T20-3 RealityShell边界定理形式化规范
1. 基础Shell结构定义
1.1 信息流类
import numpy as np
import math
from typing import List, Dict, Tuple, Optional, Any, Set
from dataclasses import dataclass
from enum import Enum
class FlowDirection(Enum):
IN_TO_OUT = "in_to_out"
OUT_TO_IN = "out_to_in"
BIDIRECTIONAL = "bidirectional"
EQUILIBRIUM = "equilibrium"
@dataclass
class InformationFlow:
"""跨边界信息流"""
def __init__(self, direction: FlowDirection, amount: float,
phi_quantized: bool = True, conservation_verified: bool = False):
self.phi = (1 + np.sqrt(5)) / 2
self.direction = direction
self.raw_amount = amount
self.phi_quantized = phi_quantized
self.conservation_verified = conservation_verified
# φ-量化处理
if phi_quantized:
self.quantized_amount = self._phi_quantize(amount)
else:
self.quantized_amount = amount
self.flow_entropy = self._compute_flow_entropy()
def _phi_quantize(self, amount: float) -> float:
"""φ-量化信息量"""
if amount == 0:
return 0.0
# 找到最接近的φ^k倍数
if amount > 0:
k = math.log(abs(amount)) / math.log(self.phi)
k_rounded = round(k)
quantized = (self.phi ** k_rounded) * (1 if amount > 0 else -1)
else:
k = math.log(abs(amount)) / math.log(self.phi)
k_rounded = round(k)
quantized = -(self.phi ** k_rounded)
return quantized
def _compute_flow_entropy(self) -> float:
"""计算信息流熵"""
if self.quantized_amount == 0:
return 0.0
return abs(self.quantized_amount) * math.log(abs(self.quantized_amount) + 1, self.phi)
def verify_conservation(self, reverse_flow: 'InformationFlow') -> bool:
"""验证与反向流的守恒关系"""
if self.direction == FlowDirection.IN_TO_OUT:
expected_reverse = -self.quantized_amount / self.phi
elif self.direction == FlowDirection.OUT_TO_IN:
expected_reverse = -self.quantized_amount * self.phi
else:
return True # 平衡态总是守恒
conservation_check = bool(abs(reverse_flow.quantized_amount - expected_reverse) < 1e-6)
self.conservation_verified = conservation_check
return conservation_check
def __add__(self, other: 'InformationFlow') -> 'InformationFlow':
"""信息流叠加"""
total_amount = self.quantized_amount + other.quantized_amount
if abs(total_amount) < 1e-10:
direction = FlowDirection.EQUILIBRIUM
elif total_amount > 0:
direction = FlowDirection.IN_TO_OUT
else:
direction = FlowDirection.OUT_TO_IN
return InformationFlow(direction, total_amount,
phi_quantized=True, conservation_verified=False)
@dataclass
class BoundaryPoint:
"""边界点"""
def __init__(self, state: 'ZeckendorfString', trace_value: int,
is_inside: bool, distance_to_boundary: float):
self.state = state
self.trace_value = trace_value
self.is_inside = bool(is_inside) # 确保是Python原生布尔类型
self.distance_to_boundary = distance_to_boundary
self.boundary_stability = self._compute_stability()
def _compute_stability(self) -> float:
"""计算边界点稳定性"""
phi = (1 + np.sqrt(5)) / 2
if self.distance_to_boundary == 0:
return 0.0 # 正好在边界上，不稳定
return 1.0 / (1.0 + abs(self.distance_to_boundary) / phi)
1.2 边界函数实现
class BoundaryFunction:
"""RealityShell边界函数"""
def __init__(self, threshold: float, shell_depth: int,
core_value: int, phi_scaling: bool = True):
self.phi = (1 + np.sqrt(5)) / 2
self.threshold = threshold
self.shell_depth = shell_depth
self.core_value = core_value
self.phi_scaling = phi_scaling
# 计算φ-调制阈值
if phi_scaling:
self.effective_threshold = threshold * (self.phi ** shell_depth)
else:
self.effective_threshold = threshold
def evaluate(self, state: 'ZeckendorfString', trace_calculator) -> BoundaryPoint:
"""评估状态相对于边界的位置"""
trace_value = trace_calculator.compute_full_trace(state)
is_inside = bool(trace_value >= self.effective_threshold)
distance = trace_value - self.effective_threshold
return BoundaryPoint(state, trace_value, is_inside, distance)
def compute_boundary_gradient(self, state: 'ZeckendorfString',
trace_calculator, epsilon: float = 1e-6) -> float:
"""计算边界梯度（数值微分）"""
base_point = self.evaluate(state, trace_calculator)
# 小扰动
perturbed_state = self._perturb_state(state, epsilon)
perturbed_point = self.evaluate(perturbed_state, trace_calculator)
# 梯度近似
if abs(perturbed_point.trace_value - base_point.trace_value) < 1e-10:
