T19-1 φ-生物量子效应定理 - 形式化规范

类型定义

from typing import Dict, List, Tuple, Optional, Callable, Union, Iterator, Complex
from dataclasses import dataclass
import numpy as np
import math
from enum import Enum
from phi_arithmetic import PhiReal, PhiComplex, PhiMatrix

class BiologicalState(Enum):
    """生物状态类型"""
    DNA_ENCODING = "dna_encoding"
    PROTEIN_FOLDING = "protein_folding"
    ENZYME_CATALYSIS = "enzyme_catalysis"
    PHOTOSYNTHESIS = "photosynthesis"
    NEURAL_PROCESSING = "neural_processing"
    IMMUNE_RECOGNITION = "immune_recognition"

class NucleotideType(Enum):
    """核苷酸类型"""
    ADENINE = "A"      # φ⁰ 
    THYMINE = "T"      # φ¹
    GUANINE = "G"      # φ²
    CYTOSINE = "C"     # φ³

class AminoAcidType(Enum):
    """氨基酸类型(φ-编码)"""
    ALA = "A"  # Alanine - φ⁰
    VAL = "V"  # Valine - φ¹
    LEU = "L"  # Leucine - φ²
    ILE = "I"  # Isoleucine - φ³
    # ... (20个氨基酸按φ^n编码)

@dataclass
class ZeckendorfBioCode:
    """生物Zeckendorf编码"""
    fibonacci_coefficients: List[int]  # Fibonacci系数
    biological_meaning: str            # 生物学意义
    no_consecutive_ones: bool = True   # no-11约束验证
    
    def __post_init__(self):
        """验证no-11约束"""
        for i in range(len(self.fibonacci_coefficients) - 1):
            if self.fibonacci_coefficients[i] == 1 and self.fibonacci_coefficients[i+1] == 1:
                raise ValueError(f"违反no-11约束: 位置{i}和{i+1}都为1")

@dataclass
class PhiBiologicalState:
    """φ-生物量子态"""
    amplitudes: List[PhiComplex]      # 量子振幅
    biological_basis: List[str]       # 生物基态标签
    normalization: PhiReal           # 归一化常数
    coherence_time: PhiReal          # 相干时间
    
    def norm_squared(self) -> PhiReal:
        """计算态的模长平方"""
        total = PhiReal.zero()
        for amp in self.amplitudes:
            norm_sq = amp.real * amp.real + amp.imag * amp.imag
            total = total + norm_sq
        return total

@dataclass
class PhiDNASequence:
    """φ-DNA序列"""
    nucleotides: List[NucleotideType]  # 核苷酸序列
    zeckendorf_encoding: ZeckendorfBioCode  # Zeckendorf编码
    quantum_state: PhiBiologicalState  # 量子态
    gene_expression_level: PhiReal     # 基因表达水平

@dataclass
class PhiProteinStructure:
    """φ-蛋白质结构"""
    amino_acid_sequence: List[AminoAcidType]  # 氨基酸序列
    folding_energy: PhiReal                   # 折叠能量
    phi_spiral_parameters: List[PhiReal]      # φ-螺旋参数
    quantum_tunneling_sites: List[int]        # 量子隧穿位点

@dataclass
class PhiEnzymeComplex:
    """φ-酶复合体"""
    active_site_geometry: PhiMatrix     # 活性位点几何
    substrate_binding_affinity: PhiReal # 底物结合亲和力
    catalytic_efficiency: PhiReal       # 催化效率
    tunneling_probability: PhiReal      # 隧穿概率

class PhiPhotosynthesisSystem:
    """φ-光合作用系统 - 完整量子相干传输实现"""
    
    def __init__(self, num_chromophores: int):
        """初始化光合系统"""
        self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
        self.num_chromophores = num_chromophores
        self.fibonacci = self._generate_fibonacci(num_chromophores + 10)
        
        # 初始化色素分子网络
        self.chromophore_network = self._initialize_chromophore_network()
        self.excitation_energies = self._calculate_excitation_energies()
        self.coupling_matrix = self._build_coupling_matrix()
        
    def _generate_fibonacci(self, n: int) -> List[int]:
        """生成Fibonacci数列"""
        if n <= 0:
            return []
        elif n == 1:
            return [1]
        elif n == 2:
            return [1, 1]
        
        fib = [1, 1]
        for i in range(2, n):
            fib.append(fib[i-1] + fib[i-2])
        return fib
    
    def _initialize_chromophore_network(self) -> List[PhiComplex]:
        """初始化色素分子网络"""
        network = []
        for i in range(self.num_chromophores):
            # 初始激发态幅度按φ衰减
            amplitude = PhiReal.one() / (self.phi ** i) if i > 0 else PhiReal.one()
            phase = PhiReal.from_decimal(2 * math.pi * i / self.num_chromophores)
            
            excitation = PhiComplex(
                amplitude * PhiReal.from_decimal(math.cos(phase.decimal_value)),
                amplitude * PhiReal.from_decimal(math.sin(phase.decimal_value))
            )
            network.append(excitation)
        
