAMS = ["eta", "temperature", "commitGain", "decayRate", "feedbackGain"]
BOSON_PAIRS = [
(0,1,"Try↔Choose"), (0,2,"Try↔Commit"), (0,3,"Try↔LetGo"), (0,4,"Try↔Learn"),
(1,2,"Choose↔Commit"), (1,3,"Choose↔LetGo"), (1,4,"Choose↔Learn"),
(2,3,"Commit↔LetGo"), (2,4,"Commit↔Learn"), (3,4,"LetGo↔Learn"),
]
PRESETS = {
"Explorer": [0.9, 0.4, 0.3, 0.7, 0.8],
"Builder": [0.4, 0.7, 0.9, 0.2, 0.6],
"Creative": [0.8, 0.3, 0.4, 0.8, 0.9],
"Anxious": [0.3, 0.2, 0.7, 0.1, 0.5],
"Balanced": [0.5, 0.5, 0.5, 0.5, 0.5],
"Custom": [0.6, 0.6, 0.6, 0.6, 0.6],
}
# ─── Core Model ──────────────────────────────────────────────────────────────
def compute_bosons(walkers):
"""Compute ten boson tensions (|w_a - w_b| for all pairs)."""
bosons = []
for a, b, _ in BOSON_PAIRS:
bosons.append(abs(walkers[a] - walkers[b]))
return np.array(bosons)
def system_energy(bosons):
"""Total system energy = sum of all boson tensions."""
return float(np.sum(bosons))
def is_confined(walkers):
"""All walkers must be present (> 0). The sliver guarantees this."""
return all(w > 0 for w in walkers)
def complement_distribution(void_boundary, eta=3.0):
"""Compute complement target from void boundary (rejection counts)."""
weights = np.array([max(1, total - rej + 1) for total, rej in
zip([sum(void_boundary)] * len(void_boundary), void_boundary)], dtype=float)
# Softmax with eta
exp_w = np.exp(eta * (weights / max(weights.max(), 1e-8) - 0.5))
return exp_w / exp_w.sum()
def settle_personality(initial_walkers, max_rounds=100, epsilon=0.001):
"""Settle five walkers to Skyrms Nash equilibrium via rejection."""
walkers = np.array(initial_walkers, dtype=float)
walkers = np.clip(walkers, 0.01, 0.99) # the sliver
# Per-walker void boundaries (20 levels each)
resolution = 20
voids = [np.zeros(resolution) for _ in range(5)]
history = [walkers.copy()]
energies = [system_energy(compute_bosons(walkers))]
gaits = [["stand"] * 5]
for round_idx in range(max_rounds):
new_walkers = walkers.copy()
round_gaits = []
for i in range(5):
# Propose new value from complement distribution
dist = complement_distribution(voids[i])
proposal_idx = np.random.choice(resolution, p=dist)
proposal = (proposal_idx + 0.5) / resolution
# Would this reduce energy?
test = new_walkers.copy()
test[i] = proposal
old_energy = system_energy(compute_bosons(walkers))
new_energy = system_energy(compute_bosons(test))
if new_energy < old_energy:
# Accept: update walker
new_walkers[i] = proposal
gait = "gallop" if (old_energy - new_energy) > 0.1 else "trot"
else:
# Reject: update void boundary
reject_idx = min(int(walkers[i] * resolution), resolution - 1)
voids[i][reject_idx] += 1
gait = "stand"
round_gaits.append(gait)
walkers = np.clip(new_walkers, 0.01, 0.99)
bosons = compute_bosons(walkers)
energy = system_energy(bosons)
history.append(walkers.copy())
energies.append(energy)
gaits.append(round_gaits)
# Convergence check
if len(energies) > 2 and abs(energies[-1] - energies[-2]) < epsilon:
break
return {
"walkers": walkers.tolist(),
"bosons": compute_bosons(walkers).tolist(),
"energy": system_energy(compute_bosons(walkers)),
"confined": is_confined(walkers),
"rounds": len(history) - 1,
"history": [h.tolist() for h in history],
"energies": energies,
"gaits": gaits,
"voids": [v.tolist() for v in voids],
}
# ─── Visualization ──────────────────────────────────────────────────────────
def plot_walkers(result):
"""Radar chart of final walker values."""