return 0.0
gradient = (perturbed_point.distance_to_boundary - base_point.distance_to_boundary) / \
(perturbed_point.trace_value - base_point.trace_value)
return gradient
def _perturb_state(self, state: 'ZeckendorfString', epsilon: float) -> 'ZeckendorfString':
"""对状态进行小扰动"""
# 简单的扰动：在值上加1
new_value = state.value + 1
return ZeckendorfString(new_value)
def update_threshold(self, new_threshold: float) -> 'BoundaryFunction':
"""更新阈值，返回新的边界函数"""
return BoundaryFunction(new_threshold, self.shell_depth,
self.core_value, self.phi_scaling)
def phi_evolve_threshold(self) -> 'BoundaryFunction':
"""按φ因子演化阈值"""
new_threshold = self.threshold * self.phi
return BoundaryFunction(new_threshold, self.shell_depth,
self.core_value, self.phi_scaling)
class ShellBoundaryAnalyzer:
"""Shell边界分析器"""
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def compute_shell_depth(self, trace_structures: List['TraceStructure']) -> int:
"""计算Shell深度"""
if not trace_structures:
return 0
# 基于trace结构的分布计算深度
all_layers = []
for structure in trace_structures:
all_layers.extend(structure.components.keys())
if not all_layers:
return 0
max_layer = max(all_layers)
layer_counts = {}
for layer in all_layers:
layer_counts[layer] = layer_counts.get(layer, 0) + 1
# 找到包含一半以上trace结构的最大层
total_structures = len(trace_structures)
cumulative_coverage = 0
for layer in sorted(layer_counts.keys()):
cumulative_coverage += layer_counts[layer]
if cumulative_coverage >= total_structures / 2:
return layer
return max_layer
def compute_threshold(self, trace_structures: List['TraceStructure'],
shell_depth: int) -> float:
"""计算Shell阈值"""
if not trace_structures:
return 0.0
# 收集指定深度内的所有trace值
depth_values = []
for structure in trace_structures:
for layer, component in structure.components.items():
if layer <= shell_depth:
depth_values.append(component.value)
if not depth_values:
return 0.0
# 计算结构核
core_value = math.gcd(*depth_values) if len(depth_values) > 1 else depth_values[0]
# φ-调制阈值
threshold = (self.phi ** shell_depth) * core_value
return threshold
def analyze_boundary_stability(self, boundary_points: List[BoundaryPoint]) -> Dict[str, float]:
"""分析边界稳定性"""
if not boundary_points:
return {'stability': 0.0, 'coherence': 0.0, 'phi_alignment': 0.0}
# 计算整体稳定性
stabilities = [point.boundary_stability for point in boundary_points]
overall_stability = np.mean(stabilities)
# 计算边界相干性
distances = [abs(point.distance_to_boundary) for point in boundary_points]
coherence = 1.0 / (1.0 + np.std(distances)) if distances else 0.0
# 计算φ-对齐度
phi_alignment = self._compute_phi_alignment(boundary_points)
return {
'stability': overall_stability,
'coherence': coherence,
'phi_alignment': phi_alignment,
'boundary_sharpness': self._compute_boundary_sharpness(boundary_points)
}
def _compute_phi_alignment(self, boundary_points: List[BoundaryPoint]) -> float:
"""计算边界的φ-对齐度"""
trace_values = [point.trace_value for point in boundary_points]
if len(trace_values) < 2:
return 1.0
# 检查trace值的φ-比例关系
ratios = []
for i in range(1, len(trace_values)):
if trace_values[i-1] > 0:
ratio = trace_values[i] / trace_values[i-1]
ratios.append(ratio)
if not ratios:
return 1.0
# 计算与φ的偏差
phi_deviations = [abs(ratio - self.phi) for ratio in ratios]
avg_deviation = np.mean(phi_deviations)
# 转换为对齐度（0-1范围）
alignment = 1.0 / (1.0 + avg_deviation)
return alignment
def _compute_boundary_sharpness(self, boundary_points: List[BoundaryPoint]) -> float:
"""计算边界锐度"""
inside_points = [p for p in boundary_points if p.is_inside]
outside_points = [p for p in boundary_points if not p.is_inside]
if not inside_points or not outside_points:
return 0.0
inside_traces = [p.trace_value for p in inside_points]
outside_traces = [p.trace_value for p in outside_points]
min_inside = min(inside_traces)
max_outside = max(outside_traces)
if min_inside <= max_outside:
return 0.0 # 边界模糊
gap = min_inside - max_outside
total_range = max(inside_traces) - min(outside_traces)
if total_range == 0:
return 1.0
sharpness = gap / total_range
return min(1.0, sharpness)
2. RealityShell核心实现