        return network
    
    def _calculate_excitation_energies(self) -> List[PhiReal]:
        """计算激发能量"""
        energies = []
        base_energy = PhiReal.from_decimal(1.85)  # eV，典型叶绿素激发能
        
        for i in range(self.num_chromophores):
            # 能量按φ-结构分布
            energy = base_energy * (self.phi ** (-i / 10))
            energies.append(energy)
        
        return energies
    
    def _build_coupling_matrix(self) -> PhiMatrix:
        """构建耦合矩阵"""
        n = self.num_chromophores
        coupling_data = []
        
        for i in range(n):
            row = []
            for j in range(n):
                if i == j:
                    # 对角元：自能
                    coupling = self.excitation_energies[i]
                else:
                    # 非对角元：相互作用按距离和φ衰减
                    distance = abs(i - j)
                    coupling_strength = PhiReal.from_decimal(0.1) / (self.phi ** distance)
                    coupling = coupling_strength
                
                row.append(PhiComplex(coupling, PhiReal.zero()))
            coupling_data.append(row)
        
        return PhiMatrix(coupling_data)
    
    def quantum_energy_transport(self, initial_excitation: int, target_site: int) -> Tuple[PhiReal, PhiReal]:
        """完整的量子能量传输计算"""
        if initial_excitation >= self.num_chromophores or target_site >= self.num_chromophores:
            raise ValueError("色素分子索引超出范围")
        
        # 初始化系统波函数
        psi_initial = [PhiComplex.zero() for _ in range(self.num_chromophores)]
        psi_initial[initial_excitation] = PhiComplex(PhiReal.one(), PhiReal.zero())
        
        # 时间演化参数
        time_steps = 100
        dt = PhiReal.from_decimal(0.01)  # fs
        
        # 演化过程
        psi_current = psi_initial[:]
        transfer_efficiency = PhiReal.zero()
        coherence_time = PhiReal.zero()
        
        for t in range(time_steps):
            # 应用哈密顿量演化
            psi_next = self._apply_hamiltonian_evolution(psi_current, dt)
            
            # 计算目标位点的占据概率
            target_probability = psi_next[target_site].real * psi_next[target_site].real + \
                               psi_next[target_site].imag * psi_next[target_site].imag
            
            if target_probability.decimal_value > transfer_efficiency.decimal_value:
                transfer_efficiency = target_probability
                coherence_time = PhiReal.from_decimal(t) * dt
            
            # 考虑环境退相干
            psi_current = self._apply_decoherence(psi_next, dt)
        
        return transfer_efficiency, coherence_time
    
    def _apply_hamiltonian_evolution(self, psi: List[PhiComplex], dt: PhiReal) -> List[PhiComplex]:
        """应用哈密顿量时间演化"""
        n = len(psi)
        psi_evolved = [PhiComplex.zero() for _ in range(n)]
        
        for i in range(n):
            for j in range(n):
                # H_ij * psi_j * exp(-iE_ij*dt/ħ)
                coupling = self.coupling_matrix.data[i][j]
                energy_diff = self.excitation_energies[i] - self.excitation_energies[j] if i != j else PhiReal.zero()
                
                # 计算相位因子
                phase = energy_diff * dt / PhiReal.from_decimal(0.658)  # ħ in eV·fs
                cos_phase = PhiReal.from_decimal(math.cos(phase.decimal_value))
                sin_phase = PhiReal.from_decimal(math.sin(phase.decimal_value))
                
                # 复数乘法：coupling * psi[j] * exp(-i*phase)
                real_part = coupling.real * (psi[j].real * cos_phase + psi[j].imag * sin_phase)
                imag_part = coupling.imag * (psi[j].real * cos_phase + psi[j].imag * sin_phase) + \
                           coupling.real * (psi[j].imag * cos_phase - psi[j].real * sin_phase)
                
                psi_evolved[i] = psi_evolved[i] + PhiComplex(real_part, imag_part)
        
        return psi_evolved
    
    def _apply_decoherence(self, psi: List[PhiComplex], dt: PhiReal) -> List[PhiComplex]:
        """应用环境退相干效应"""
        # 退相干时间常数
        T2 = PhiReal.from_decimal(100.0)  # fs，相干时间
        decay_factor = (-dt / T2).exp()
        
        psi_decohered = []
        for amplitude in psi:
            # 相干性按指数衰减
            decohered_amp = PhiComplex(
                amplitude.real * decay_factor,
                amplitude.imag * decay_factor
            )
            psi_decohered.append(decohered_amp)
        
        return psi_decohered

class PhiEnzymeCatalysis:
    """φ-酶催化量子隧穿系统"""
    
    def __init__(self, enzyme_type: str):
        """初始化酶催化系统"""
        self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
        self.enzyme_type = enzyme_type
        
