T16-6 φ-因果结构形式化规范

1. 基础数学对象

1.1 φ-时空点

class PhiSpacetimePoint:
    def __init__(self, t: 'PhiNumber', x: 'PhiNumber', y: 'PhiNumber', z: 'PhiNumber'):
        self.t = t  # 时间坐标（离散化）
        self.x = x  # 空间坐标x
        self.y = y  # 空间坐标y
        self.z = z  # 空间坐标z
        self.phi = (1 + np.sqrt(5)) / 2
        self._verify_coordinates()
        
    def _verify_coordinates(self):
        """验证坐标满足no-11约束"""
        # 时间必须是Fibonacci时间量子的倍数

1.2 φ-因果关系

class PhiCausalRelation:
    def __init__(self, p: 'PhiSpacetimePoint', q: 'PhiSpacetimePoint'):
        self.p = p  # 起点
        self.q = q  # 终点
        self.phi = (1 + np.sqrt(5)) / 2
        
    def is_causal(self) -> bool:
        """判断是否存在因果关系"""
        
    def is_timelike(self) -> bool:
        """判断是否类时"""
        
    def is_lightlike(self) -> bool:
        """判断是否类光"""
        
    def is_spacelike(self) -> bool:
        """判断是否类空"""
        
    def causal_distance(self) -> 'PhiNumber':
        """计算因果距离"""

1.3 φ-光锥结构

class PhiLightCone:
    def __init__(self, vertex: 'PhiSpacetimePoint'):
        self.vertex = vertex
        self.phi = (1 + np.sqrt(5)) / 2
        self.tau_phi = PhiNumber(1)  # φ-时间量子
        
    def future_cone(self) -> Set['PhiSpacetimePoint']:
        """返回未来光锥中的离散点集"""
        
    def past_cone(self) -> Set['PhiSpacetimePoint']:
        """返回过去光锥中的离散点集"""
        
    def is_in_future(self, point: 'PhiSpacetimePoint') -> bool:
        """判断点是否在未来光锥内"""
        
    def is_in_past(self, point: 'PhiSpacetimePoint') -> bool:
        """判断点是否在过去光锥内"""

2. 因果结构核心

2.1 φ-因果集

class PhiCausalSet:
    def __init__(self):
        self.points = set()  # 时空点集合
        self.relations = set()  # 因果关系集合
        self.phi = (1 + np.sqrt(5)) / 2
        
    def add_point(self, point: 'PhiSpacetimePoint'):
        """添加时空点"""
        
    def add_relation(self, p: 'PhiSpacetimePoint', q: 'PhiSpacetimePoint') -> bool:
        """添加因果关系（检查一致性）"""
        
    def causal_future(self, point: 'PhiSpacetimePoint') -> Set['PhiSpacetimePoint']:
        """点的因果未来 J+(p)"""
        
    def causal_past(self, point: 'PhiSpacetimePoint') -> Set['PhiSpacetimePoint']:
        """点的因果过去 J-(p)"""
        
    def is_causally_connected(self, p: 'PhiSpacetimePoint', 
                             q: 'PhiSpacetimePoint') -> bool:
        """判断两点是否有因果联系"""
        
    def verify_no_closed_timelike_curves(self) -> bool:
        """验证无闭合类时曲线"""

2.2 φ-因果钻石

class PhiCausalDiamond:
    def __init__(self, bottom: 'PhiSpacetimePoint', top: 'PhiSpacetimePoint'):
        self.bottom = bottom
        self.top = top
        self.phi = (1 + np.sqrt(5)) / 2
        
    def volume(self) -> 'PhiNumber':
        """计算因果钻石的量子化体积"""
        
    def boundary(self) -> Set['PhiSpacetimePoint']:
        """返回边界点集"""
        
    def contains(self, point: 'PhiSpacetimePoint') -> bool:
        """判断点是否在钻石内"""
        
    def information_capacity(self) -> 'PhiNumber':
        """计算信息容量（比特）"""
        
    def shortest_path_length(self) -> 'PhiNumber':
        """最短因果路径长度"""

