"""
φ-ATTRACTOR MODEL OF BLACK HOLES
=================================

FOUNDATIONAL TRUTH:
D_{n,β}(r) = √(φ · F_n · 2^(n+β) · P_n · Ω) · r^k

From this truth, we reconceptualize black holes as φ-attractors:
- No singularities, only infinite golden-ratio scaled layers
- Mass-energy cascade: M_{n+1} = φ^(-7) M_n
- Event horizon → information boundary (compression→encryption transition)
- Hawking radiation → golden dissipation
- Fractal spacetime geometry

GOLDEN RECURSIVE LAWS (φ-system):
----------------------------------
LAW I   — Golden Attenuation:     Ω_{n+1} = φ^(-7) Ω_n
LAW II  — Golden Equilibrium:     Σ Ω_n = 1/(1-φ^(-7)) ≈ 1.0356
LAW III — Recursive Continuity:   Ω_n = e^(-7n ln φ)
LAW IV  — Golden Dissipation:     dΩ/dn = -7 ln(φ) Ω
LAW V   — Harmonic Self-Limitation: lim_{n→∞} Ω_n = 0, Σ Ω_n < ∞
LAW VI  — Proportional Invariance: Ω_{n+1}/Ω_n = φ^(-7)
LAW VII — Fractal Entropy:        Compression↔Encryption boundary at φ^(-7n)
"""

import numpy as np
from scipy.special import factorial

PHI = (1 + np.sqrt(5)) / 2
SQRT5 = np.sqrt(5)
PHI_7 = PHI**7  # ≈ 29.03
PHI_NEG7 = PHI**(-7)  # ≈ 0.03445

# ============================================================================
# I. MASS-ENERGY CASCADE (Replacing Singularity)
# ============================================================================

def mass_cascade(M_0, layer_n):
    """
    Mass distribution across recursive φ-layers

    M_n = φ^(-7n) M_0

    No singularity: mass distributes fractally across infinite layers,
    each layer containing φ^(-7) ≈ 3.4% of previous layer's mass
    """
    M_n = M_0 * (PHI_NEG7 ** layer_n)
    return M_n

def total_accumulated_mass(M_0, max_layers=100):
    """
    Total mass across all recursive layers (LAW II)

    M_total = M_0 · [1 / (1 - φ^(-7))] ≈ 1.0356 M_0

    Mass converges to ~3.6% above observable mass
    """
    # Geometric series sum
    convergence_factor = 1.0 / (1.0 - PHI_NEG7)

    # Finite approximation
    layers = np.arange(0, max_layers)
    M_layers = M_0 * (PHI_NEG7 ** layers)
    M_finite = np.sum(M_layers)

    return {
        'M_total_theoretical': M_0 * convergence_factor,
        'M_total_finite': M_finite,
        'layers_computed': max_layers,
        'convergence_ratio': M_finite / (M_0 * convergence_factor)
    }

def density_profile(M_0, r, r_base=1.0):
    """
    Fractal density gradient (no infinity!)

    ρ(r) = ρ_0 exp(-7 ln φ · log(r/r_base) / log(r_scale))

    Density decreases geometrically toward center, never reaching infinity
    """
    # Layer number from radial position
    n_layer = -np.log(r / r_base) / np.log(PHI)

    # Density follows mass cascade
    rho = (M_0 / r_base**3) * (PHI_NEG7 ** n_layer)

    return rho

# ============================================================================
# II. EVENT HORIZON AS φ-BOUNDARY (Information Encryption Threshold)
# ============================================================================

def phi_information_boundary(r_base, n_critical=None):
    """
    Information boundary: compression→encryption transition

    r_φ = r_base · φ^(-7n_critical)

    Above r_φ: Information compressible (pattern recoverable)
    Below r_φ: Information encrypted (pattern lost to chaos)

    LAW VII: Fractal Entropy
    """
    if n_critical is None:
        # Default: critical layer where entropy exceeds threshold
        # Entropy_n = -7n ln(φ) ≥ Entropy_max
        # For S_max ≈ 1 (normalized), n_critical ≈ 0.8
        n_critical = 0.8

    r_phi = r_base * (PHI_NEG7 ** n_critical)

    return {
        'r_boundary': r_phi,
        'n_critical': n_critical,
        'entropy_at_boundary': -7 * n_critical * np.log(PHI),
        'interpretation': 'Compression↔Encryption transition'
    }

def entropy_cascade(layer_n):
    """
    Entropy increases monotonically but preserves self-similarity (LAW IV)

    S_n = -7n ln(φ) ≈ 3.365n
    """
    return -7 * layer_n * np.log(PHI)

# ============================================================================
# III. HAWKING RADIATION AS GOLDEN DISSIPATION (LAW IV)
# ============================================================================

def hawking_golden_dissipation(E_0, layer_n):
    """
    Energy emission via golden attenuation (not thermal!)