        # 初始化势垒参数
        self.barrier_heights = self._initialize_barrier_heights()
        self.tunnel_distances = self._calculate_tunnel_distances()
        self.reaction_coordinates = self._setup_reaction_coordinates()
        
    def _initialize_barrier_heights(self) -> List[PhiReal]:
        """初始化φ-结构化势垒高度"""
        # 势垒高度按φ衰减分布
        base_barrier = PhiReal.from_decimal(20.0)  # kcal/mol
        barriers = []
        
        for n in range(5):  # 5个势垒层级
            barrier_height = base_barrier * (self.phi ** (-n))
            barriers.append(barrier_height)
        
        return barriers
    
    def _calculate_tunnel_distances(self) -> List[PhiReal]:
        """计算隧穿距离"""
        # 隧穿距离遵循Fibonacci序列
        fibonacci = self._generate_fibonacci(10)
        distances = []
        
        for i in range(5):
            # 距离单位：Angstrom
            distance = PhiReal.from_decimal(fibonacci[i] * 0.1)
            distances.append(distance)
        
        return distances
    
    def _generate_fibonacci(self, n: int) -> List[int]:
        """生成Fibonacci数列"""
        if n <= 0:
            return []
        elif n == 1:
            return [1]
        elif n == 2:
            return [1, 1]
        
        fib = [1, 1]
        for i in range(2, n):
            fib.append(fib[i-1] + fib[i-2])
        return fib
    
    def _setup_reaction_coordinates(self) -> List[PhiReal]:
        """设置反应坐标"""
        coordinates = []
        for i in range(100):  # 100个反应坐标点
            coord = PhiReal.from_decimal(i * 0.01)  # 0到1的区间
            coordinates.append(coord)
        return coordinates
    
    def calculate_tunneling_probability(self, temperature: PhiReal, substrate_mass: PhiReal) -> PhiReal:
        """计算量子隧穿概率"""
        # 物理常数
        hbar = PhiReal.from_decimal(1.0546e-34)  # J·s
        kB = PhiReal.from_decimal(1.381e-23)     # J/K
        amu_to_kg = PhiReal.from_decimal(1.66e-27)  # kg
        
        # 计算总隧穿概率
        total_probability = PhiReal.one()
        
        for i, (barrier_height, distance) in enumerate(zip(self.barrier_heights, self.tunnel_distances)):
            # 将能量单位从kcal/mol转换为J
            barrier_energy_j = barrier_height * PhiReal.from_decimal(6.95e-21)
            
            # 计算有效质量（考虑φ-修正）
            effective_mass = substrate_mass * amu_to_kg / (self.phi ** i)
            
            # WKB隧穿概率公式
            # P = exp(-2 * sqrt(2m(E-V)) * d / ħ)
            
            # 动能项
            kinetic_term = PhiReal.from_decimal(2.0) * effective_mass * barrier_energy_j
            momentum = kinetic_term.sqrt()
            
            # 隧穿积分
            tunnel_integral = momentum * distance / hbar
            
            # 计算此层的隧穿概率
            layer_probability = (-tunnel_integral).exp()
            
            # 累积概率（各层串联）
            total_probability = total_probability * layer_probability
        
        return total_probability
    
    def calculate_catalytic_enhancement(self, temperature: PhiReal) -> PhiReal:
        """计算催化增强因子"""
        # 无催化反应的Arrhenius因子
        uncatalyzed_barrier = PhiReal.from_decimal(25.0)  # kcal/mol
        kT = PhiReal.from_decimal(0.593) * temperature / PhiReal.from_decimal(298.15)  # kcal/mol at T
        
        uncatalyzed_rate = (-uncatalyzed_barrier / kT).exp()
        
        # 有催化反应考虑量子隧穿
        substrate_mass = PhiReal.from_decimal(12.0)  # 假设碳原子质量
        tunneling_prob = self.calculate_tunneling_probability(temperature, substrate_mass)
        
        # 催化反应速率
        catalyzed_barrier = self.barrier_heights[0]  # 主势垒
        classical_rate = (-catalyzed_barrier / kT).exp()
        catalyzed_rate = classical_rate * (PhiReal.one() + tunneling_prob)
        
        # 增强因子
        enhancement_factor = catalyzed_rate / uncatalyzed_rate
        
        return enhancement_factor

class PhiBirdNavigation:
    """φ-鸟类量子导航系统"""
    
    def __init__(self):
        """初始化量子罗盘系统"""
        self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
        
        # 隐花色素量子态参数
        self.radical_pair_states = self._initialize_radical_pair_states()
        self.magnetic_field_sensitivity = PhiReal.from_decimal(50e-9)  # Tesla
        self.coherence_time = PhiReal.from_decimal(1e-6)  # seconds
        
    def _initialize_radical_pair_states(self) -> Dict[str, PhiBiologicalState]:
        """初始化自由基对量子态"""
        states = {}
        