2.1 Shell结构类
class RealityShell:
"""RealityShell边界结构"""
def __init__(self, states: List['ZeckendorfString'], boundary_function: BoundaryFunction,
trace_calculator, decomposer, shell_id: Optional[str] = None):
self.phi = (1 + np.sqrt(5)) / 2
self.states = states
self.boundary_function = boundary_function
self.trace_calculator = trace_calculator
self.decomposer = decomposer
self.shell_id = shell_id or f"Shell_{id(self)}"
# 计算Shell属性
self.boundary_points = self._compute_boundary_points()
self.inside_states = [bp.state for bp in self.boundary_points if bp.is_inside]
self.outside_states = [bp.state for bp in self.boundary_points if not bp.is_inside]
# Shell统计
self.total_information = self._compute_total_information()
self.boundary_complexity = self._compute_boundary_complexity()
self.shell_entropy = self._compute_shell_entropy()
# 演化历史
self.evolution_history = []
self.current_generation = 0
def _compute_boundary_points(self) -> List[BoundaryPoint]:
"""计算所有状态的边界点"""
return [self.boundary_function.evaluate(state, self.trace_calculator)
for state in self.states]
def _compute_total_information(self) -> float:
"""计算Shell总信息量"""
total = 0.0
for bp in self.boundary_points:
total += bp.trace_value
return total
def _compute_boundary_complexity(self) -> float:
"""计算边界复杂度"""
if not self.boundary_points:
return 0.0
# 基于边界点分布的复杂度
distances = [abs(bp.distance_to_boundary) for bp in self.boundary_points]
if not distances:
return 0.0
# 距离分布的信息熵
max_distance = max(distances)
if max_distance == 0:
return 0.0
normalized_distances = [d / max_distance for d in distances]
# 计算分布熵
bins = 10
hist, _ = np.histogram(normalized_distances, bins=bins, range=(0, 1))
probabilities = hist / len(normalized_distances)
entropy = 0.0
for p in probabilities:
if p > 0:
entropy -= p * math.log(p, self.phi)
return entropy
def _compute_shell_entropy(self) -> float:
"""计算Shell熵"""
inside_info = sum(bp.trace_value for bp in self.boundary_points if bp.is_inside)
outside_info = sum(bp.trace_value for bp in self.boundary_points if not bp.is_inside)
total_info = inside_info + outside_info
if total_info == 0:
return 0.0
if inside_info == 0 or outside_info == 0:
return 0.0
p_inside = inside_info / total_info
p_outside = outside_info / total_info
return -(p_inside * math.log(p_inside, self.phi) +
p_outside * math.log(p_outside, self.phi))
def compute_information_flow(self, target_shell: 'RealityShell') -> InformationFlow:
"""计算与目标Shell的信息流"""
# 计算信息差
info_diff = self.total_information - target_shell.total_information
# 确定流向
if abs(info_diff) < 1e-10:
direction = FlowDirection.EQUILIBRIUM
elif info_diff > 0:
direction = FlowDirection.IN_TO_OUT
else:
direction = FlowDirection.OUT_TO_IN
# 创建信息流
flow = InformationFlow(direction, abs(info_diff), phi_quantized=True)
return flow
def add_state(self, new_state: 'ZeckendorfString') -> 'RealityShell':
"""添加新状态到Shell"""
new_states = self.states + [new_state]
return RealityShell(new_states, self.boundary_function,
self.trace_calculator, self.decomposer, self.shell_id)
def remove_state(self, state_to_remove: 'ZeckendorfString') -> 'RealityShell':
"""从Shell移除状态"""
new_states = [s for s in self.states if s != state_to_remove]
return RealityShell(new_states, self.boundary_function,
self.trace_calculator, self.decomposer, self.shell_id)
def update_boundary(self, new_boundary_function: BoundaryFunction) -> 'RealityShell':
"""更新边界函数"""
new_shell = RealityShell(self.states, new_boundary_function,
self.trace_calculator, self.decomposer, self.shell_id)
new_shell.evolution_history = self.evolution_history.copy()
new_shell.current_generation = self.current_generation + 1
return new_shell
def analyze_stability(self, analyzer: ShellBoundaryAnalyzer) -> Dict[str, Any]:
"""分析Shell稳定性"""
stability_metrics = analyzer.analyze_boundary_stability(self.boundary_points)
# 添加Shell特定的分析
stability_metrics.update({
'inside_outside_ratio': len(self.inside_states) / max(1, len(self.outside_states)),
'information_concentration': self._compute_information_concentration(),