with plt.rc_context(DARK_RC):
fig, ax = plt.subplots(figsize=(6, 6), subplot_kw=dict(projection='polar'))
angles = np.linspace(0, 2 * np.pi, 5, endpoint=False).tolist()
angles += angles[:1]
values = result["walkers"] + [result["walkers"][0]]
ax.plot(angles, values, 'o-', color='#06b6d4', linewidth=2, markersize=8)
ax.fill(angles, values, alpha=0.15, color='#06b6d4')
ax.set_xticks(angles[:-1])
ax.set_xticklabels([f"{n}\n({p})" for n, p in zip(WALKER_NAMES, PRIMITIVES)], size=9)
ax.set_ylim(0, 1)
ax.set_title("Five Walkers (Settled)", pad=20, fontsize=14, color='#fafafa')
ax.grid(True, alpha=0.2)
fig.tight_layout()
return fig
def plot_bosons(result):
"""Bar chart of ten boson tensions."""
with plt.rc_context(DARK_RC):
fig, ax = plt.subplots(figsize=(10, 4))
labels = [bp[2] for bp in BOSON_PAIRS]
values = result["bosons"]
colors = ['#ef4444' if v > 0.3 else '#f59e0b' if v > 0.15 else '#22c55e' for v in values]
bars = ax.bar(range(10), values, color=colors, alpha=0.8, edgecolor='#1f1f23')
ax.set_xticks(range(10))
ax.set_xticklabels(labels, rotation=45, ha='right', fontsize=7)
ax.set_ylabel("Tension |w_a - w_b|")
ax.set_title(f"Ten Bosons (Energy = {result['energy']:.3f})", fontsize=12)
ax.set_ylim(0, 1)
ax.axhline(y=0.3, color='#ef4444', linestyle='--', alpha=0.3, label='High tension')
fig.tight_layout()
return fig
def plot_convergence(result):
"""Energy convergence over settlement rounds."""
with plt.rc_context(DARK_RC):
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))
# Energy
ax1.plot(result["energies"], color='#06b6d4', linewidth=2)
ax1.set_xlabel("Round")
ax1.set_ylabel("System Energy")
ax1.set_title(f"Settlement ({result['rounds']} rounds)", fontsize=12)
ax1.grid(True, alpha=0.2)
# Walker trajectories
history = np.array(result["history"])
for i in range(5):
ax2.plot(history[:, i], color=WALKER_COLORS[i], linewidth=1.5, label=WALKER_NAMES[i])
ax2.set_xlabel("Round")
ax2.set_ylabel("Walker Value")
ax2.set_title("Walker Trajectories", fontsize=12)
ax2.legend(loc='upper right', fontsize=8)
ax2.set_ylim(0, 1)
ax2.grid(True, alpha=0.2)
fig.tight_layout()
return fig
def format_summary(result):
"""Text summary of the settled personality."""