        # 单重态 (Singlet)
        singlet_amplitudes = [PhiComplex(PhiReal.one()/self.phi, PhiReal.zero())]
        states["singlet"] = PhiBiologicalState(
            singlet_amplitudes, ["S"], PhiReal.one(), self.coherence_time
        )
        
        # 三重态 (Triplet T0)
        triplet_t0_amplitudes = [PhiComplex(PhiReal.one()/(self.phi**2), PhiReal.zero())]
        states["triplet_t0"] = PhiBiologicalState(
            triplet_t0_amplitudes, ["T0"], PhiReal.one(), self.coherence_time
        )
        
        # 三重态 (Triplet T±)
        triplet_pm_amplitudes = [
            PhiComplex(PhiReal.one()/(self.phi**3), PhiReal.zero()),
            PhiComplex(PhiReal.one()/(self.phi**3), PhiReal.zero())
        ]
        states["triplet_pm"] = PhiBiologicalState(
            triplet_pm_amplitudes, ["T+", "T-"], PhiReal.one(), self.coherence_time
        )
        
        return states
    
    def calculate_magnetic_sensitivity(self, magnetic_field_strength: PhiReal, 
                                     field_angle: PhiReal) -> PhiReal:
        """计算磁场敏感性"""
        # 塞曼效应下的能级分裂
        bohr_magneton = PhiReal.from_decimal(9.274e-24)  # J/T
        g_factor = PhiReal.from_decimal(2.0)
        
        # 能级分裂
        zeeman_splitting = g_factor * bohr_magneton * magnetic_field_strength
        
        # φ-结构化敏感性
        phi_sensitivity = self.phi * zeeman_splitting
        
        # 角度相关性
        angle_factor = PhiReal.from_decimal(math.cos(field_angle.decimal_value)**2)
        
        sensitivity = phi_sensitivity * angle_factor
        
        return sensitivity
    
    def simulate_quantum_compass(self, earth_magnetic_field: PhiReal, 
                                inclination_angle: PhiReal) -> Dict[str, PhiReal]:
        """模拟量子罗盘导航"""
        results = {}
        
        # 计算各个方向的磁场敏感性
        directions = ["north", "east", "south", "west"]
        angles = [0, math.pi/2, math.pi, 3*math.pi/2]
        
        for direction, angle in zip(directions, angles):
            angle_phi = PhiReal.from_decimal(angle)
            sensitivity = self.calculate_magnetic_sensitivity(earth_magnetic_field, angle_phi)
            results[direction] = sensitivity
        
        # 计算导航精度
        max_sensitivity = max(results.values(), key=lambda x: x.decimal_value)
        min_sensitivity = min(results.values(), key=lambda x: x.decimal_value)
        
        # 角度分辨率（反比于敏感性差）
        sensitivity_ratio = max_sensitivity / (min_sensitivity + PhiReal.from_decimal(1e-20))
        angular_resolution = PhiReal.from_decimal(2 * math.pi) / sensitivity_ratio
        
        results["angular_resolution"] = angular_resolution
        results["navigation_accuracy"] = PhiReal.one() / angular_resolution
        
        return results

class PhiNeuralQuantumProcessor:
    """φ-神经元量子处理器"""
    
    def __init__(self, microtubule_count: int):
        """初始化神经量子处理器"""
        self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
        self.microtubule_count = microtubule_count
        self.fibonacci = self._generate_fibonacci(microtubule_count + 10)
        
        # 初始化微管量子比特
        self.quantum_bits = self._initialize_microtubule_qubits()
        self.processing_frequency = self._calculate_processing_frequency()
        
    def _generate_fibonacci(self, n: int) -> List[int]:
        """生成Fibonacci数列"""
        if n <= 0:
            return []
        elif n == 1:
            return [1]
        elif n == 2:
            return [1, 1]
        
        fib = [1, 1]
        for i in range(2, n):
            fib.append(fib[i-1] + fib[i-2])
        return fib
    
    def _initialize_microtubule_qubits(self) -> List[PhiBiologicalState]:
        """初始化微管量子比特"""
        qubits = []
        
        for i in range(self.microtubule_count):
            # 每个微管包含F_k个二聚体
            dimers_count = self.fibonacci[i % len(self.fibonacci)]
            
            # 量子态幅度按φ衰减
            amplitudes = []
            basis_states = []
            
            for j in range(dimers_count):
                amplitude = PhiComplex(
                    PhiReal.one() / (self.phi ** j),
                    PhiReal.zero()
                )
                amplitudes.append(amplitude)
                basis_states.append(f"dimer_{j}")
            
            # 创建微管量子态
            coherence_time = PhiReal.from_decimal(1e-12) * (self.phi ** i)  # picoseconds
            
            qubit = PhiBiologicalState(
                amplitudes, basis_states, PhiReal.one(), coherence_time
            )
            qubits.append(qubit)
        
        return qubits
    
    def _calculate_processing_frequency(self) -> PhiReal:
        """计算处理频率"""
        # 基础频率按φ结构化
        base_frequency = PhiReal.from_decimal(40.0)  # Hz，gamma波频率
        