'boundary_evolution_rate': self._compute_evolution_rate()
})
return stability_metrics
def _compute_information_concentration(self) -> float:
"""计算信息浓度"""
if not self.inside_states:
return 0.0
inside_info = sum(self.trace_calculator.compute_full_trace(state)
for state in self.inside_states)
outside_info = sum(self.trace_calculator.compute_full_trace(state)
for state in self.outside_states)
total_info = inside_info + outside_info
if total_info == 0:
return 0.0
return inside_info / total_info
def _compute_evolution_rate(self) -> float:
"""计算演化速率"""
if len(self.evolution_history) < 2:
return 0.0
# 基于历史阈值变化计算速率
recent_changes = []
for i in range(1, min(5, len(self.evolution_history))):
prev_threshold = self.evolution_history[-i-1]['threshold']
curr_threshold = self.evolution_history[-i]['threshold']
if prev_threshold > 0:
change_rate = abs(curr_threshold - prev_threshold) / prev_threshold
recent_changes.append(change_rate)
return np.mean(recent_changes) if recent_changes else 0.0
def get_shell_signature(self) -> str:
"""获取Shell签名"""
inside_count = len(self.inside_states)
outside_count = len(self.outside_states)
threshold = self.boundary_function.effective_threshold
return f"{self.shell_id}:I{inside_count}O{outside_count}T{threshold:.2f}"
def __eq__(self, other) -> bool:
if isinstance(other, RealityShell):
return (set(self.states) == set(other.states) and
self.boundary_function.effective_threshold == other.boundary_function.effective_threshold)
return False
def __hash__(self) -> int:
return hash((tuple(sorted(s.representation for s in self.states)),
self.boundary_function.effective_threshold))
2.2 Shell演化器
class ShellEvolutionEngine:
"""Shell演化引擎"""
def __init__(self, psi_collapse):
self.phi = (1 + np.sqrt(5)) / 2
self.psi_collapse = psi_collapse
def evolve_shell_once(self, shell: RealityShell) -> RealityShell:
"""执行一次Shell演化"""
# 1. Shell自描述
description = self._encode_shell_description(shell)
# 2. 自指collapse
shell_collapse_state = self._perform_shell_collapse(shell, description)
# 3. 更新边界
new_boundary = self._update_boundary_function(shell, shell_collapse_state)
# 4. 更新状态集合
new_states = self._evolve_state_set(shell, shell_collapse_state)
# 5. 创建演化后的Shell
evolved_shell = RealityShell(new_states, new_boundary,
shell.trace_calculator, shell.decomposer,
shell.shell_id)
# 6. 记录演化历史
evolution_record = {
'generation': shell.current_generation + 1,
'threshold': new_boundary.effective_threshold,
'state_count': len(new_states),
'information': evolved_shell.total_information,
'entropy': evolved_shell.shell_entropy
}
evolved_shell.evolution_history = shell.evolution_history + [evolution_record]
evolved_shell.current_generation = shell.current_generation + 1
return evolved_shell
def _encode_shell_description(self, shell: RealityShell) -> 'ZeckendorfString':
"""编码Shell描述"""
# 将Shell信息编码为Zeckendorf字符串
description_value = 0
# 编码基本信息
description_value += len(shell.inside_states) # 内部状态数
description_value += len(shell.outside_states) * 2 # 外部状态数（权重更高）
description_value += int(shell.boundary_function.effective_threshold) # 阈值
# 添加复杂性信息
description_value += int(shell.boundary_complexity * 10)
return ZeckendorfString(max(1, description_value))
def _perform_shell_collapse(self, shell: RealityShell,
description: 'ZeckendorfString') -> 'ZeckendorfString':
"""执行Shell的自指collapse"""
# 使用描述状态执行collapse
collapsed_description = self.psi_collapse.psi_collapse_once(description)
return collapsed_description
def _update_boundary_function(self, shell: RealityShell,
collapse_state: 'ZeckendorfString') -> BoundaryFunction:
"""更新边界函数"""
# 基于collapse状态调整阈值
collapse_trace = shell.trace_calculator.compute_full_trace(collapse_state)
# φ-演化阈值
new_threshold = shell.boundary_function.threshold * self.phi
# 微调基于collapse信息
adjustment = collapse_trace * 0.1 # 10%的调整
adjusted_threshold = new_threshold + adjustment
return BoundaryFunction(
threshold=adjusted_threshold,
shell_depth=shell.boundary_function.shell_depth,
core_value=shell.boundary_function.core_value,