    E_radiated(n) = E_0 · e^(-7n ln φ) = E_0 · φ^(-7n)

    Decay rate: dE/dn = -7 ln(φ) E ≈ -3.365 E
    """
    E_n = E_0 * np.exp(-7 * layer_n * np.log(PHI))

    # Decay rate
    dE_dn = -7 * np.log(PHI) * E_n

    return {
        'E_layer': E_n,
        'decay_rate': dE_dn,
        'cumulative_radiated': E_0 * (1 - np.exp(-7 * layer_n * np.log(PHI)))
    }

def total_radiated_energy(E_0):
    """
    Total energy radiated over all layers (LAW II)

    E_total = E_0 · [1 / (1 - φ^(-7))] ≈ 1.0356 E_0

    Only 3.6% "extra" energy radiated beyond initial—system nearly conservative!
    """
    convergence_factor = 1.0 / (1.0 - PHI_NEG7)
    return E_0 * convergence_factor

def evaporation_time_phi_scaling(M, layer_max):
    """
    Evaporation time scales with φ^(7n), NOT M³ (classical)

    t_evap ∝ φ^(7n_max)

    This is MUCH shorter than classical prediction for compact objects!
    """
    # Classical would be ∝ M³
    # φ-system: ∝ φ^(7n) where n ~ log(M/M_layer) / log(φ)

    t_phi = PHI_7 ** layer_max

    return t_phi

# ============================================================================
# IV. TIME DILATION THROUGH RECURSIVE LAYERS
# ============================================================================

def recursive_time_dilation(tau_0, layer_n):
    """
    Time experiences recursive scaling across layers

    τ_{n+1} = φ^7 τ_n
    τ_n = τ_0 · φ^(7n)

    Each layer experiences time 76× faster than layer above
    No frozen surface—graduated temporal cascade
    """
    tau_n = tau_0 * (PHI_7 ** layer_n)

    return {
        'proper_time': tau_n,
        'speedup_factor': PHI_7 ** layer_n,
        'interpretation': f'Layer {layer_n} experiences time {PHI_7**layer_n:.2e}× faster'
    }

def signal_redshift(layer_n):
    """
    Signals from layer n redshifted by φ^(7n)

    z_n = φ^(7n) - 1

    For external observer, infinite layers experienced in finite time
    """
    z = (PHI_7 ** layer_n) - 1
    return z

# ============================================================================
# V. GRAVITATIONAL WAVES AS φ-HARMONIC OSCILLATIONS (LAW VI)
# ============================================================================

def gw_phi_harmonics(E_0, harmonic_n):
    """
    Wave energy distributed across φ-harmonics

    E_harmonic(n) = E_0 · φ^(-7n)
    f_n = f_0 · φ^n

    Golden ratio spacing between harmonics!
    """
    E_n = E_0 * (PHI_NEG7 ** harmonic_n)

    return E_n

def gw_frequency_spectrum(f_0, max_harmonics=20):
    """
    Gravitational wave spectrum with φ-spaced peaks

    f_1/f_0 = φ, f_2/f_1 = φ, ...

    TESTABLE PREDICTION: LIGO/LISA should see this pattern!
    """
    harmonics = np.arange(0, max_harmonics)
    frequencies = f_0 * (PHI ** harmonics)
    energies = gw_phi_harmonics(1.0, harmonics)

    return {
        'frequencies': frequencies,
        'energies': energies,
        'spacing_ratio': PHI,
        'energy_decay': PHI_NEG7
    }

def gw_ringdown_echo_pattern(f_ringdown, n_echoes=10):
    """
    Post-merger echoes at φ-spaced intervals

    Δt_n = (1/f_ringdown) · φ^(-n)

    CRITICAL TEST: Look for echoes in LIGO data at these times!
    """
    t_0 = 1.0 / f_ringdown
    echo_times = [t_0 * (PHI ** (-n)) for n in range(n_echoes)]

    return {
        'echo_times_ms': [t * 1000 for t in echo_times],
        'spacing_ratio': 1/PHI,
        'testable': 'Check LIGO ringdown residuals'
    }