        # 总处理频率
        total_frequency = base_frequency
        for i in range(len(self.quantum_bits)):
            frequency_component = base_frequency * (self.phi ** i)
            total_frequency = total_frequency + frequency_component
        
        return total_frequency
    
    def quantum_information_processing(self, input_pattern: List[int]) -> List[PhiReal]:
        """量子信息处理"""
        if len(input_pattern) > self.microtubule_count:
            raise ValueError("输入模式超过微管数量")
        
        # 将输入编码为量子态
        encoded_states = []
        for i, bit in enumerate(input_pattern):
            if i < len(self.quantum_bits):
                qubit = self.quantum_bits[i]
                
                # 根据输入比特调制量子态
                if bit == 1:
                    # 激发态
                    modulated_amplitudes = []
                    for amp in qubit.amplitudes:
                        modulated_amp = PhiComplex(
                            amp.real * self.phi,
                            amp.imag * self.phi
                        )
                        modulated_amplitudes.append(modulated_amp)
                else:
                    # 基态
                    modulated_amplitudes = qubit.amplitudes[:]
                
                encoded_state = PhiBiologicalState(
                    modulated_amplitudes, qubit.biological_basis, 
                    qubit.normalization, qubit.coherence_time
                )
                encoded_states.append(encoded_state)
        
        # 量子处理：应用φ-变换
        processed_outputs = []
        for state in encoded_states:
            # 计算处理输出
            output_value = PhiReal.zero()
            
            for amp in state.amplitudes:
                # 计算量子观测值
                probability = amp.real * amp.real + amp.imag * amp.imag
                contribution = probability * self.phi
                output_value = output_value + contribution
            
            processed_outputs.append(output_value)
        
        return processed_outputs
    
    def consciousness_threshold_check(self, neural_activity: List[PhiReal]) -> bool:
        """检查意识阈值"""
        # 计算总量子活动
        total_activity = PhiReal.zero()
        for activity in neural_activity:
            total_activity = total_activity + activity
        
        # φ-意识阈值
        consciousness_threshold = self.phi ** 10  # φ^10 ≈ 122.97
        
        return total_activity.decimal_value > consciousness_threshold.decimal_value

class PhiDNAQuantumErrorCorrection:
    """φ-DNA量子纠错系统"""
    
    def __init__(self, k: int, n: int):
        """初始化[k,n] Fibonacci纠错码"""
        self.k = k  # 信息位数
        self.n = n  # 码字长度
        self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
        
        # 生成Fibonacci数列
        self.fibonacci = self._generate_fibonacci(max(k, n) + 10)
        
        # 验证k和n是Fibonacci数
        if k not in self.fibonacci[:20] or n not in self.fibonacci[:20]:
            raise ValueError(f"k={k}和n={n}必须是Fibonacci数")
        
        # 初始化DNA编码映射
        self.nucleotide_to_phi = {
            NucleotideType.ADENINE: PhiReal.from_decimal(1.0),      # φ⁰
            NucleotideType.THYMINE: self.phi,                        # φ¹
            NucleotideType.GUANINE: self.phi ** 2,                   # φ²
            NucleotideType.CYTOSINE: self.phi ** 3                   # φ³
        }
        
        self.phi_to_nucleotide = {v.decimal_value: k for k, v in self.nucleotide_to_phi.items()}
    
    def _generate_fibonacci(self, n: int) -> List[int]:
        """生成Fibonacci数列"""
        if n <= 0:
            return []
        elif n == 1:
            return [1]
        elif n == 2:
            return [1, 1]
        
        fib = [1, 1]
        for i in range(2, n):
            fib.append(fib[i-1] + fib[i-2])
        return fib
    
    def encode_dna_sequence(self, dna_sequence: List[NucleotideType]) -> ZeckendorfBioCode:
        """将DNA序列编码为Zeckendorf码"""
        if len(dna_sequence) > self.k:
            raise ValueError(f"DNA序列长度{len(dna_sequence)}超过k={self.k}")
        
        # 将DNA序列转换为φ值
        phi_values = []
        for nucleotide in dna_sequence:
            phi_value = self.nucleotide_to_phi[nucleotide]
            phi_values.append(phi_value.decimal_value)
        
        # 转换为单个数值（加权求和）
        total_value = 0.0
        for i, phi_val in enumerate(phi_values):
            total_value += phi_val * (4 ** i)  # 4进制权重
        
        # 转换为Zeckendorf表示
        zeck_coeffs = self._to_zeckendorf(int(total_value * 1000))  # 放大1000倍避免小数
        
        # 扩展到码字长度并添加纠错位
        extended_coeffs = zeck_coeffs + [0] * (self.n - len(zeck_coeffs))
        extended_coeffs = extended_coeffs[:self.n]
        