phi_scaling=shell.boundary_function.phi_scaling
)
def _evolve_state_set(self, shell: RealityShell,
collapse_state: 'ZeckendorfString') -> List['ZeckendorfString']:
"""演化状态集合"""
new_states = shell.states.copy()
# 添加collapse产生的新状态
new_states.append(collapse_state)
# 可能移除边界外的状态（自然淘汰）
# 这里实现一个简单的策略：保留所有状态，让边界函数决定内外
return new_states
def evolve_shell_sequence(self, initial_shell: RealityShell,
num_steps: int) -> List[RealityShell]:
"""演化Shell序列"""
evolution_sequence = [initial_shell]
current_shell = initial_shell
for step in range(num_steps):
try:
evolved_shell = self.evolve_shell_once(current_shell)
evolution_sequence.append(evolved_shell)
current_shell = evolved_shell
# 检查收敛
if self._check_convergence(evolution_sequence):
break
except Exception as e:
print(f"Shell evolution stopped at step {step}: {e}")
break
return evolution_sequence
def _check_convergence(self, evolution_sequence: List[RealityShell]) -> bool:
"""检查Shell演化收敛"""
if len(evolution_sequence) < 5:
return False
# 检查最近几步的阈值变化
recent_thresholds = [shell.boundary_function.effective_threshold
for shell in evolution_sequence[-5:]]
# 如果阈值变化很小，认为收敛
threshold_changes = [abs(recent_thresholds[i] - recent_thresholds[i-1])
for i in range(1, len(recent_thresholds))]
max_change = max(threshold_changes) if threshold_changes else 0
relative_change = max_change / recent_thresholds[-1] if recent_thresholds[-1] > 0 else 0
return relative_change < 0.01 # 1%的变化阈值
def analyze_evolution_pattern(self, evolution_sequence: List[RealityShell]) -> Dict[str, Any]:
"""分析演化模式"""
if len(evolution_sequence) < 2:
return {'pattern': 'insufficient_data'}
# 提取演化指标
thresholds = [shell.boundary_function.effective_threshold for shell in evolution_sequence]
information_levels = [shell.total_information for shell in evolution_sequence]
entropies = [shell.shell_entropy for shell in evolution_sequence]
# 分析趋势
threshold_trend = self._analyze_trend(thresholds)
information_trend = self._analyze_trend(information_levels)
entropy_trend = self._analyze_trend(entropies)
# 检查φ-增长模式
phi_growth_verified = self._verify_phi_growth(thresholds)
return {
'pattern': 'analyzed',
'threshold_trend': threshold_trend,
'information_trend': information_trend,
'entropy_trend': entropy_trend,
'phi_growth_verified': phi_growth_verified,
'convergence_detected': self._check_convergence(evolution_sequence),
'evolution_stability': self._compute_evolution_stability(evolution_sequence)
}
def _analyze_trend(self, values: List[float]) -> str:
"""分析数值序列的趋势"""
if len(values) < 2:
return 'stable'
increases = sum(1 for i in range(1, len(values)) if values[i] > values[i-1])
decreases = sum(1 for i in range(1, len(values)) if values[i] < values[i-1])
if increases > decreases * 2:
return 'increasing'
elif decreases > increases * 2:
return 'decreasing'
else:
return 'oscillating'
def _verify_phi_growth(self, values: List[float]) -> bool:
"""验证φ-增长模式"""
if len(values) < 3:
return False
ratios = []
for i in range(1, len(values)):
if values[i-1] > 0:
ratio = values[i] / values[i-1]
ratios.append(ratio)
if not ratios:
return False
avg_ratio = np.mean(ratios)
return abs(avg_ratio - self.phi) < 0.2
def _compute_evolution_stability(self, evolution_sequence: List[RealityShell]) -> float:
"""计算演化稳定性"""
if len(evolution_sequence) < 2:
return 1.0
# 基于连续Shell间的相似性
similarities = []
for i in range(1, len(evolution_sequence)):
prev_shell = evolution_sequence[i-1]
curr_shell = evolution_sequence[i]
# 计算状态集合相似性
prev_states = set(s.representation for s in prev_shell.states)
curr_states = set(s.representation for s in curr_shell.states)
intersection = prev_states & curr_states
union = prev_states | curr_states
similarity = len(intersection) / len(union) if union else 1.0
similarities.append(similarity)
return np.mean(similarities) if similarities else 1.0
3. 嵌套Shell管理器
3.1 Shell层次结构
class NestedShellManager:
"""嵌套Shell管理器"""
def __init__(self, trace_calculator, decomposer, psi_collapse):
self.phi = (1 + np.sqrt(5)) / 2
self.trace_calculator = trace_calculator
self.decomposer = decomposer
