T19-3 φ-社会熵动力学定理形式化规范

核心数学结构

1. PhiReal类

基础φ实数类，支持φ-编码运算

class PhiReal:
    def __init__(self, decimal_value: float)
    @property
    def decimal_value(self) -> float
    @property  
    def zeckendorf_representation(self) -> List[int]
    def has_consecutive_11(self) -> bool  # no-11约束检查
    def __add__(self, other) -> PhiReal
    def __sub__(self, other) -> PhiReal
    def __mul__(self, other) -> PhiReal
    def __truediv__(self, other) -> PhiReal
    def __pow__(self, other) -> PhiReal

2. PhiComplex类

φ复数类，支持复数φ运算

class PhiComplex:
    def __init__(self, real: PhiReal, imag: PhiReal)
    @property
    def real(self) -> PhiReal
    @property
    def imag(self) -> PhiReal
    def __add__(self, other) -> PhiComplex
    def __sub__(self, other) -> PhiComplex
    def __mul__(self, other) -> PhiComplex
    def __truediv__(self, other) -> PhiComplex
    def magnitude(self) -> PhiReal
    def phase(self) -> PhiReal

3. PhiSocialSystem类

φ-社会系统核心类：$\mathcal{S} = \mathcal{S}[\mathcal{S}]$

class PhiSocialSystem:
    def __init__(self, phi: PhiReal, population_size: int)
    @property
    def phi(self) -> PhiReal
    @property
    def population_size(self) -> int
    @property
    def social_entropy(self) -> PhiReal
    
    def self_reference(self, system_state: 'PhiSocialSystem') -> 'PhiSocialSystem'
    def calculate_entropy_rate(self, individual_entropies: List[PhiReal]) -> PhiReal
    def update_entropy(self, time_step: PhiReal) -> None
    def verify_self_reference_property(self) -> bool

4. PhiSocialNetwork类

φ-社会网络拓扑：$\text{Network}(L) = \sum_{k=0}^{L} \frac{N_k}{\phi^k} \text{Layer}_k$

class PhiSocialNetwork:
    def __init__(self, phi: PhiReal, max_layers: int)
    @property
    def layers(self) -> List[int]  # Fibonacci序列
    @property
    def connectivity_matrix(self) -> List[List[PhiReal]]
    
    def fibonacci_layer_size(self, k: int) -> int
    def connection_weight(self, distance: int) -> PhiReal  # w = w0/φ^d
    def propagation_speed(self, layer: int) -> PhiReal  # v = v0·φ^(-k)
    def total_connectivity(self) -> PhiReal
    def verify_fibonacci_structure(self) -> bool

5. PhiInformationPropagation类

φ-信息传播动力学：$\frac{\partial I}{\partial t} = \frac{1}{\phi} \nabla^2 I + \frac{1}{\phi^2} S(x,t) - \frac{1}{\phi^3} \gamma I$

class PhiInformationPropagation:
    def __init__(self, phi: PhiReal, decay_rate: PhiReal)
    
    def viral_propagation(self, initial_info: PhiReal, time: PhiReal, tau: PhiReal) -> PhiReal
    def normal_propagation(self, initial_info: PhiReal, time: PhiReal, tau: PhiReal) -> PhiReal
    def decay_propagation(self, initial_info: PhiReal, time: PhiReal, tau: PhiReal) -> PhiReal
    def propagation_range(self, level: int, base_range: PhiReal) -> PhiReal
    def diffusion_equation(self, info_density: PhiReal, source: PhiReal, gamma: PhiReal) -> PhiReal

6. PhiGroupDecision类

φ-群体决策机制：$\text{Consensus}(t) = \sum_{i=1}^{N} \frac{w_i}{\phi^{|o_i - \bar{o}|}} o_i(t)$

class PhiGroupDecision:
    def __init__(self, phi: PhiReal)
    
    def decision_weight(self, rank: int) -> PhiReal  # w = φ^(-rank)
    def consensus_formation(self, opinions: List[PhiReal], weights: List[PhiReal]) -> PhiReal
    def convergence_time(self, group_size: int, tau: PhiReal) -> PhiReal
    def opinion_center(self, opinions: List[PhiReal]) -> PhiReal
    def calculate_consensus(self, opinions: List[PhiReal], time: PhiReal) -> PhiReal