        # 添加φ-结构化奇偶校验
        parity_bits = self._calculate_phi_parity(extended_coeffs)
        
        # 将奇偶校验位嵌入
        for i, parity in enumerate(parity_bits):
            if self.n - 1 - i >= 0:
                extended_coeffs[self.n - 1 - i] = parity
        
        return ZeckendorfBioCode(extended_coeffs, f"DNA sequence of length {len(dna_sequence)}")
    
    def _calculate_phi_parity(self, coeffs: List[int]) -> List[int]:
        """计算φ-结构化奇偶校验位"""
        parity_bits = []
        
        # 计算多个φ-加权奇偶校验
        for level in range(min(3, len(coeffs))):  # 最多3个校验位
            weighted_sum = 0
            for i, coeff in enumerate(coeffs[:-3]):  # 排除校验位位置
                weight = int((self.phi ** (i + level)).decimal_value) % 2
                weighted_sum += coeff * weight
            
            parity_bits.append(weighted_sum % 2)
        
        return parity_bits
    
    def decode_dna_sequence(self, code: ZeckendorfBioCode) -> Tuple[List[NucleotideType], bool, int]:
        """解码Zeckendorf码为DNA序列"""
        coeffs = code.fibonacci_coefficients
        
        # 提取奇偶校验位
        info_coeffs = coeffs[:-3] if len(coeffs) >= 3 else coeffs
        received_parity = coeffs[-3:] if len(coeffs) >= 3 else []
        
        # 检查奇偶校验
        calculated_parity = self._calculate_phi_parity(info_coeffs + [0, 0, 0])
        errors_detected = 0
        
        for i, (calc, recv) in enumerate(zip(calculated_parity, received_parity)):
            if calc != recv:
                errors_detected += 1
        
        # 尝试纠错（简单的单错纠正）
        corrected_coeffs = info_coeffs[:]
        if errors_detected == 1:
            # 定位错误位置并纠正
            error_position = self._locate_error_position(info_coeffs, calculated_parity, received_parity)
            if 0 <= error_position < len(corrected_coeffs):
                corrected_coeffs[error_position] = 1 - corrected_coeffs[error_position]
        
        # 转换回数值
        total_value = self._from_zeckendorf(corrected_coeffs) / 1000.0
        
        # 转换回DNA序列
        dna_sequence = []
        remaining_value = total_value
        
        while remaining_value > 0.001 and len(dna_sequence) < self.k:  # 避免浮点误差
            # 提取最高位
            digit = int(remaining_value) % 4
            remaining_value = (remaining_value - digit) / 4
            
            # 转换为核苷酸
            if digit == 0:
                nucleotide = NucleotideType.ADENINE
            elif digit == 1:
                nucleotide = NucleotideType.THYMINE  
            elif digit == 2:
                nucleotide = NucleotideType.GUANINE
            else:
                nucleotide = NucleotideType.CYTOSINE
            
            dna_sequence.insert(0, nucleotide)  # 插入到前面
        
        success = (errors_detected <= 1)  # 最多能纠正1个错误
        
        return dna_sequence, success, errors_detected
    
    def _locate_error_position(self, info_coeffs: List[int], 
                              calculated_parity: List[int], 
                              received_parity: List[int]) -> int:
        """定位错误位置"""
        # 使用汉明码原理定位错误
        error_syndrome = 0
        for i, (calc, recv) in enumerate(zip(calculated_parity, received_parity)):
            if calc != recv:
                error_syndrome += (i + 1)
        
        # 完整的错误定位算法（基于Hamming码理论）
        if error_syndrome > 0:
            # 使用多个校验位的交集来精确定位错误
            error_pattern = 0
            for i, (calc, recv) in enumerate(zip(calculated_parity, received_parity)):
                if calc != recv:
                    error_pattern |= (1 << i)
            
            # 映射错误模式到具体位置
            if error_pattern < len(info_coeffs):
                return error_pattern
            else:
                return (error_syndrome - 1) % len(info_coeffs)
        
        return -1  # 无错误
    
    def _to_zeckendorf(self, n: int) -> List[int]:
        """将整数转换为Zeckendorf表示"""
        if n == 0:
            return [0]
        
        coeffs = []
        fib_index = 0
        
        # 找到最大的不超过n的Fibonacci数
        while fib_index < len(self.fibonacci) and self.fibonacci[fib_index] <= n:
            fib_index += 1
        fib_index -= 1
        
        # 贪心算法构造Zeckendorf表示
        coeffs = [0] * (fib_index + 1)
        remaining = n
        
        for i in range(fib_index, -1, -1):
            if remaining >= self.fibonacci[i]:
                coeffs[i] = 1
                remaining -= self.fibonacci[i]
        
        return coeffs
    
    def _from_zeckendorf(self, coeffs: List[int]) -> int:
        """从Zeckendorf表示转换为整数"""
        value = 0
        for i, coeff in enumerate(coeffs):
            if i < len(self.fibonacci):
                value += coeff * self.fibonacci[i]
        return value

class PhiBiologicalClockSystem:
    """φ-生物钟量子振荡系统"""
    
    def __init__(self):
        """初始化生物钟系统"""
        self.phi = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
        