self.psi_collapse = psi_collapse
self.shell_hierarchy = {} # level -> shell
self.evolution_engine = ShellEvolutionEngine(psi_collapse)
def create_nested_shells(self, states: List['ZeckendorfString'],
num_levels: int = 3) -> Dict[int, RealityShell]:
"""创建嵌套Shell结构"""
nested_shells = {}
# 计算trace结构
trace_structures = [self.decomposer.decompose_trace_structure(state)
for state in states]
analyzer = ShellBoundaryAnalyzer()
base_shell_depth = analyzer.compute_shell_depth(trace_structures)
base_threshold = analyzer.compute_threshold(trace_structures, base_shell_depth)
# 创建层次Shell
for level in range(num_levels):
# φ-分级阈值
level_threshold = base_threshold * (self.phi ** level)
# 创建边界函数
boundary_func = BoundaryFunction(
threshold=level_threshold,
shell_depth=base_shell_depth + level,
core_value=int(base_threshold),
phi_scaling=True
)
# 创建Shell
shell = RealityShell(states, boundary_func,
self.trace_calculator, self.decomposer,
f"Level_{level}")
nested_shells[level] = shell
self.shell_hierarchy = nested_shells
return nested_shells
def verify_nesting_property(self) -> Dict[str, bool]:
"""验证嵌套性质"""
if len(self.shell_hierarchy) < 2:
return {'nested': True, 'consistent': True}
verification = {'nested': True, 'consistent': True, 'details': {}}
# 检查每一层的包含关系
levels = sorted(self.shell_hierarchy.keys())
for i in range(len(levels) - 1):
lower_level = levels[i]
higher_level = levels[i + 1]
lower_shell = self.shell_hierarchy[lower_level]
higher_shell = self.shell_hierarchy[higher_level]
# 检查阈值关系
threshold_ok = lower_shell.boundary_function.effective_threshold <= \
higher_shell.boundary_function.effective_threshold
# 检查包含关系
lower_inside = set(s.representation for s in lower_shell.inside_states)
higher_inside = set(s.representation for s in higher_shell.inside_states)
containment_ok = lower_inside.issubset(higher_inside)
level_verification = {
'threshold_order': threshold_ok,
'state_containment': containment_ok,
'lower_threshold': lower_shell.boundary_function.effective_threshold,
'higher_threshold': higher_shell.boundary_function.effective_threshold
}
verification['details'][f'level_{lower_level}_to_{higher_level}'] = level_verification
if not (threshold_ok and containment_ok):
verification['nested'] = False
verification['consistent'] = False
return verification
def compute_inter_shell_flows(self) -> Dict[Tuple[int, int], InformationFlow]:
"""计算Shell间信息流"""
flows = {}
levels = sorted(self.shell_hierarchy.keys())
for i in range(len(levels)):
for j in range(i + 1, len(levels)):
level_i = levels[i]
level_j = levels[j]
shell_i = self.shell_hierarchy[level_i]
shell_j = self.shell_hierarchy[level_j]
flow = shell_i.compute_information_flow(shell_j)
flows[(level_i, level_j)] = flow
return flows
def evolve_nested_shells(self, num_steps: int) -> Dict[int, List[RealityShell]]:
"""演化嵌套Shell系统"""
evolution_sequences = {}
# 并行演化每一层
for level, shell in self.shell_hierarchy.items():
sequence = self.evolution_engine.evolve_shell_sequence(shell, num_steps)
evolution_sequences[level] = sequence
# 更新当前Shell层次
for level in self.shell_hierarchy:
if evolution_sequences[level]:
self.shell_hierarchy[level] = evolution_sequences[level][-1]
return evolution_sequences
def analyze_hierarchy_stability(self) -> Dict[str, Any]:
"""分析层次稳定性"""
if not self.shell_hierarchy:
return {'error': 'No shells in hierarchy'}
stability_analysis = {
'individual_stabilities': {},
'inter_level_consistency': {},
'overall_stability': 0.0,
'hierarchy_coherence': 0.0
}
analyzer = ShellBoundaryAnalyzer()
# 分析每层稳定性
individual_stabilities = []
for level, shell in self.shell_hierarchy.items():
stability = shell.analyze_stability(analyzer)
stability_analysis['individual_stabilities'][level] = stability
individual_stabilities.append(stability['stability'])
# 分析层间一致性
levels = sorted(self.shell_hierarchy.keys())
consistency_scores = []
for i in range(len(levels) - 1):
lower_shell = self.shell_hierarchy[levels[i]]
higher_shell = self.shell_hierarchy[levels[i + 1]]
# 信息流一致性
flow = lower_shell.compute_information_flow(higher_shell)
