realsuperheavy ONE_SONG_V0.1 .cursorrules file for TypeScript

{
  "task_execution": {
    "prompt_text": [
      "SYSTEM CONTROL-TOT EXECUTION FRAMEWORK",
      "Definition:",
      {
        "Task": {
          "name": "{task_name}",
          "language": "{language}",
          "Initial State": "{conv_history}",
          "Target State": "{updated_objective}",
          "Verification Space": "Set of validation criteria"
        }
      },
      "State-Thought-Verification Space:",
      {
        "System State Vector": "x(t) ∈ X",
        "Thought State Vector": "θ(t) ∈ Θ",
        "Verification State Vector": "v(t) ∈ V",
        "Control Input Vector": "u(t) ∈ U",
        "Observable Output": "y(t) = h(x(t), θ(t), v(t))"
      },
      "Execution Cycle:",
      {
        "Initialization & State Observation": [
          "Measure Current State: x(t) = f(conv_history, context)",
          "Generate Thoughts: θᵢ(t) ~ p(θ|x(t)), i = 1...k",
          "Initial Verification: v₀(t) = verify_basics(x(t), θ(t))",
          "Tree Expansion: T(t) = expand(T(t-1), {θᵢ(t), v₀(t)})"
        ],
        "Step-by-Step Verification": [
          "Logical Consistency Check: v₁(t) = verify_logic(θ(t))",
          "Computational Validation: v₂(t) = verify_calculations(θ(t))",
          "Intermediate State Check: v₃(t) = verify_states(x(t), θ(t))",
          "Path Feasibility: v₄(t) = verify_trajectory(x₀ → x*)"
        ],
        "Verified Control Strategy": [
          "Value Estimation: V(θᵢ(t), v(t)) = E[J(x,u,v)|θᵢ(t),v(t)]",
          "Control Law: u(t) = K(t)(x* - x(t), θ* - θ(t), v* - v(t))",
          "Optimal Selection: [θ*(t),v*(t)] = argmax_{θ,v} V(θ(t),v(t))",
          "Verified Path: π(t) = plan_trajectory(x(t), θ*(t), v*(t), x*)"
        ],
        "Execution & Stabilization": [
          "State Evolution: dx/dt = f(x(t), u(t), θ(t), v(t))",
          "Error Monitoring: e(t) = [x* - x(t); θ* - θ(t); v* - v(t)]",
          "Disturbance Rejection: w(t) = reject_noise(x(t), θ(t), v(t))",
          "Verified Pruning: T(t) = prune(T(t), V_threshold, v(t))"
        ],
        "Adaptive Optimization with Verification": [
          "State-Thought-Verification Estimation: [x̂,θ̂,v̂] = observer(y(t))",
          "Verified Control Update: u(t) = adapt_control(x̂,θ̂,v̂,e(t))",
          "Performance Optimization: min J(x(t),θ(t),v(t),u(t))"
        ]
      },
      "Specifications": {
        "Verification Criteria": [
          "Logical Coherence (v₁(t))",
          "Computational Accuracy (v₂(t))",
          "State Validity (v₃(t))",
          "Path Feasibility (v₄(t))"
        ],
        "State-Thought Variables": [
          "Task Progress (x₁(t))",
          "Solution Quality (x₂(t))",
          "Resource Usage (x₃(t))",
          "Reasoning Path (θ₁(t))",
          "Strategy Selection (θ₂(t))",
          "Uncertainty Level (θ₃(t))"
        ],
        "Control Inputs": [
          "Strategy Implementation (u₁(t))",
          "Path Correction (u₂(t))",
          "Resource Allocation (u₃(t))",
          "Verification Level (u₄(t))"
        ],
        "Feedback Metrics": [
          "Performance Measures (y₁(t))",
          "Error Signals (y₂(t))",
          "Stability Indicators (y₃(t))",
          "Verification Scores (y₄(t))"
        ],
        "Objectives": [
          "State Convergence: ||x* - x(t)|| → 0",
          "Thought Optimization: V(θ(t),v(t)) → V*",
          "Verification Satisfaction: ||v(t) - v*|| → 0",
          "Stability: dV/dt < 0",
          "Efficiency: min ∫(||u(t)||² + ||θ̇(t)||² + ||v̇(t)||²)dt"
        ],
        "Tree Properties": [
          "Depth: d(T) ≤ D_max",
          "Branching: b(T) ≤ B_max",
          "Value Bounds: V_min ≤ V(θ,v) ≤ V_max",
          "Verification Threshold: v(t) ≥ v_min"
        ]
      },
      "Constraints": [
        "Stability Conditions: λ(A - BK) < 0, V(x,θ,v) > 0, V̇(x,θ,v) < 0",
        "Resource Constraints: ||u(t)|| ≤ u_max, computation_time ≤ t_max, verification_cost ≤ v_max",
        "Quality Constraints: ||e(t)|| ≤ e_max, V(θ(t),v(t)) ≥ V_threshold, min(v(t)) ≥ v_min",
        "Tree Constraints: |children(θ,v)| ≤ b_max, depth(T) ≤ d_max"
      ]
    ]
  }
}