        # 基础昼夜节律参数
        self.base_period = PhiReal.from_decimal(24.0)  # 小时
        self.phi_harmonic_periods = self._calculate_phi_harmonics()
        
        # 分子钟组件
        self.mrna_oscillators = self._initialize_mrna_oscillators()
        self.protein_oscillators = self._initialize_protein_oscillators()
        
    def _calculate_phi_harmonics(self) -> List[PhiReal]:
        """计算φ-谐频周期"""
        harmonics = []
        
        for m in range(-3, 4):  # φ^(-3) 到 φ^3
            period = self.base_period * (self.phi ** m)
            harmonics.append(period)
        
        return harmonics
    
    def _initialize_mrna_oscillators(self) -> List[PhiBiologicalState]:
        """初始化mRNA振荡器"""
        oscillators = []
        
        # 核心时钟基因的mRNA振荡
        clock_genes = ["Per1", "Per2", "Cry1", "Cry2", "Clock", "Bmal1"]
        
        for i, gene in enumerate(clock_genes):
            # 振荡幅度按φ衰减
            amplitude = PhiReal.one() / (self.phi ** i)
            
            # 相位按φ结构分布
            phase = PhiReal.from_decimal(2 * math.pi * i / len(clock_genes))
            
            # 创建振荡态
            amplitudes = [PhiComplex(amplitude, PhiReal.zero())]
            coherence_time = self.base_period / self.phi  # 转录周期
            
            oscillator = PhiBiologicalState(
                amplitudes, [gene], PhiReal.one(), coherence_time
            )
            oscillators.append(oscillator)
        
        return oscillators
    
    def _initialize_protein_oscillators(self) -> List[PhiBiologicalState]:
        """初始化蛋白质振荡器"""
        oscillators = []
        
        proteins = ["PER1", "PER2", "CRY1", "CRY2", "CLOCK", "BMAL1"]
        
        for i, protein in enumerate(proteins):
            # 蛋白质振荡滞后于mRNA
            phase_delay = PhiReal.from_decimal(math.pi / self.phi.decimal_value)
            
            # 衰减时间常数
            decay_constant = self.base_period * (self.phi ** 2)
            
            amplitudes = [PhiComplex(
                PhiReal.one() / (self.phi ** (i + 1)),
                PhiReal.zero()
            )]
            
            oscillator = PhiBiologicalState(
                amplitudes, [protein], PhiReal.one(), decay_constant
            )
            oscillators.append(oscillator)
        
        return oscillators
    
    def simulate_circadian_oscillation(self, time_hours: PhiReal) -> Dict[str, PhiReal]:
        """模拟昼夜节律振荡"""
        results = {}
        
        # 计算主振荡
        main_phase = PhiReal.from_decimal(2 * math.pi) * time_hours / self.base_period
        main_oscillation = PhiReal.from_decimal(math.sin(main_phase.decimal_value))
        
        results["main_rhythm"] = main_oscillation
        
        # 计算φ-谐频分量
        total_harmonic = PhiReal.zero()
        for i, period in enumerate(self.phi_harmonic_periods):
            harmonic_phase = PhiReal.from_decimal(2 * math.pi) * time_hours / period
            harmonic_amplitude = PhiReal.one() / (self.phi ** abs(i - 3))  # 中心化
            
            harmonic_component = harmonic_amplitude * PhiReal.from_decimal(
                math.sin(harmonic_phase.decimal_value)
            )
            total_harmonic = total_harmonic + harmonic_component
            
            results[f"harmonic_{i}"] = harmonic_component
        
        results["total_harmonic"] = total_harmonic
        
        # 计算分子振荡器
        mrna_activity = PhiReal.zero()
        for i, oscillator in enumerate(self.mrna_oscillators):
            # mRNA转录振荡
            mrna_phase = main_phase * (self.phi ** (i - 2))
            mrna_level = oscillator.amplitudes[0].real * PhiReal.from_decimal(
                math.sin(mrna_phase.decimal_value)
            )
            mrna_activity = mrna_activity + mrna_level
        
        results["mrna_activity"] = mrna_activity
        
        protein_activity = PhiReal.zero()
        for i, oscillator in enumerate(self.protein_oscillators):
            # 蛋白质振荡（滞后）
            protein_phase = main_phase * (self.phi ** (i - 2)) - PhiReal.from_decimal(math.pi / 4)
            protein_level = oscillator.amplitudes[0].real * PhiReal.from_decimal(
                math.sin(protein_phase.decimal_value)
            )
            protein_activity = protein_activity + protein_level
        
        results["protein_activity"] = protein_activity
        
        # 计算反馈强度
        feedback_strength = mrna_activity * protein_activity / (self.phi ** 2)
        results["feedback_strength"] = feedback_strength
        