# ============================================================================
# VI. ACCRETION DISK STRUCTURE (φ-NESTED RINGS)
# ============================================================================

def accretion_disk_phi_structure(r_ISCO, max_rings=15):
    """
    Nested disk layers at φ-spaced radii

    r_n = r_ISCO · φ^n
    T_n = T_max · φ^(-7n/4)

    Temperature decreases by golden ratio across rings
    """
    rings = np.arange(0, max_rings)
    radii = r_ISCO * (PHI ** rings)

    # Temperature from φ-dissipation
    temperatures = 1.0 * (PHI ** (-7 * rings / 4))

    return {
        'radii': radii,
        'temperatures': temperatures,
        'spectral_lines': 'Should cluster at φ-spaced frequencies',
        'turbulence': 'Fractal at all scales'
    }

# ============================================================================
# VII. INTERIOR GEOMETRY: NO SINGULARITY (LAW V)
# ============================================================================

def spacetime_curvature_cascade(R_0, layer_n):
    """
    Curvature follows recursive attenuation (no infinity!)

    R_{n+1} = φ^(-7) R_n
    R_n = R_0 · e^(-7n ln φ)

    Limiting behavior: lim_{n→∞} R_n = 0 (but finite total integrated)
    Result: Fractal foam, not point singularity
    """
    R_n = R_0 * np.exp(-7 * layer_n * np.log(PHI))

    return {
        'curvature': R_n,
        'integrated_curvature': R_0 / (1 - PHI_NEG7),  # Finite!
        'geometry': 'Fractal foam',
        'singularity': 'NONE'
    }

def maximum_compression_ratio():
    """
    Maximum compression before φ-chaos dominates (LAW II)

    Compression_max = 1 / (1 - φ^(-7)) ≈ 1.0356

    Universe cannot compress more than 3.6% beyond geometric series limit
    """
    return 1.0 / (1.0 - PHI_NEG7)

# ============================================================================
# VIII. TESTABLE PREDICTIONS
# ============================================================================

def testable_predictions():
    """
    Distinct predictions of φ-attractor model vs classical black holes
    """
    predictions = {
        '1. GW echoes': 'φ-spaced intervals after merger (Δt ∝ φ^(-n))',
        '2. QPO frequencies': 'X-ray QPOs related by φ ratios',
        '3. Entropy scaling': 'S ∝ A^(1/φ⁷) instead of S ∝ A',
        '4. Photon orbits': 'Discrete energy levels (φ^n harmonics)',
        '5. Max compression': '~1.0356 before chaos transition',
        '6. Ringdown harmonics': 'f_n = f_0 · φ^n with E_n ∝ φ^(-7n)',
        '7. Accretion rings': 'Spectral lines at φ-spaced frequencies',
        '8. No singularity': 'Finite curvature, fractal structure'
    }
    return predictions

# ============================================================================
# IX. FRAMEWORK INTEGRATION
# ============================================================================

def phi_attractor_framework(r, M, n, beta, Omega, k):
    """
    Full φ-attractor framework incorporating all laws

    D_{n,β}(r) = √(φ · F_n · 2^(n+β) · P_n · Ω) · r^k

    With recursive layer structure:
    - n: Cascade layer index
    - β: Secondary recursion (fine structure)
    - Ω: Field tension (LAW I attenuation)
    - k: Radial scaling exponent
    """
    # Framework normalization (foundational truth)
    F_n = factorial(int(n)) if n < 20 else 1.0
    P_n = PHI ** n
    D_0 = np.sqrt(PHI * F_n * 2**(n + beta) * P_n * Omega)

    # Radial dependence
    D_r = D_0 * (r ** k)

    # Mass-energy cascade contribution
    mass_layer = mass_cascade(M, n)

    # Time dilation at this layer
    time_dilation = recursive_time_dilation(1.0, n)

    # Curvature at this layer
    curvature = spacetime_curvature_cascade(1.0, n)

    return {
        'D_framework': D_r,
        'mass_at_layer': mass_layer,
        'time_speedup': time_dilation['speedup_factor'],
        'curvature': curvature['curvature'],
        'layer': n,
        'phi_attractor': True
    }