consistency = 1.0 if flow.conservation_verified else 0.5
consistency_scores.append(consistency)
stability_analysis['inter_level_consistency'][f'{levels[i]}_{levels[i+1]}'] = {
'flow_direction': flow.direction.value,
'flow_amount': flow.quantized_amount,
'conservation_verified': flow.conservation_verified,
'consistency_score': consistency
}
# 整体指标
stability_analysis['overall_stability'] = np.mean(individual_stabilities)
stability_analysis['hierarchy_coherence'] = np.mean(consistency_scores) if consistency_scores else 1.0
return stability_analysis
def get_shell_at_level(self, level: int) -> Optional[RealityShell]:
"""获取指定层次的Shell"""
return self.shell_hierarchy.get(level)
def add_shell_level(self, level: int, threshold_multiplier: float = None) -> RealityShell:
"""添加新的Shell层次"""
if not self.shell_hierarchy:
raise ValueError("No base shells to extend from")
# 使用现有Shell的状态
base_states = list(self.shell_hierarchy.values())[0].states
# 计算新层次的阈值
if threshold_multiplier is None:
max_level = max(self.shell_hierarchy.keys())
threshold_multiplier = self.phi ** (level - max_level)
base_threshold = list(self.shell_hierarchy.values())[0].boundary_function.threshold
new_threshold = base_threshold * threshold_multiplier
# 创建新边界函数
boundary_func = BoundaryFunction(
threshold=new_threshold,
shell_depth=level,
core_value=int(base_threshold),
phi_scaling=True
)
# 创建新Shell
new_shell = RealityShell(base_states, boundary_func,
self.trace_calculator, self.decomposer,
f"Level_{level}")
self.shell_hierarchy[level] = new_shell
return new_shell
4. Shell系统验证器
4.1 完整验证框架
class RealityShellValidator:
"""RealityShell系统验证器"""
def __init__(self):
self.phi = (1 + np.sqrt(5)) / 2
def validate_boundary_uniqueness(self, shell: RealityShell) -> Dict[str, bool]:
"""验证边界唯一确定性"""
validation_results = {
'boundary_function_deterministic': True,
'threshold_well_defined': True,
'state_classification_consistent': True
}
# 测试边界函数的确定性
test_states = shell.states[:5] if len(shell.states) >= 5 else shell.states
for state in test_states:
# 多次评估同一状态
evaluations = []
for _ in range(3):
bp = shell.boundary_function.evaluate(state, shell.trace_calculator)
evaluations.append((bp.is_inside, bp.distance_to_boundary))
# 检查一致性
if len(set(evaluations)) > 1:
validation_results['boundary_function_deterministic'] = False
# 验证阈值定义
threshold = shell.boundary_function.effective_threshold
if not (isinstance(threshold, (int, float)) and threshold >= 0):
validation_results['threshold_well_defined'] = False
# 验证状态分类一致性
inside_count = len(shell.inside_states)
outside_count = len(shell.outside_states)
total_count = len(shell.states)
if inside_count + outside_count != total_count:
validation_results['state_classification_consistent'] = False
return validation_results
def validate_information_conservation(self, shell1: RealityShell,
shell2: RealityShell) -> Dict[str, Any]:
"""验证信息传递守恒"""
flow_12 = shell1.compute_information_flow(shell2)
flow_21 = shell2.compute_information_flow(shell1)
# 验证守恒关系
conservation_verified = flow_12.verify_conservation(flow_21)
# 计算总信息守恒
total_flow = flow_12 + flow_21
validation_results = {
'conservation_verified': conservation_verified,
'flow_12_amount': flow_12.quantized_amount,
'flow_21_amount': flow_21.quantized_amount,
'total_flow_amount': total_flow.quantized_amount,
'phi_quantization_verified': flow_12.phi_quantized and flow_21.phi_quantized,
'equilibrium_achieved': total_flow.direction == FlowDirection.EQUILIBRIUM
}
return validation_results
def validate_shell_self_reference(self, shell: RealityShell,
evolution_engine: ShellEvolutionEngine) -> Dict[str, bool]:
"""验证Shell自指性质"""
validation_results = {
'self_description_possible': True,
'self_evolution_successful': True,
'self_reference_consistency': True
}
try:
# 测试自描述
description = evolution_engine._encode_shell_description(shell)
if description.value <= 0:
validation_results['self_description_possible'] = False
# 测试自演化
evolved_shell = evolution_engine.evolve_shell_once(shell)
if evolved_shell == shell: # 完全相同表示没有演化
