# 解题路径生成器核心逻辑（简化版）
def generate_reasoning_trace(problem: str) -> List[Dict]:
    # 1. 意图识别：区分求值/证明/建模等任务类型
    task_type = classify_task(problem)  
    # 2. 调用对应子Agent并注入上下文约束
    if task_type == "algebra":
        return algebra_agent.invoke({"problem": problem, "constraints": ["保留分数形式", "标注每步依据"]})
    elif task_type == "geometry":
        return geo_agent.invoke({"problem": problem, "diagram_hint": extract_diagram_keywords(problem)})
    # 3. 合并结果并插入教学提示点（TIP节点）
    return inject_tips(trace)

# 基于SPARQL模板动态生成rdfs:subClassOf与owl:equivalentClass断言
CONSTRUCT {
  ?concept a owl:Class ;
           rdfs:subClassOf edu:CrossDisciplinaryConcept .
} WHERE {
  ?standard edu:mentions ?concept .
  FILTER(CONTAINS(STR(?concept), "scale") || CONTAINS(STR(?concept), "system"))
}

# 将ASR片段关联至OCR概念节点
graph.merge(
    ConceptNode(name="动能定理"),
    "Concept", 
    "name"
)
graph.create(Relationship(
    node_asr, "EXPLAINS", node_concept,
    timestamp="2024-05-11T09:23:17Z",
    confidence=0.89  # ASR置信度 + OCR语义匹配分加权
))

class TemporalGNNLayer(nn.Module):
    def __init__(self, in_dim, hidden_dim, dropout=0.2):
        super().__init__()
        self.time_gate = nn.Linear(in_dim + 1, hidden_dim)  # +1 for timestamp embedding
        self.msg_func = nn.Linear(in_dim * 2, hidden_dim)
        self.update_func = nn.GRUCell(hidden_dim, hidden_dim)

SELECT ?x ?reasoning_path WHERE {
  :Q123 rdfs:label "阿尔茨海默病" .
  :Q123 :hasSymptom ?x .
  ?x rdfs:label ?symptom_label .
  BIND(CONCAT("症状→", ?symptom_label) AS ?reasoning_path)
}

// 新增语义对齐权重模块（sits2026/graph/align.go）
func ComputeAlignmentScore(src, tgt *KnowledgeNode) float64 {
    // α=0.4：课程大纲TF-IDF相似度；β=0.35：教育部标准术语嵌入余弦距离
    return 0.4*tfidfSim(src.Text, tgt.Text) + 
           0.35*embedCosine(src.Embed, tgt.Embed) + 
           0.25*curricularCooccur(src.CourseID, tgt.CourseID) // 课程共现频次修正项
}

# ACT-R扩展模型：双参数衰减-激活耦合
def cognitive_dynamics(t, c, tau_w=1.2, tau_l=8.5, gamma=0.3):
    w, l = c
    dw_dt = -w / tau_w + gamma * l  # 工作记忆受长时记忆正向驱动
    dl_dt = -l / tau_l + 0.1 * w   # 长时记忆受工作记忆反向再激活
    return [dw_dt, dl_dt]

# 行为流滑动窗口微分计算
def compute_cognitive_gradient(events, window=500):
    # events: [{'x':120,'y':80,'ts':1698765432100,'action':'click'}, ...]
    dt = np.diff([e['ts'] for e in events]) / 1000.0  # 秒级时间差
    dtau = np.gradient([e.get('duration', 0) for e in events])  # 停留变化率
    return np.column_stack([dtau, np.gradient(dt)])  # 输出 [dτ/dt, d²t/dt²]

# 时间戳对齐：将键盘事件映射至最近眼动采样点
def align_timestamps(keystrokes, eye_samples):
    aligned = []
    for ks in keystrokes:
        nearest = min(eye_samples, key=lambda e: abs(e['t'] - ks['t']))
        aligned.append({**ks, 'eye_t': nearest['t'], 'pupil_dilation': nearest['pd']})
    return aligned

def calc_adj_density(graph: nx.DiGraph) -> float:
    n = len(graph.nodes())
    actual_edges = len(graph.edges())  # 实际有向边数
    max_possible = n * (n - 1)         # 完全有向图边数
    return actual_edges / max_possible if max_possible else 0
# 参数说明：graph为用户-标签-行为三元组构建的有向图；
# 返回值ρ∈[0,1]，越接近0表明图谱拓扑越稀疏、泛化支撑越弱。

def detect_step_jump(log_seq, threshold_entropy=1.8, threshold_explain=0.7):
    # log_seq: [(timestamp, action_type, has_self_explain), ...]
    entropy = compute_interval_entropy(log_seq)  # 基于相邻操作时间差分布
    explain_ratio = sum(1 for _, _, exp in log_seq if exp) / len(log_seq)
    return entropy > threshold_entropy and explain_ratio < threshold_explain

def drift_align(embed_a, embed_b, alpha=0.3):
    # embed_a, embed_b: [N, 768] float tensors
    # alpha: alignment strength (0.1~0.5 empirically optimal)
    mu_a, mu_b = embed_a.mean(0), embed_b.mean(0)
    return embed_a - alpha * (mu_a - mu_b)  # center-shift correction

# RLHF reward shaping function
def compute_intervention_reward(state, action, feedback):
    # state: (cognitive_gap_score, engagement_level)
    # action: intervention_type ∈ {scaffold, hint, resequence, pause}
    return 0.6 * gap_closure_rate(action, state) \
         + 0.3 * engagement_delta(feedback) \
         + 0.1 * cognitive_load_penalty(action)

# 动态提示工程：根据学生错题类型注入领域约束
def build_tutor_prompt(student_profile: dict, error_cluster: str) -> str:
    constraints = {
        "几何证明": "必须分步标注公理/定理来源，禁用向量法",
        "方程求解": "优先展示等价变形过程，标注每步合法性依据"
    }
    return f"""你是一名资深初中数学教练。学生当前水平：{student_profile['grade']}/{student_profile['mastery_score']}。
请严格遵循{constraints.get(error_cluster, '通用启发式引导')}规则响应。"""

[学生终端] → WebSocket → [API网关] → [Auth Service] + [Tutor Agent] → [Neo4j知识图谱]