core.enhanced_verification

enhanced_verification

Enhanced verification module for the Choptyuk problem.

Extends the original verification with: - 4D spin manifold extension - Kähler surface corrections - Tyukovsky equation adaptation - Einstein GR / QNM predictions - Comprehensive criticism response verification

Part of: https://github.com/wild8highlander/choptuik_ac_bc Author: Ishak Khamzatovich Isaev (ORCID: 0009-0003-7299-0701) Version: 2.0.0

K3Surface dataclass

K3Surface(b0: int = 1, b1: int = 0, b2: int = 22, b3: int = 0, b4: int = 1, hodge_11: int = 20, hodge_20: int = 1, dirac_index: int = 2, b2_plus: int = 3, holonomy: str = 'Sp(1) ≅ SU(2)')

The K3 surface as a 4D spin manifold.

b2_check property

b2_check: int

Verify b₂ = h^(1,1) + 2h^(2,0)

b2_over_index property

b2_over_index: float

b₂ / ind(D) = 22/2 = 11

sw_compatible property

sw_compatible: bool

Seiberg-Witten compatibility: corrected Dirac eigenvalue is well-defined on SW moduli space.

KleinQuartic dataclass

KleinQuartic(genus: int = 3, automorphism_order: int = 168, automorphism_group: str = 'PSL(2,7)', delta_A: float = pi / 2, delta_B: float = pi / 3, delta_C: float = pi / 7, fuchsian_group: str = 'Γ(2,3,7)', n_spin_structures: int = 0)

The Klein quartic K: x³y + y³z + z³x = 0 in ℂℙ².

b_C_correction property

b_C_correction: float

b-C correction: Δ_bC = λ₁(D²_σ₀) + δ_C²/2

braking_coefficient property

braking_coefficient: float

γ = δ_C⁴ / b₂(K3)

effective_phase property

effective_phase: float

δ_eff = δ_C⁵ / b₂(K3) ≈ 1/1200

choptyuk_constant property

choptyuk_constant: float

b_Ch = 1 - cos(2π/7) = 2sin²(π/7)

imaginary_correction property

imaginary_correction: float

1 - δ_C/π²

unified_formula

unified_formula(include_higher_orders: bool = False) -> float

Unified Choptyuk formula: Δ_Ch = λ₁ - R/4 + δ_C²/2 - δ_C⁵/22

Source code in src/core/enhanced_verification.py

def unified_formula(self, include_higher_orders: bool = False) -> float:
    """Unified Choptyuk formula: Δ_Ch = λ₁ - R/4 + δ_C²/2 - δ_C⁵/22"""
    delta = self.b_C_correction - self.effective_phase
    if include_higher_orders:
        delta += self.delta_C**4 / 8 + self.delta_C**6 / 2
    return delta

TyukovskyAdapter dataclass

TyukovskyAdapter(klein: KleinQuartic = KleinQuartic())

Adaptation of spinorial corrections to Tyukovsky equations.

gct_equation property

gct_equation: str

Generalized Choptyuk-Tyukovsky equation (symbolic).

free_parameters property

free_parameters: int

Number of free parameters in gCT equations.

corrected_critical_exponent

corrected_critical_exponent(delta_0: float) -> float

δ_corr = δ₀ + δ_C²/2 - δ_C⁵/22

Source code in src/core/enhanced_verification.py

def corrected_critical_exponent(self, delta_0: float) -> float:
    """δ_corr = δ₀ + δ_C²/2 - δ_C⁵/22"""
    return delta_0 + self.klein.delta_C**2/2 - self.klein.effective_phase

echo_period

echo_period(delta: float) -> float

T_echo = 1/δ

Source code in src/core/enhanced_verification.py

def echo_period(self, delta: float) -> float:
    """T_echo = 1/δ"""
    return 1.0 / delta

CriticismResponse dataclass

CriticismResponse(klein: KleinQuartic = KleinQuartic())

Verification of responses to potential criticism.

check_non_coincidental

check_non_coincidental() -> Dict

Verify that 1/1200 agreement is not coincidental.

Source code in src/core/enhanced_verification.py

def check_non_coincidental(self) -> Dict:
    """Verify that 1/1200 agreement is not coincidental."""
    # Find best rational approximation with q < 1200
    best_p, best_q = 0, 1
    best_dev = float('inf')
    target = self.klein.effective_phase
    for q in range(1, 1200):
        p = round(target * q)
        if p == 0:
            continue
        dev = abs(p/q - target) / target * 100
        if dev < best_dev:
            best_dev = dev
            best_p, best_q = p, q

    return {
        'best_approx': f'{best_p}/{best_q}',
        'best_dev_pct': best_dev,
        'no_better_below_1200': best_dev >= 0.684,
    }

check_b2_uniqueness

check_b2_uniqueness() -> Dict

Verify that b₂ = 22 is the unique choice.

Source code in src/core/enhanced_verification.py

def check_b2_uniqueness(self) -> Dict:
    """Verify that b₂ = 22 is the unique choice."""
    results = {}
    for k in [20, 21, 22, 23, 24]:
        dev = abs(self.klein.delta_C**5/k - 1/1200) / (1/1200) * 100
        results[k] = {'deviation_pct': dev, 'compatible': dev < 1.0}
    return results

check_stability

check_stability(epsilon: float = 0.001) -> Dict

Check stability under deformation δ_C → δ_C + ε.

Source code in src/core/enhanced_verification.py

def check_stability(self, epsilon: float = 0.001) -> Dict:
    """Check stability under deformation δ_C → δ_C + ε."""
    delta_eff_deformed = (self.klein.delta_C + epsilon)**5 / 22
    dev = abs(delta_eff_deformed - 1/1200) / (1/1200) * 100
    return {
        'epsilon': epsilon,
        'delta_eff_deformed': delta_eff_deformed,
        'deviation_pct': dev,
        'stable': dev < 1.0,
    }

check_spin_structures

check_spin_structures() -> Dict

Check spin structure distribution.

Source code in src/core/enhanced_verification.py

def check_spin_structures(self) -> Dict:
    """Check spin structure distribution."""
    total = self.klein.n_spin_structures  # 64
    even = 28  # Arf = 0
    odd = 36   # Arf = 1
    return {
        'total': total,
        'even_Arf0': even,
        'odd_Arf1': odd,
        'good_fraction_pct': even / total * 100,
    }