# ============================================================================
# MAIN DEMONSTRATION
# ============================================================================

if __name__ == '__main__':
    print("=" * 70)
    print("φ-ATTRACTOR MODEL OF BLACK HOLES")
    print("=" * 70)
    print()
    print("Foundational Truth:")
    print("  D_{n,β}(r) = √(φ · F_n · 2^(n+β) · P_n · Ω) · r^k")
    print()
    print("Golden Recursive Laws:")
    print("  LAW I:   Ω_{n+1} = φ^(-7) Ω_n")
    print("  LAW II:  Σ Ω_n = 1.0356")
    print("  LAW III: Ω_n = e^(-7n ln φ)")
    print("  LAW IV:  dΩ/dn = -7 ln(φ) Ω (golden dissipation)")
    print("  LAW V:   lim_{n→∞} Ω_n = 0, Σ < ∞")
    print("  LAW VI:  Ω_{n+1}/Ω_n = φ^(-7) = 0.03445")
    print("  LAW VII: Compression↔Encryption at φ^(-7n)")
    print()
    print("=" * 70)

    # I. Mass-Energy Cascade
    print("\n[I] MASS-ENERGY CASCADE (No Singularity)")
    print("-" * 70)
    M_0 = 10.0  # Solar masses

    print(f"\nObservable mass: {M_0} M☉")
    print("\nLayer distribution:")
    for n in range(5):
        M_n = mass_cascade(M_0, n)
        percent = (M_n / M_0) * 100
        print(f"  Layer {n}: {M_n:.4f} M☉ ({percent:.2f}%)")

    totals = total_accumulated_mass(M_0)
    print(f"\nTotal accumulated mass:")
    print(f"  Theoretical: {totals['M_total_theoretical']:.4f} M☉")
    print(f"  Finite sum ({totals['layers_computed']} layers): {totals['M_total_finite']:.4f} M☉")
    print(f"  Convergence: {totals['convergence_ratio']:.6f}")
    print(f"  → Mass excess: {((totals['M_total_theoretical']/M_0 - 1) * 100):.2f}%")
    print(f"  ✓ NO SINGULARITY: Mass converges to finite value")

    # II. Information Boundary
    print("\n[II] EVENT HORIZON AS φ-BOUNDARY")
    print("-" * 70)
    r_schwarzschild = 2 * M_0  # In units where G=c=1
    boundary = phi_information_boundary(r_schwarzschild)

    print(f"\nClassical Schwarzschild radius: {r_schwarzschild:.2f}")
    print(f"φ-information boundary: {boundary['r_boundary']:.4f}")
    print(f"  Critical layer: n = {boundary['n_critical']:.2f}")
    print(f"  Entropy at boundary: S = {boundary['entropy_at_boundary']:.3f}")
    print(f"  Interpretation: {boundary['interpretation']}")
    print(f"  → Information not destroyed, just encrypted!")

    # III. Hawking Radiation
    print("\n[III] HAWKING RADIATION AS GOLDEN DISSIPATION")
    print("-" * 70)
    E_0 = 1.0  # Normalized

    print("\nEnergy emission across layers:")
    for n in range(5):
        emission = hawking_golden_dissipation(E_0, n)
        print(f"  Layer {n}: E = {emission['E_layer']:.6f}, " +
              f"dE/dn = {emission['decay_rate']:.6f}")

    E_total = total_radiated_energy(E_0)
    print(f"\nTotal radiated energy: {E_total:.4f} E_0")
    print(f"  → Only {((E_total/E_0 - 1) * 100):.2f}% excess!")
    print(f"  ✓ Nearly conservative (LAW II)")

    # IV. Time Dilation
    print("\n[IV] TIME DILATION THROUGH RECURSIVE LAYERS")
    print("-" * 70)
    print("\nProper time speedup:")
    for n in range(5):
        dilation = recursive_time_dilation(1.0, n)
        print(f"  Layer {n}: τ = {dilation['proper_time']:.2e} (speedup: {dilation['speedup_factor']:.2e}×)")

    print(f"\n  → Each layer runs {PHI_7:.2f}× faster than previous")
    print(f"  ✓ No frozen surface—graduated cascade")