2.3 φ-因果传播

class PhiCausalPropagator:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        self.tau_phi = PhiNumber(1)  # 时间量子
        
    def propagate(self, initial: Set['PhiSpacetimePoint'], 
                  time_steps: int) -> Set['PhiSpacetimePoint']:
        """因果影响的Fibonacci传播"""
        
    def fibonacci_evolution(self, t: int) -> 'PhiNumber':
        """时刻t的因果域大小 |F^φ(t)|"""
        
    def butterfly_effect(self, perturbation: 'PhiNumber', 
                        time: 'PhiNumber') -> 'PhiNumber':
        """蝴蝶效应的φ-调制"""

3. 因果度量

3.1 φ-因果度量

class PhiCausalMetric:
    def __init__(self, manifold: 'PhiManifold'):
        self.manifold = manifold
        self.phi = (1 + np.sqrt(5)) / 2
        
    def interval(self, p: 'PhiSpacetimePoint', 
                 q: 'PhiSpacetimePoint') -> 'PhiNumber':
        """计算时空间隔 ds²"""
        
    def proper_time(self, path: List['PhiSpacetimePoint']) -> 'PhiNumber':
        """计算固有时（离散路径）"""
        
    def geodesic_distance(self, p: 'PhiSpacetimePoint', 
                         q: 'PhiSpacetimePoint') -> 'PhiNumber':
        """测地线距离"""

3.2 φ-Cauchy面

class PhiCauchySurface:
    def __init__(self, causal_set: 'PhiCausalSet'):
        self.causal_set = causal_set
        self.phi = (1 + np.sqrt(5)) / 2
        
    def find_surface(self) -> Set['PhiSpacetimePoint']:
        """找到Cauchy面"""
        
    def is_complete(self, surface: Set['PhiSpacetimePoint']) -> bool:
        """验证完备性"""
        
    def evolution_data(self) -> Dict[str, 'PhiNumber']:
        """提取演化初始数据"""

3.3 φ-事件视界

class PhiEventHorizon:
    def __init__(self, spacetime: 'PhiSpacetime'):
        self.spacetime = spacetime
        self.phi = (1 + np.sqrt(5)) / 2
        
    def locate_horizon(self) -> Set['PhiSpacetimePoint']:
        """定位事件视界（离散点集）"""
        
    def hawking_temperature(self) -> 'PhiNumber':
        """计算φ-修正的Hawking温度"""
        
    def information_paradox_resolution(self) -> str:
        """信息悖论的φ-解决方案"""

4. 因果序结构

4.1 φ-偏序关系

class PhiPartialOrder:
    def __init__(self, causal_set: 'PhiCausalSet'):
        self.causal_set = causal_set
        self.phi = (1 + np.sqrt(5)) / 2
        
    def precedes(self, p: 'PhiSpacetimePoint', 
                 q: 'PhiSpacetimePoint') -> bool:
        """p ≺^φ q"""
        
    def is_irreflexive(self) -> bool:
        """验证非自反性"""
        
    def is_transitive(self) -> bool:
        """验证传递性"""
        
    def is_antisymmetric(self) -> bool:
        """验证反对称性"""
        
    def chains(self) -> List[List['PhiSpacetimePoint']]:
        """所有因果链"""

4.2 φ-因果维度

class PhiCausalDimension:
    def __init__(self, causal_set: 'PhiCausalSet'):
        self.causal_set = causal_set
        self.phi = (1 + np.sqrt(5)) / 2
        
    def hausdorff_dimension(self) -> 'PhiNumber':
        """计算Hausdorff维度"""
        
    def effective_dimension(self, scale: 'PhiNumber') -> 'PhiNumber':
        """尺度相关的有效维度"""
        
    def dimension_deficit(self) -> 'PhiNumber':
        """no-11约束导致的维度缺失 ε_φ"""