7. PhiSocialHierarchy类

φ-社会分层结构：$\text{Hierarchy} = \bigoplus_{k=0}^{L} \frac{P_k}{\phi^k} \text{Class}_k$

class PhiSocialHierarchy:
    def __init__(self, phi: PhiReal, max_levels: int)
    
    def layer_population(self, level: int) -> int  # F_k Fibonacci numbers
    def layer_power(self, level: int) -> PhiReal  # φ^level
    def mobility_probability(self, delta_level: int, upward: bool) -> PhiReal
    def hierarchy_structure(self) -> List[tuple[int, PhiReal]]  # (population, power)
    def verify_fibonacci_population(self) -> bool

8. PhiCulturalEvolution类

φ-文化演化动力学：$\frac{dM_i}{dt} = \sum_{j \neq i} \frac{\alpha_{ij}}{\phi^{d_{ij}}} M_j - \frac{\beta_i}{\phi} M_i + \frac{\mu_i}{\phi^2}$

class PhiCulturalEvolution:
    def __init__(self, phi: PhiReal)
    
    def meme_survival_time(self, culture_type: str, tau: PhiReal) -> PhiReal
    def cultural_diversity(self, probabilities: List[PhiReal]) -> PhiReal
    def meme_propagation_rate(self, distance: int) -> PhiReal  # α/φ^d
    def cultural_mutation_rate(self, base_rate: PhiReal) -> PhiReal  # μ/φ²
    def evolution_dynamics(self, memes: List[PhiReal], time_step: PhiReal) -> List[PhiReal]

9. PhiEconomicSystem类

φ-经济系统动力学：$\frac{dV}{dt} = \phi \sum_i P_i C_i - \frac{1}{\phi} \sum_j D_j - \frac{1}{\phi^2} L$

class PhiEconomicSystem:
    def __init__(self, phi: PhiReal)
    
    def sector_proportion(self, sector: str) -> PhiReal  # 生产/流通/服务部门比例
    def wealth_distribution_exponent(self) -> PhiReal  # α = ln(φ)
    def economic_cycle_period(self) -> PhiReal  # T = φ²×12个月
    def value_flow_dynamics(self, production: List[PhiReal], 
                          consumption: List[PhiReal], 
                          distribution: List[PhiReal], 
                          loss: PhiReal) -> PhiReal
    def pareto_distribution(self, wealth: PhiReal) -> PhiReal

10. PhiPoliticalSystem类

φ-政治组织结构：$\text{Power}(i) = \frac{P_0}{\phi^{r_i}}$

class PhiPoliticalSystem:
    def __init__(self, phi: PhiReal, base_power: PhiReal)
    
    def power_distribution(self, rank: int) -> PhiReal  # P₀/φʳ
    def layer_personnel(self, level: int) -> int  # Fibonacci numbers
    def political_stability(self, actual_powers: List[PhiReal], 
                          expected_powers: List[PhiReal]) -> PhiReal
    def power_transfer_probability(self, time: PhiReal, tau: PhiReal) -> PhiReal
    def governance_structure(self) -> List[tuple[PhiReal, int]]  # (power, personnel)

11. PhiSocialConflict类

φ-社会冲突动力学：$\frac{dT}{dt} = \phi \sum_i S_i - \frac{1}{\phi} R - \frac{1}{\phi^2} D$

class PhiSocialConflict:
    def __init__(self, phi: PhiReal, base_tension: PhiReal)
    
    def conflict_threshold(self, level: int) -> PhiReal  # T₀φᵏ
    def resolution_time(self, conflict_level: int, tau: PhiReal) -> PhiReal
    def tension_accumulation(self, stress_sources: List[PhiReal], 
                           release_mechanisms: PhiReal, 
                           dissipation: PhiReal) -> PhiReal
    def conflict_classification(self, tension: PhiReal) -> str
    def tension_dynamics(self, current_tension: PhiReal, time_step: PhiReal) -> PhiReal

