from typing import Dict, List, Tuple, Optional, Protocol, Set
from dataclasses import dataclass
import numpy as np
from phi_arithmetic import PhiReal, PhiComplex, PhiMatrix
@dataclass
class UniverseBranch:
"""宇宙分支"""
branch_id: int
probability: PhiReal
entropy: PhiReal
parent_id: Optional[int] = None
def is_valid_branch(self) -> bool:
"""验证分支有效性"""
return 0 < self.probability.decimal_value <= 1
@dataclass
class BranchingEvent:
"""分支事件"""
time: PhiReal
parent_branch: UniverseBranch
child_branches: List[UniverseBranch]
def verify_probability_conservation(self) -> bool:
"""验证概率守恒"""
total_prob = sum(b.probability for b in self.child_branches)
return abs(total_prob.decimal_value - self.parent_branch.probability.decimal_value) < 1e-10
@dataclass
class MultiverseState:
"""多宇宙状态"""
branches: Dict[int, UniverseBranch]
entanglement_matrix: PhiMatrix
total_entropy: PhiReal
def get_active_branches(self) -> List[UniverseBranch]:
"""获取活跃分支（满足no-11约束）"""
active = []
for branch in self.branches.values():
if self._satisfies_no11_constraint(branch):
active.append(branch)
return active
def _satisfies_no11_constraint(self, branch: UniverseBranch) -> bool:
"""检查分支是否满足no-11约束"""
adjacent_ids = [branch.branch_id - 1, branch.branch_id + 1]
for adj_id in adjacent_ids:
if adj_id in self.branches and self.branches[adj_id].probability.decimal_value > 1e-10:
return False
return True
class PhiMultiverse:
"""φ-多宇宙系统"""
def __init__(self):
self.phi = PhiReal.from_decimal(1.618033988749895)
self.branches: Dict[int, UniverseBranch] = {}
self.current_max_id = 0
self._initialize_primordial_branch()
def _initialize_primordial_branch(self):
"""初始化原初分支"""
primordial = UniverseBranch(
branch_id=0,
probability=PhiReal.one(),
entropy=PhiReal.zero()
)
self.branches[0] = primordial
def compute_branch_probability(self, n: int) -> PhiReal:
"""计算第n个分支的概率: p_n = φ^(-n) * (φ-1) / φ"""
phi_minus_one = self.phi - PhiReal.one()
numerator = phi_minus_one * (self.phi ** (-n))
return numerator / self.phi
def create_branching_event(self, parent_id: int) -> BranchingEvent:
"""创建分支事件"""
parent = self.branches[parent_id]
child_branches = []
n_branches = self._compute_branch_count()
for i in range(n_branches):
child_id = self._get_next_valid_id()
prob = self.compute_branch_probability(i) * parent.probability
entropy = self._compute_branch_entropy(parent.entropy, prob)
child = UniverseBranch(
branch_id=child_id,
probability=prob,
entropy=entropy,
parent_id=parent_id
)
child_branches.append(child)
self.branches[child_id] = child
return BranchingEvent(
time=PhiReal.from_decimal(0),
parent_branch=parent,
child_branches=child_branches
)
def _compute_branch_count(self) -> int:
"""计算分支数（Fibonacci数）"""
fibonacci = [1, 2, 3, 5, 8]
level = min(len(self.branches), len(fibonacci) - 1)
return fibonacci[level]
def _get_next_valid_id(self) -> int:
"""获取下一个满足no-11约束的有效ID"""
self.current_max_id += 2
return self.current_max_id
def _compute_branch_entropy(self, parent_entropy: PhiReal, prob: PhiReal) -> PhiReal:
"""计算分支熵"""
if prob.decimal_value > 0:
ln_p = PhiReal.from_decimal(np.log(prob.decimal_value))
return parent_entropy - prob * ln_p
return parent_entropy
def compute_entanglement_matrix(self) -> PhiMatrix:
"""计算分支间纠缠矩阵"""
n = len(self.branches)
elements = []
for i in range(n):
row = []
for j in range(n):
if abs(i - j) == 1:
element = PhiComplex.zero()
else:
strength = self.phi ** (-abs(i - j) / 2)
element = PhiComplex(strength, PhiReal.zero())
row.append(element)
elements.append(row)
return PhiMatrix(elements=elements, dimensions=(n, n))
def compute_total_entropy(self) -> PhiReal:
"""计算多宇宙总熵"""
total = PhiReal.zero()
for branch in self.branches.values():
if branch.probability.decimal_value > 0:
ln_p = PhiReal.from_decimal(np.log(branch.probability.decimal_value))
total = total - branch.probability * ln_p
return total
def verify_self_reference(self) -> bool:
"""验证自指性: U = U(U)"""
return all(branch.parent_id is not None or branch.branch_id == 0
for branch in self.branches.values())
def compute_interference_pattern(self, observable: str) -> PhiReal:
"""计算可观测量的干涉图样"""
base_intensity = PhiReal.one()
modulation = self.phi ** (-len(self.branches) / 2)
return base_intensity * modulation
def get_branch_tree_structure(self) -> Dict[int, List[int]]:
"""获取分支树结构"""
tree = {}
for branch in self.branches.values():
if branch.parent_id is not None:
if branch.parent_id not in tree:
tree[branch.parent_id] = []
tree[branch.parent_id].append(branch.branch_id)
return tree
class MultiverseObserver(Protocol):
"""多宇宙观察者接口"""
def observe_branch(self, branch_id: int) -> Optional[UniverseBranch]:
"""观察特定分支"""
...
def measure_interference(self) -> PhiReal:
"""测量分支间干涉"""
...
PHI = PhiReal.from_decimal(1.618033988749895)
BRANCH_ENTROPY_INCREASE = PhiReal.from_decimal(1.741)
MAX_BRANCH_DEPTH = 10
def verify_probability_normalization(branches: List[UniverseBranch]) -> bool:
"""验证概率归一化"""
total = sum(b.probability for b in branches)
return abs(total.decimal_value - 1.0) < 1e-10
def verify_entropy_increase(before: PhiReal, after: PhiReal) -> bool:
"""验证熵增"""
return after.decimal_value > before.decimal_value
def verify_no11_pattern(branch_ids: List[int]) -> bool:
"""验证分支ID模式满足no-11约束"""
for i in range(len(branch_ids) - 1):
if branch_ids[i+1] - branch_ids[i] == 1:
return False
return True