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54 lines
2 KiB
Python
54 lines
2 KiB
Python
#!/usr/bin/env python3
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import sys
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from pathlib import Path
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# Add project root to path
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project_root = Path(__file__).parent.parent.parent
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sys.path.insert(0, str(project_root))
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from infra.deepseek_adapter import DeepSeekV4
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def main():
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client = DeepSeekV4(use_local=True)
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model = "deepseek-r1:8b"
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# The "Suspect Equation" from the ENE ingest
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equation = "u_t + u u_x = nu u_{xx} + eta(x,t) - lambda d_x Phi_Omega(x,t)"
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complexity = "Omega[u] = 1/2 sum_{n=1}^N n^2 |a_n|^2"
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prompt = f"""
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You are a mathematical physicist and formal verification expert.
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I am auditing a "Field-Native Witness Hierarchy" model based on a regularized Burgers' equation.
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Equation under audit:
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∂u/∂t + u(∂u/∂x) = ν(∂²u/∂x²) + η(x,t) - λ(∂/∂x)Φ_Ω(x,t)
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Where the "Complexity Metric" Ω[u] is defined as:
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Ω[u] = (1/2) * ∑_{{n=1}}^N n² |a_n|²
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The user claims this allows for "Lossless Symbolic Reconstruction" and "Near-Zero Error" in tracking shock wave development.
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An earlier AI audit suggested this model has "suspect math" regarding:
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1. UV Divergence in the Ω[u] term.
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2. Frame anchoring (the exclusion/trap center problem).
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3. Convergence claims (errors going to zero).
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TASK:
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1. Identify the "Suspect Math": Where does this equation likely break down in a real physical or numerical simulation?
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2. Formalize the UV Divergence check: If u(x) has a discontinuity (shock), how does Ω[u] behave?
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3. Propose a Lean 4 theorem statement that would verify the "well-posedness" or "energy boundedness" of this system.
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Provide your reasoning in thinking tags and then the final audit report.
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"""
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print(f"--- Auditing Regularized Burgers Equation with {model} ---")
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try:
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# Using the streaming support I just added (but I'll handle the output manually here)
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res = client.chat([{"role": "user", "content": prompt}], model=model)
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print("\nAudit Results:")
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print(res["message"]["content"])
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except Exception as e:
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print(f"Error: {e}")
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if __name__ == "__main__":
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main()
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