1.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
ETVP v13.0 — ПРОЕКЦИИ СОБСТВЕННЫХ ВЕКТОРОВ E8
Цельная система. Веса w_ij. Связь с Φ, π, √3.
"""

import numpy as np

# =============================================================================
# 0. ГЕОМЕТРИЯ
# =============================================================================

PHI = (1.0 + np.sqrt(5.0)) / 2.0
PI  = np.pi
SQ3 = np.sqrt(3.0)
SQ2 = np.sqrt(2.0)

# =============================================================================
# 1. E8
# =============================================================================

E8 = np.array([
    [ 2, -1,  0,  0,  0,  0,  0,  0],
    [-1,  2, -1,  0,  0,  0,  0,  0],
    [ 0, -1,  2, -1,  0,  0,  0,  0],
    [ 0,  0, -1,  2, -1,  0,  0,  0],
    [ 0,  0,  0, -1,  2, -1,  0, -1],
    [ 0,  0,  0,  0, -1,  2, -1,  0],
    [ 0,  0,  0,  0,  0, -1,  2,  0],
    [ 0,  0,  0,  0, -1,  0,  0,  2]
], dtype=float)

# =============================================================================
# 2. СОБСТВЕННЫЕ ЗНАЧЕНИЯ И ВЕКТОРА
# =============================================================================

print("=" * 80)
print("🌀 ETVP v13.0 — ПРОЕКЦИИ СОБСТВЕННЫХ ВЕКТОРОВ E8")
print("=" * 80)

eigvals, eigvecs = np.linalg.eigh(E8)
idx = np.argsort(eigvals)
eigvals = eigvals[idx]
eigvecs = eigvecs[:, idx]

print(f"\n📊 Собственные значения E8:")
for i, lam in enumerate(eigvals):
    print(f"   λ[{i}] = {lam:.10f}")

# =============================================================================
# 3. МАТРИЦА ПРОЕКЦИЙ (СКАЛЯРНЫЕ ПРОИЗВЕДЕНИЯ)
# =============================================================================

print("\n" + "=" * 80)
print("📊 МАТРИЦА ПРОЕКЦИЙ W_IJ = ⟨v_i, v_j⟩")
print("=" * 80)

W = np.zeros((8, 8))
for i in range(8):
    for j in range(8):
        W[i, j] = np.dot(eigvecs[:, i], eigvecs[:, j])

print("\n   Матрица проекций (8×8):")
for i in range(8):
    row = "   " + "  ".join(f"{W[i,j]:>8.5f}" for j in range(8))
    print(row)

# Проверка ортонормальности
print("\n   Проверка: W должна быть единичной (ортонормальность).")
print(f"   ||W - I|| = {np.linalg.norm(W - np.eye(8)):.10f}")

# =============================================================================
# 4. ПРОЕКЦИИ НА БАЗИСНЫЕ ВЕКТОРА
# =============================================================================

print("\n" + "=" * 80)
print("📊 ПРОЕКЦИИ НА БАЗИСНЫЕ ВЕКТОРА e_i")
print("=" * 80)

# Проекция каждого собственного вектора на каждый базисный
print("\n   Матрица проекций v_j на e_i (8×8):")
proj_matrix = np.zeros((8, 8))
for i in range(8):  # базисный
    for j in range(8):  # собственный
        e_i = np.zeros(8)
        e_i[i] = 1.0
        proj_matrix[i, j] = np.dot(e_i, eigvecs[:, j])

for i in range(8):
    row = "   " + "  ".join(f"{proj_matrix[i,j]:>8.5f}" for j in range(8))
    print(row)

# =============================================================================
# 5. ВЕСА W_IJ ИЗ ГЕОМЕТРИИ
# =============================================================================

print("\n" + "=" * 80)
print("📊 ВЕСА W_IJ ЧЕРЕЗ Φ, π, √3")
print("=" * 80)

# Проверяем гипотезы о весах
print("\n   Гипотеза: w_ij = f(Φ, π, √3)")
print("\n   Смотрим на |v_j[i]| для каждого j:")

for j in range(8):
    print(f"\n   Вектор {j} (λ = {eigvals[j]:.6f}):")
    abs_vals = np.abs(eigvecs[:, j])
    for i in range(8):
        v = eigvecs[i, j]
        av = abs(v)
        # Проверяем совпадение с геометрическими константами
        found = []
        for name, val in [
            ("1/Φ²", 1/PHI**2), ("1/Φ", 1/PHI), ("1/√3", 1/SQ3),
            ("1/√2", 1/SQ2), ("1/2", 0.5), ("1/π", 1/PI),
            ("1/Φ³", 1/PHI**3), ("1/3", 1/3), ("1/4", 0.25),
            ("Φ/4", PHI/4), ("√3/4", SQ3/4), ("π/8", PI/8),
        ]:
            if av > 1e-6:
                r = av / val
                if 0.98 < r < 1.02:
                    found.append(f"{name} (r={r:.4f})")
        if found:
            print(f"      v[{i}] = {v:>10.6f}  |v| ≈ {', '.join(found)}")

# =============================================================================
# 6. СУММЫ С ВЕСАМИ
# =============================================================================

print("\n" + "=" * 80)
print("📊 СУММЫ С ВЕСАМИ: K_i = Σ λ_j · w_ij")
print("=" * 80)