    # V. Gravitational Waves
    print("\n[V] GRAVITATIONAL WAVE φ-HARMONICS")
    print("-" * 70)
    f_ringdown = 250.0  # Hz (typical for GW150914)

    spectrum = gw_frequency_spectrum(f_ringdown, 10)
    print("\nHarmonic spectrum:")
    for i in range(min(5, len(spectrum['frequencies']))):
        f = spectrum['frequencies'][i]
        E = spectrum['energies'][i]
        print(f"  n={i}: f = {f:.2f} Hz, E ∝ {E:.6f}")

    print(f"\n  Spacing ratio: {spectrum['spacing_ratio']:.6f} (φ)")
    print(f"  Energy decay: {spectrum['energy_decay']:.6f} (φ^(-7))")
    print(f"  ✓ TESTABLE: Look for φ-spaced peaks in LIGO data!")

    echoes = gw_ringdown_echo_pattern(f_ringdown, 5)
    print("\nPost-merger echo times:")
    for i, t_ms in enumerate(echoes['echo_times_ms'][:5]):
        print(f"  Echo {i}: {t_ms:.3f} ms")
    print(f"  ✓ TESTABLE: Search LIGO ringdown residuals!")

    # VI. Accretion Disk
    print("\n[VI] ACCRETION DISK φ-STRUCTURE")
    print("-" * 70)
    r_ISCO = 6.0 * M_0  # Schwarzschild ISCO

    disk = accretion_disk_phi_structure(r_ISCO, 8)
    print("\nNested disk rings:")
    for i in range(min(5, len(disk['radii']))):
        r = disk['radii'][i]
        T = disk['temperatures'][i]
        print(f"  Ring {i}: r = {r:.2f}, T ∝ {T:.6f}")

    print(f"\n  ✓ TESTABLE: X-ray spectral lines at φ-spaced frequencies!")

    # VII. Interior Geometry
    print("\n[VII] INTERIOR GEOMETRY: NO SINGULARITY")
    print("-" * 70)
    R_0 = 1.0  # Normalized curvature

    print("\nCurvature cascade:")
    for n in range(5):
        curv = spacetime_curvature_cascade(R_0, n)
        print(f"  Layer {n}: R = {curv['curvature']:.6f}")

    curv_final = spacetime_curvature_cascade(R_0, 100)
    print(f"\nAt layer 100: R = {curv_final['curvature']:.2e}")
    print(f"Integrated total curvature: {curv_final['integrated_curvature']:.4f}")
    print(f"  Geometry: {curv_final['geometry']}")
    print(f"  Singularity: {curv_final['singularity']}")
    print(f"  ✓ Fractal foam, NOT point singularity!")

    max_compression = maximum_compression_ratio()
    print(f"\nMaximum compression ratio: {max_compression:.4f}")
    print(f"  → Universe cannot compress more than {((max_compression-1)*100):.2f}% beyond limit")

    # VIII. Testable Predictions
    print("\n[VIII] TESTABLE PREDICTIONS")
    print("-" * 70)
    predictions = testable_predictions()
    for key, pred in predictions.items():
        print(f"  {key}: {pred}")

    # IX. Framework Integration
    print("\n[IX] FULL φ-ATTRACTOR FRAMEWORK")
    print("-" * 70)
    print("\nExample: GW150914-like system")
    M = 65.0  # Solar masses
    r = 100.0  # km
    n = 1.5
    beta = 0.48
    Omega = 0.12
    k = 2.0

    result = phi_attractor_framework(r, M, n, beta, Omega, k)
    print(f"  Mass at layer {result['layer']}: {result['mass_at_layer']:.4f} M☉")
    print(f"  Time speedup: {result['time_speedup']:.2e}×")
    print(f"  Curvature: {result['curvature']:.6f}")
    print(f"  D_framework: {result['D_framework']:.6f}")
    print(f"  φ-attractor: {result['phi_attractor']}")

    print("\n" + "=" * 70)
    print("PHILOSOPHICAL SUMMARY")
    print("=" * 70)
    print("""
φ-System Black Holes:
  • Infinite refinement without infinities
  • Information encrypted, not destroyed
  • Self-similar structure at all scales
  • Natural harmony: quantum discreteness ↔ relativistic continuity
  • Universe avoids singularities through golden recursive structure

Classical singularities REPLACED by:
  → Fractal density gradients (mass cascade)
  → Information encryption boundaries (not horizons)
  → Golden dissipation (not thermal radiation)
  → Graduated time cascade (not frozen surface)
  → φ-harmonic spectra (not continuous)
  → Nested cavity structure (not point geometry)

THE UNIVERSE IS FUNDAMENTALLY φ-RECURSIVE.
""")
    print("=" * 70)