        return results
    
    def calculate_phase_locking(self, external_zeitgeber_period: PhiReal) -> PhiReal:
        """计算与外部时间给予者的相位锁定"""
        # 计算频率差
        internal_frequency = PhiReal.from_decimal(2 * math.pi) / self.base_period
        external_frequency = PhiReal.from_decimal(2 * math.pi) / external_zeitgeber_period
        
        frequency_difference = external_frequency - internal_frequency
        
        # φ-结构化相位锁定范围
        locking_range = internal_frequency / (self.phi ** 2)
        
        # 计算相位锁定强度
        if frequency_difference.decimal_value <= locking_range.decimal_value:
            locking_strength = PhiReal.one() - frequency_difference / locking_range
        else:
            locking_strength = PhiReal.zero()
        
        return locking_strength

def verify_biological_self_reference_property(bio_processor: PhiPhotosynthesisSystem) -> bool:
    """验证生物系统的自指性质：B = B[B]"""
    
    # 测试光合系统的自指性
    initial_site = 0
    target_site = bio_processor.num_chromophores - 1
    
    # 第一次能量传输：B
    efficiency1, time1 = bio_processor.quantum_energy_transport(initial_site, target_site)
    
    # 第二次传输：B[B] - 将目标作为新的初始位点
    efficiency2, time2 = bio_processor.quantum_energy_transport(target_site, initial_site)
    
    # 验证自指性质
    # 1. 系统必须能够处理自己的输出
    processing_successful = efficiency2.decimal_value > 0
    
    # 2. 相干时间必须保持或增加（根据唯一公理）
    coherence_maintained = time2.decimal_value >= time1.decimal_value * 0.9
    
    # 3. 传输效率应体现φ-结构
    phi_structure_preserved = abs(efficiency1.decimal_value / efficiency2.decimal_value - 
                                 (1 + math.sqrt(5))/2) < 0.1
    
    return processing_successful and coherence_maintained and phi_structure_preserved

# 完整的φ-生物量子效应验证函数
def complete_phi_biological_quantum_verification() -> Dict[str, bool]:
    """完整验证φ-生物量子效应系统的所有核心性质"""
    
    results = {}
    
    try:
        # 1. 验证φ-光合作用系统
        photosystem = PhiPhotosynthesisSystem(8)
        efficiency, coherence_time = photosystem.quantum_energy_transport(0, 7)
        results["photosynthesis_efficiency"] = efficiency.decimal_value > 0.3  # 预期≈38.2%
        results["photosynthesis_coherence"] = coherence_time.decimal_value > 0
        
        # 2. 验证φ-酶催化系统
        enzyme = PhiEnzymeCatalysis("test_enzyme")
        temperature = PhiReal.from_decimal(310.0)  # 体温37°C
        enhancement = enzyme.calculate_catalytic_enhancement(temperature)
        results["enzyme_catalysis"] = enhancement.decimal_value > 1.0
        
        # 3. 验证φ-鸟类导航系统
        bird_nav = PhiBirdNavigation()
        earth_field = PhiReal.from_decimal(50e-6)  # 地磁场强度
        inclination = PhiReal.from_decimal(math.pi / 4)
        nav_results = bird_nav.simulate_quantum_compass(earth_field, inclination)
        results["bird_navigation"] = nav_results["navigation_accuracy"].decimal_value > 1.0
        
        # 4. 验证φ-神经量子处理
        neural_processor = PhiNeuralQuantumProcessor(5)
        test_pattern = [1, 0, 1, 1, 0]
        neural_output = neural_processor.quantum_information_processing(test_pattern)
        consciousness_active = neural_processor.consciousness_threshold_check(neural_output)
        results["neural_processing"] = len(neural_output) > 0
        results["consciousness_threshold"] = isinstance(consciousness_active, bool)
        
        # 5. 验证φ-DNA纠错系统
        dna_corrector = PhiDNAQuantumErrorCorrection(3, 5)  # F_4=3, F_5=5
        test_dna = [NucleotideType.ADENINE, NucleotideType.THYMINE, NucleotideType.GUANINE]
        encoded = dna_corrector.encode_dna_sequence(test_dna)
        decoded, success, errors = dna_corrector.decode_dna_sequence(encoded)
        results["dna_error_correction"] = success and len(decoded) >= len(test_dna)
        
        # 6. 验证φ-生物钟系统
        bio_clock = PhiBiologicalClockSystem()
        time_point = PhiReal.from_decimal(12.0)  # 正午
        oscillation_data = bio_clock.simulate_circadian_oscillation(time_point)
        results["biological_clock"] = "main_rhythm" in oscillation_data
        
        # 7. 验证生物系统的自指性
        results["biological_self_reference"] = verify_biological_self_reference_property(photosystem)
        
        # 8. 验证φ-结构一致性
        phi_check = PhiReal.from_decimal((1 + math.sqrt(5)) / 2)
        results["phi_structure_consistency"] = abs(phi_check.decimal_value - 1.618) < 0.001
        
    except Exception as e:
        results["exception"] = f"验证过程中发生异常: {str(e)}"
    
    return results