# Гипотеза: веса — из проекций на базисные вектора
print("\n   Гипотеза 1: w_ij = |v_j[i]|²")

sums = np.zeros(8)
for i in range(8):
    for j in range(8):
        sums[i] += eigvals[j] * abs(eigvecs[i, j])**2
print("   Суммы (i = 0..7):")
for i, s in enumerate(sums):
    print(f"      K[{i}] = {s:.10f}")

# Сравнение с CODATA
CODATA = {
    "1/α": 137.035999084,
    "m_p/m_e": 1836.15267343,
    "G": 6.67430e-11,
}

print("\n   Сравнение с CODATA:")
for name, val in CODATA.items():
    print(f"\n   {name} = {val:.9f}")
    for i, s in enumerate(sums):
        if abs(s) > 1e-12:
            ratio = val / s
            if 0.1 < ratio < 10:
                print(f"      CODATA/K[{i}] = {ratio:.6f}")

# =============================================================================
# 7. ГИПОТЕЗА: СУММА С ПРОЕКЦИЯМИ
# =============================================================================

print("\n" + "=" * 80)
print("📊 ГИПОТЕЗА 2: СУММА С ПРОЕКЦИЯМИ")
print("=" * 80)

# w_ij = проекция v_j на e_i
print("\n   Гипотеза 2: w_ij = |⟨e_i, v_j⟩|")

sums2 = np.zeros(8)
for i in range(8):
    for j in range(8):
        e_i = np.zeros(8)
        e_i[i] = 1.0
        w = abs(np.dot(e_i, eigvecs[:, j]))
        sums2[i] += eigvals[j] * w

print("\n   Суммы (i = 0..7):")
for i, s in enumerate(sums2):
    print(f"      K[{i}] = {s:.10f}")

print("\n   Сравнение с CODATA:")
for name, val in CODATA.items():
    print(f"\n   {name} = {val:.9f}")
    for i, s in enumerate(sums2):
        if abs(s) > 1e-12:
            ratio = val / s
            if 0.1 < ratio < 10:
                print(f"      CODATA/K[{i}] = {ratio:.6f}")

# =============================================================================
# 8. ГИПОТЕЗА: СУММА С КВАДРАТАМИ ПРОЕКЦИЙ
# =============================================================================

print("\n" + "=" * 80)
print("📊 ГИПОТЕЗА 3: Σ λ_j · |v_j[i]|")
print("=" * 80)

sums3 = np.zeros(8)
for i in range(8):
    for j in range(8):
        sums3[i] += eigvals[j] * abs(eigvecs[i, j])

print("\n   Суммы (i = 0..7):")
for i, s in enumerate(sums3):
    print(f"      K[{i}] = {s:.10f}")

print("\n   Сравнение с CODATA:")
for name, val in CODATA.items():
    print(f"\n   {name} = {val:.9f}")
    for i, s in enumerate(sums3):
        if abs(s) > 1e-12:
            ratio = val / s
            if 0.1 < ratio < 10:
                print(f"      CODATA/K[{i}] = {ratio:.6f}")

# =============================================================================
# 9. ПОИСК МНОЖИТЕЛЕЙ
# =============================================================================

print("\n" + "=" * 80)
print("📊 ПОИСК ГЕОМЕТРИЧЕСКИХ МНОЖИТЕЛЕЙ")
print("=" * 80)

# Для каждой суммы ищем множитель из Φ, π, √3
candidates = {
    "Φ": PHI, "Φ²": PHI**2, "Φ³": PHI**3, "Φ⁴": PHI**4, "Φ⁵": PHI**5,
    "Φ⁶": PHI**6, "Φ⁷": PHI**7, "Φ⁸": PHI**8, "Φ⁹": PHI**9, "Φ¹⁰": PHI**10,
    "1/Φ": 1/PHI, "1/Φ²": 1/PHI**2, "1/Φ³": 1/PHI**3,
    "π": PI, "π²": PI**2, "π/2": PI/2, "π/3": PI/3, "π/4": PI/4, "π/6": PI/6,
    "1/π": 1/PI, "2/π": 2/PI,
    "√3": SQ3, "√3/2": SQ3/2, "√2": SQ2, "2/√3": 2/SQ3,
    "Φ·√3": PHI*SQ3, "π/√3": PI/SQ3, "Φ·π": PHI*PI,
    "Φ·π/√3": PHI*PI/SQ3, "Φ²·√3": PHI**2*SQ3,
}

print("\n   Для каждой суммы K[i] — ближайший множитель:")
for name, val in CODATA.items():
    print(f"\n   {name} = {val:.9f}")
    for i, s in enumerate(sums2):  # используем sums2
        if abs(s) > 1e-12:
            ratio = val / s
            # Ищем множитель
            best = None
            best_diff = 1.0
            for cname, cval in candidates.items():
                r = ratio / cval
                if abs(r - 1) < best_diff:
                    best_diff = abs(r - 1)
                    best = (cname, cval, r)
            if best and best_diff < 0.1:
                print(f"      K[{i}] = {s:.6f} · {best[0]} (r={best[2]:.4f})")

print("\n✅ Анализ завершён.")