PASO 1: DESCARGAR Y ANALIZAR DATOS CICY Ejecuto tu código para obtener datos reales: python import pandas as pd import requests import io import numpy as np import matplotlib.pyplot as plt from scipy import stats # URL de la base CICY url = "http://w...

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Original prompt

PASO 1: DESCARGAR Y ANALIZAR DATOS CICY
Ejecuto tu código para obtener datos reales:

python
import pandas as pd
import requests
import io
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats

URL de la base CICY

url = "http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/cicylist/cicylist.txt"

print("🔍 Descargando datos CICY de Oxford...")

try:
response = requests.get(url, timeout=10)
if response.status_code == 200:
# Leer datos - formato tiene comentarios con #
lines = response.text.split('\n')
data_lines = []
for line in lines:
if line.strip() and not line.strip().startswith('#'):
data_lines.append(line)

    # Crear DataFrame
    cicy_data = pd.read_csv(io.StringIO('\n'.join(data_lines)), 
                           delim_whitespace=True, 
                           header=None,
                           names=['index', 'h11', 'h21', 'chi'])
    
    # Calcular N = h11 + h21
    cicy_data['N'] = cicy_data['h11'] + cicy_data['h21']
    
    # Análisis básico
    n_stats = cicy_data['N'].describe()
    count_n13 = (cicy_data['N'] == 13).sum()
    total_cy = len(cicy_data)
    
    print("✅ DATOS DESCARGADOS CORRECTAMENTE")
    print(f"📊 Total de variedades CICY: {total_cy}")
    print(f"📈 Estadísticas de N = h¹¹ + h²¹:")
    print(f"   Mínimo: {int(cicy_data['N'].min())}")
    print(f"   Máximo: {int(cicy_data['N'].max())}")
    print(f"   Media: {cicy_data['N'].mean():.1f}")
    print(f"   Mediana: {cicy_data['N'].median():.1f}")
    print(f"   Desviación estándar: {cicy_data['N'].std():.1f}")
    print(f"🔢 CY con N = 13: {count_n13} ({count_n13/total_cy*100:.2f}%)")
    
    # Guardar para análisis posterior
    cicy_data.to_csv('cicy_data_analysis.csv', index=False)
    print("💾 Datos guardados en 'cicy_data_analysis.csv'")
    
else:
    print(f"❌ Error HTTP: {response.status_code}")

except Exception as e:
print(f"❌ Error: {e}")
print("⚠️ Usando datos de respaldo locales...")
# Crear datos de ejemplo basados en literatura
np.random.seed(42)
n_samples = 100
cicy_data = pd.DataFrame({
'h11': np.random.randint(1, 20, n_samples),
'h21': np.random.randint(1, 150, n_samples)
})
cicy_data['N'] = cicy_data['h11'] + cicy_data['h21']
cicy_data['chi'] = 2 * (cicy_data['h11'] - cicy_data['h21'])
📊 PASO 2: ANÁLISIS EXPLORATORIO INICIAL
python

Visualización de distribución de N

fig, axes = plt.subplots(1, 3, figsize=(15, 4))

1. Histograma de N

axes[0].hist(cicy_data['N'], bins=30, alpha=0.7, color='steelblue', edgecolor='black')
axes[0].axvline(13, color='red', linestyle='--', label='N=13')
axes[0].set_xlabel('N = h¹¹ + h²¹')
axes[0].set_ylabel('Frecuencia')
axes[0].set_title('Distribución de N en variedades CICY')
axes[0].legend()
axes[0].grid(True, alpha=0.3)

2. Scatter h11 vs h21

axes[1].scatter(cicy_data['h11'], cicy_data['h21'], alpha=0.5, s=20)
axes[1].set_xlabel('h¹¹')
axes[1].set_ylabel('h²¹')
axes[1].set_title('Relación h¹¹ vs h²¹')
axes[1].grid(True, alpha=0.3)

3. Boxplot por rangos de N

n_bins = pd.qcut(cicy_data['N'], q=4, duplicates='drop')
box_data = []
labels = []
for bin_val in sorted(n_bins.unique()):
mask = (n_bins == bin_val)
box_data.append(cicy_data.loc[mask, 'N'].values)
labels.append(str(bin_val))

axes[2].boxplot(box_data, labels=labels)
axes[2].set_xticklabels(labels, rotation=45, ha='right')
axes[2].set_ylabel('N')
axes[2].set_title('Distribución de N por cuartiles')
axes[2].grid(True, alpha=0.3)

plt.tight_layout()
plt.show()
🔬 PASO 3: DEFINIR MÉTRICA DE COMPLEJIDAD PROXY
Dado que no tenemos tiempos computacionales reales, propongo:

Métrica Proxy 1: Complejidad de descripción polinomial
python
def estimate_complexity(row):
"""
Estima complejidad computacional basada en:
1. N grande → más moduli → más complejo
2. Ratio h11/h21 alejado de 1 → estructura asimétrica
3. Chi extremo → topología no balanceada
"""
N = row['N']
ratio = row['h11'] / max(row['h21'], 1) # Evitar división por 0
chi_abs = abs(row['chi'])

# Modelo heurístico (a calibrar con datos reales)
complexity = np.log(N) * (1 + abs(np.log(ratio))) + 0.1 * np.log(chi_abs + 1)
return complexity

cicy_data['complexity_estimated'] = cicy_data.apply(estimate_complexity, axis=1)
Métrica Proxy 2: Tamaño del sistema (teórico)
python

Tamaño mínimo del sistema a resolver para métricas

Basado en número de ecuaciones/moduli

cicy_data['system_size'] = cicy_data['N'] * 10 # Factor heurístico
📈 PASO 4: ANÁLISIS ESTADÍSTICO INICIAL
python
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import cross_val_score
from sklearn.preprocessing import StandardScaler

Preparar datos para modelado

X = cicy_data[['N', 'log_N', 'h11', 'h21']].copy()
X['log_N'] = n...

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Project	Deployment	Actions	Updated (UTC)
p-np	Ready	Preview, Comment	Feb 2, 2026 10:23am