5. 量子效应

5.1 φ-量子因果

class PhiQuantumCausality:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def bell_correlation(self, angle: 'PhiNumber') -> 'PhiNumber':
        """Bell关联的φ-修正"""
        
    def epr_causal_structure(self, separation: 'PhiNumber') -> 'PhiNumber':
        """EPR对的因果关联强度"""
        
    def quantum_channel_capacity(self, entropy: 'PhiNumber') -> 'PhiNumber':
        """量子信道容量"""

5.2 φ-引力效应

class PhiGravitationalCausality:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        self.c = PhiNumber(1)  # 光速（归一化）
        
    def effective_light_speed(self, energy: 'PhiNumber') -> 'PhiNumber':
        """能量相关的有效光速"""
        
    def causal_delay(self, energy: 'PhiNumber') -> 'PhiNumber':
        """高能过程的因果延迟"""
        
    def gravitational_wave_delay(self, frequency: 'PhiNumber', 
                                distance: 'PhiNumber') -> 'PhiNumber':
        """引力波相对延迟"""

6. 信息论结构

6.1 φ-因果信息

class PhiCausalInformation:
    def __init__(self, causal_diamond: 'PhiCausalDiamond'):
        self.diamond = causal_diamond
        self.phi = (1 + np.sqrt(5)) / 2
        
    def maximum_information(self) -> 'PhiNumber':
        """最大信息容量（比特）"""
        
    def information_propagation_speed(self) -> 'PhiNumber':
        """信息传播速度上限"""
        
    def holographic_entropy(self) -> 'PhiNumber':
        """全息熵"""

6.2 φ-因果熵

class PhiCausalEntropy:
    def __init__(self, causal_set: 'PhiCausalSet'):
        self.causal_set = causal_set
        self.phi = (1 + np.sqrt(5)) / 2
        
    def causal_entropy(self) -> 'PhiNumber':
        """因果集的熵"""
        
    def entropy_gradient(self, p: 'PhiSpacetimePoint') -> 'PhiNumber':
        """熵梯度（时间箭头）"""

7. 宇宙学应用

7.1 φ-宇宙因果结构

class PhiCosmologicalCausality:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def horizon_size(self, time: 'PhiNumber') -> 'PhiNumber':
        """因果视界大小"""
        
    def inflation_causal_patch(self, e_folds: 'PhiNumber') -> 'PhiNumber':
        """暴胀因果域"""
        
    def cosmic_censorship_check(self, singularity: 'PhiSingularity') -> bool:
        """φ-宇宙审查验证"""

8. 验证函数

8.1 理论一致性检查

def verify_causal_consistency(causal_set: 'PhiCausalSet') -> bool:
    """验证因果一致性"""
    
def verify_no_11_causality(relations: Set['PhiCausalRelation']) -> bool:
    """验证因果关系满足no-11约束"""
    
def verify_fibonacci_time_steps(path: List['PhiSpacetimePoint']) -> bool:
    """验证时间步长遵循Fibonacci序列"""

8.2 物理合理性检查

def check_causality_conditions(metric: 'PhiCausalMetric') -> bool:
    """检查因果条件（无超光速等）"""
    
def check_entropy_increase(causal_set: 'PhiCausalSet') -> bool:
    """验证熵沿时间方向增加"""

9. 关键常数

# 基础常数
PHI = (1 + np.sqrt(5)) / 2
TAU_PHI = PhiNumber(1)  # φ-时间量子

# 因果结构常数
DIMENSION_DEFICIT = np.log(2) / np.log(PHI)  # ε_φ ≈ 0.44
CAUSAL_DIMENSION = 4 - DIMENSION_DEFICIT  # ≈ 3.56

# 光速修正
LIGHT_SPEED_CORRECTION = 1e-10  # δ_φ基准值

# 信息容量因子
INFO_CAPACITY_FACTOR = np.log(PHI) / np.log(2)  # bits per φ-unit

10. 错误处理

class PhiCausalityError(Exception):
    """因果性错误基类"""
    
class ClosedTimelikeCurveError(PhiCausalityError):
    """检测到闭合类时曲线"""
    
class CausalViolationError(PhiCausalityError):
    """违反因果性"""
    
class No11CausalityError(PhiCausalityError):
    """因果结构违反no-11约束"""