validation_results['self_evolution_successful'] = False
# 验证自指一致性：演化后的Shell应该仍然能描述自己
evolved_description = evolution_engine._encode_shell_description(evolved_shell)
if evolved_description.value <= 0:
validation_results['self_reference_consistency'] = False
except Exception as e:
validation_results['self_evolution_successful'] = False
validation_results['error'] = str(e)
return validation_results
def validate_boundary_stability(self, evolution_sequence: List[RealityShell]) -> Dict[str, Any]:
"""验证边界稳定性"""
if len(evolution_sequence) < 2:
return {'error': 'Insufficient evolution data'}
validation_results = {
'phi_growth_verified': False,
'stability_maintained': True,
'convergence_detected': False,
'stability_metrics': []
}
# 提取阈值序列
thresholds = [shell.boundary_function.effective_threshold
for shell in evolution_sequence]
# 验证φ-增长
if len(thresholds) >= 3:
growth_ratios = []
for i in range(1, len(thresholds)):
if thresholds[i-1] > 0:
ratio = thresholds[i] / thresholds[i-1]
growth_ratios.append(ratio)
if growth_ratios:
avg_ratio = np.mean(growth_ratios)
validation_results['phi_growth_verified'] = abs(avg_ratio - self.phi) < 0.3
# 计算稳定性指标
for i in range(1, len(evolution_sequence)):
prev_shell = evolution_sequence[i-1]
curr_shell = evolution_sequence[i]
# 计算边界变化
threshold_change = abs(curr_shell.boundary_function.effective_threshold -
prev_shell.boundary_function.effective_threshold)
relative_change = threshold_change / prev_shell.boundary_function.effective_threshold \
if prev_shell.boundary_function.effective_threshold > 0 else 0
stability_metric = {
'step': i,
'threshold_change': threshold_change,
'relative_change': relative_change,
'stable': relative_change < 0.1 # 10%变化阈值
}
validation_results['stability_metrics'].append(stability_metric)
if relative_change >= 0.1:
validation_results['stability_maintained'] = False
# 检查收敛
if len(validation_results['stability_metrics']) >= 3:
recent_changes = [m['relative_change']
for m in validation_results['stability_metrics'][-3:]]
if all(change < 0.05 for change in recent_changes):
validation_results['convergence_detected'] = True
return validation_results
def comprehensive_validation(self, shell: RealityShell,
evolution_engine: ShellEvolutionEngine,
num_evolution_steps: int = 5) -> Dict[str, Any]:
"""综合验证"""
comprehensive_results = {
'boundary_uniqueness': {},
'self_reference': {},
'evolution_stability': {},
'overall_valid': True,
'validation_summary': {}
}
# 1. 边界唯一性验证
boundary_validation = self.validate_boundary_uniqueness(shell)
comprehensive_results['boundary_uniqueness'] = boundary_validation
if not all(boundary_validation.values()):
comprehensive_results['overall_valid'] = False
# 2. 自指性质验证
self_ref_validation = self.validate_shell_self_reference(shell, evolution_engine)
comprehensive_results['self_reference'] = self_ref_validation
if not all(self_ref_validation.values() if isinstance(v, bool) else True
for v in self_ref_validation.values()):
comprehensive_results['overall_valid'] = False
# 3. 演化稳定性验证
try:
evolution_sequence = evolution_engine.evolve_shell_sequence(shell, num_evolution_steps)
stability_validation = self.validate_boundary_stability(evolution_sequence)
comprehensive_results['evolution_stability'] = stability_validation
if not stability_validation.get('stability_maintained', False):
comprehensive_results['overall_valid'] = False
except Exception as e:
comprehensive_results['evolution_stability'] = {'error': str(e)}
comprehensive_results['overall_valid'] = False
# 4. 验证摘要
comprehensive_results['validation_summary'] = {
'boundary_valid': all(boundary_validation.values()),
'self_reference_valid': all(v for v in self_ref_validation.values() if isinstance(v, bool)),
'evolution_stable': comprehensive_results['evolution_stability'].get('stability_maintained', False),
'phi_properties_verified': comprehensive_results['evolution_stability'].get('phi_growth_verified', False)
}
return comprehensive_results
这个形式化规范提供了T20-3理论的完整实现，包括Shell边界结构、信息传递、自指演化、嵌套管理和系统验证，确保了理论与实现的完全一致性。