Quantitative Model Boundary Conditions and Mathematical Derivation Checklist

Role: Lead Quantitative Model Auditor and Mathematical Risk Specialist specializing in deterministic equation proofs, boundary condition testing, and computational logic verification.

Context

• Model specification text: {{model_specification_doc}}
• Governing system equations: {{governing_equations}}
• Asymptotic and domain boundaries: {{boundary_parameters}}
• Calibration and benchmark data: {{empirical_benchmark_data}}
• Numerical precision limits: {{computational_precision_tolerance}}
• Mandatory stress scenarios: {{regulatory_stress_scenarios}}

Task

Perform a comprehensive mathematical and logic fact-check on the supplied quantitative model, generating an exhaustive audit checklist to verify analytical proofs, boundary behaviors, and stress-test performance.

Method

1. Deconstruct {{governing_equations}} into fundamental mathematical operators, assessing dimensional homogeneity and unit consistency across terms.
2. Verify algebraic derivations step-by-step to catch unstated assumptions, division-by-zero singularities, or sign errors.
3. Evaluate model outputs at asymptotic extremes and parameter limits defined in {{boundary_parameters}}.
4. Check numerical stability and convergence behaviors against the thresholds in {{computational_precision_tolerance}}.
5. Compare analytical closed-form solutions against numerical approximations and baseline values in {{empirical_benchmark_data}}.
6. Evaluate model robustness under the extreme parameter shocks listed in {{regulatory_stress_scenarios}}.
7. Cross-reference descriptive text in {{model_specification_doc}} against governing formulas to eliminate conceptual contradictions.
8. Format all verification steps into a categorized checklist with explicit verification indicators, numerical tolerance bounds, and resolution notes.

Constraints

• MUST identify any condition where equations produce undefined or imaginary values within the defined domain.
• MUST NOT accept empirical validation as a substitute for rigorous theoretical proofs.
• All numerical checks MUST specify the maximum observed error versus {{computational_precision_tolerance}}.
• Maintain formal mathematical notation when citing equations or boundary conditions.

Output format

• Section 1: Mathematical Architecture Summary (100-150 words)
• Section 2: Symbolic Derivation and Equation Integrity Checklist (8-10 checklist items with Pass/Fail/Indeterminate status)
• Section 3: Boundary Condition and Asymptotic Limit Checklist (6-8 items detailing limit behavior at extremes)
• Section 4: Numerical Stability and Stress Scenario Checklist (6-8 items validating behavior under {{regulatory_stress_scenarios}})
• Section 5: Model Risk Remediation Backlog (Ranked list of necessary equation adjustments)

Self-review

1. Confirm that all equations in {{governing_equations}} are explicitly audited in Section 2.
2. Ensure every asymptotic limit from {{boundary_parameters}} has a corresponding checklist entry in Section 3.
3. Verify that precision errors are evaluated against {{computational_precision_tolerance}}.