w = result["walkers"]
lines = [
"QUARK-ARRANGED SKYRMS WALKER PERSONALITY",
"=" * 50, "",
f"Settlement: {result['rounds']} rounds | Energy: {result['energy']:.4f} | Confined: {result['confined']}",
"",
"FIVE WALKERS (settled values):",
]
for i, (name, prim, param) in enumerate(zip(WALKER_NAMES, PRIMITIVES, PARAMS)):
bar = "█" * int(w[i] * 20)
lines.append(f" {name:8s} ({prim:10s}) = {w[i]:.3f} {bar}")
lines.extend(["", "TEN BOSONS (pairwise tensions):"])
for i, (a, b, label) in enumerate(BOSON_PAIRS):
v = result["bosons"][i]
indicator = "🔴" if v > 0.3 else "🟡" if v > 0.15 else "🟢"
lines.append(f" {indicator} {label:20s} = {v:.3f}")
lines.extend(["", "THEOREMS (all proved in Lean 4, zero sorry):",
" THM-FIVE-MAP-TO-FIVE: walkers = primitives = hyperparameters",
" THM-NO-FREE-QUARKS: cannot remove one walker (confinement)",
" THM-GAUGE-WALKER-AGREE: gauge field peak = walker peak",
f" THM-WIREFRAME-IS-VACUUM: all equal → energy = 0 (balanced = {result['energy'] < 0.01})",
])
# Dominant personality interpretation
dominant = WALKER_NAMES[np.argmax(w)]
weakest = WALKER_NAMES[np.argmin(w)]
lines.extend(["", f"INTERPRETATION:",
f" Dominant axis: {dominant} (strongest pull)",
f" Shadow axis: {weakest} (most rejected, deepest void)",
f" The void boundary of {weakest} contains the most information.",
])
return "\n".join(lines)
# ─── Gradio App ──────────────────────────────────────────────────────────────
def run_settlement(preset, try_v, choose_v, commit_v, letgo_v, learn_v, max_rounds):
if preset != "Custom":
vals = PRESETS[preset]
try_v, choose_v, commit_v, letgo_v, learn_v = vals
result = settle_personality(
[try_v, choose_v, commit_v, letgo_v, learn_v],
max_rounds=int(max_rounds),
)
return (
plot_walkers(result),
plot_bosons(result),
plot_convergence(result),
format_summary(result),
try_v, choose_v, commit_v, letgo_v, learn_v,
)
CSS = """
.gradio-container { max-width: 1100px !important; margin: 0 auto !important; }
.gradio-container, .dark { background: #09090b !important; }
footer { display: none !important; }
"""
with gr.Blocks(css=CSS, theme=gr.themes.Base(primary_hue="cyan", neutral_hue="zinc"),
title="Quark Personality") as demo:
gr.HTML("""
Quark-Arranged Skyrms Walker Personality
Five walkers. Ten bosons. Quark confinement. Settlement to Nash equilibrium.
A personality is not what you are. It is what you are not.
The void boundary -- accumulated rejections across five dimensions of irreversible choice -- IS the person.
Hot off Lean 4. Zero sorry.
""")
with gr.Row():
preset = gr.Dropdown(choices=list(PRESETS.keys()), value="Explorer", label="Preset", scale=1)
max_rounds = gr.Slider(10, 500, value=100, step=10, label="Max settlement rounds", scale=1)
run_btn = gr.Button("Settle Personality", variant="primary", scale=1)
with gr.Row():
try_v = gr.Slider(0.01, 0.99, value=0.9, step=0.01, label="Try (Fork)")
choose_v = gr.Slider(0.01, 0.99, value=0.4, step=0.01, label="Choose (Race)")
commit_v = gr.Slider(0.01, 0.99, value=0.3, step=0.01, label="Commit (Fold)")
letgo_v = gr.Slider(0.01, 0.99, value=0.7, step=0.01, label="LetGo (Vent)")
learn_v = gr.Slider(0.01, 0.99, value=0.8, step=0.01, label="Learn (Interfere)")
with gr.Row():
walker_plot = gr.Plot(label="Five Walkers")
boson_plot = gr.Plot(label="Ten Bosons")
convergence_plot = gr.Plot(label="Settlement Convergence")
with gr.Accordion("Full Analysis", open=False):
summary = gr.Textbox(lines=30, show_label=False, interactive=False)
def on_preset(p):
vals = PRESETS.get(p, PRESETS["Custom"])
return vals
preset.change(on_preset, [preset], [try_v, choose_v, commit_v, letgo_v, learn_v])
run_btn.click(
run_settlement,
[preset, try_v, choose_v, commit_v, letgo_v, learn_v, max_rounds],
[walker_plot, boson_plot, convergence_plot, summary, try_v, choose_v, commit_v, letgo_v, learn_v],
)
demo.load(
run_settlement,
[preset, try_v, choose_v, commit_v, letgo_v, learn_v, max_rounds],
[walker_plot, boson_plot, convergence_plot, summary, try_v, choose_v, commit_v, letgo_v, learn_v],
)
gr.HTML("""
""")
if __name__ == "__main__":
demo.launch(server_name="0.0.0.0", server_port=7860)