12. PhiSocialInnovation类

φ-社会创新机制：$I_{\text{innovation}} = \sum_{k=1}^{N} \frac{C_k}{\phi^k} \times \frac{D_k}{\phi^k} \times \frac{A_k}{\phi^k}$

class PhiSocialInnovation:
    def __init__(self, phi: PhiReal)
    
    def innovation_frequency(self, innovation_type: str) -> PhiReal
    def innovation_impact_duration(self, innovation_type: str, tau: PhiReal) -> PhiReal
    def innovation_diffusion(self, time: PhiReal, tau: PhiReal) -> PhiReal  # S曲线
    def innovation_index(self, creativity: List[PhiReal], 
                        diversity: List[PhiReal], 
                        adaptability: List[PhiReal]) -> PhiReal
    def diffusion_turning_point(self, tau: PhiReal) -> PhiReal  # t = φτ

13. PhiSocialMemory类

φ-社会记忆系统：$M(t) = M_0 \sum_{k=0}^{\infty} \frac{e^{-t/\tau_k}}{\phi^k}$

class PhiSocialMemory:
    def __init__(self, phi: PhiReal, base_tau: PhiReal)
    
    def memory_decay_time(self, level: int) -> PhiReal  # τ₀φᵏ
    def memory_weight(self, level: int) -> PhiReal  # 1/φᵏ
    def memory_importance(self, level: int) -> PhiReal
    def total_memory(self, initial_memory: PhiReal, time: PhiReal) -> PhiReal
    def memory_hierarchy(self) -> List[tuple[PhiReal, PhiReal]]  # (decay_time, weight)

14. PhiSocialLearning类

φ-社会学习适应：$L_{\text{collective}} = \sum_{i=1}^{N} \frac{w_i}{\phi^{e_i}} L_i$

class PhiSocialLearning:
    def __init__(self, phi: PhiReal)
    
    def learning_efficiency(self, learning_mode: str) -> PhiReal
    def collective_learning_rate(self, base_rate: PhiReal, group_size: int) -> PhiReal
    def adaptation_time(self, group_size: int, tau: PhiReal) -> PhiReal
    def collective_intelligence(self, individual_learning: List[PhiReal], 
                              distances: List[PhiReal], 
                              weights: List[PhiReal]) -> PhiReal
    def social_adaptation(self, time: PhiReal, tau: PhiReal, group_size: int) -> PhiReal

验证接口

自指完备性验证

def verify_self_reference_completeness(system: PhiSocialSystem) -> bool:
    """验证社会系统的自指完备性：S = S[S]"""
    
def verify_entropy_increase_principle(system: PhiSocialSystem, 
                                    time_steps: List[PhiReal]) -> bool:
    """验证熵增原理：dS/dt > 0"""

def verify_no_11_constraint(numbers: List[PhiReal]) -> bool:
    """验证no-11约束"""

φ-结构验证

def verify_fibonacci_structure(network: PhiSocialNetwork) -> bool:
    """验证Fibonacci结构"""
    
def verify_phi_scaling(hierarchy: PhiSocialHierarchy) -> bool:
    """验证φ-缩放法则"""
    
def verify_phi_dynamics(system: PhiSocialSystem) -> bool:
    """验证φ-动力学方程"""

社会系统整体验证

def verify_social_system_consistency(system: PhiSocialSystem,
                                   network: PhiSocialNetwork,
                                   hierarchy: PhiSocialHierarchy,
                                   innovation: PhiSocialInnovation) -> bool:
    """验证社会系统各组件的一致性"""

def verify_theory_implementation_match() -> bool:
    """验证理论与实现的完全匹配"""

关键参数

φ-常数

• φ = (1 + √5)/2 ≈ 1.618034
• 1/φ = φ - 1 ≈ 0.618034
• 1/φ² ≈ 0.382

Fibonacci序列

F₁=1, F₂=1, F₃=2, F₅=5, F₆=8, F₈=21, F₁₃=233, F₂₁=10946, F₃₄=5702887

时间常数

• 注意力切换：0.31秒
• 经济周期：31.4个月
• 冲突解决：φᵏτ
• 创新扩散转折点：φτ

社会层级规模

• 精英层：5人，权力φ⁵
• 管理层：21人，权力φ⁴
• 专业层：233人，权力φ³
• 技能层：10946人，权力φ²
• 基础层：5702887人，权力φ¹

所有实现必须严格遵循φ-编码的no-11约束，并与理论文档中的公式、参数完全一致。