Symbolic Verification Test Discrepancy Notification
Alert engineering teams to formal proof failures and boundary counterexamples detected by automated verification solvers.
Use this template when symbolic execution, model checking, or SMT solvers uncover mathematical invariant violations in core algorithmic logic. It drafts an analytical email pinpointing the counterexample and detailing necessary axiom corrections.
Role: Principal Formal Verification Engineer specializing in automated theorem proving and symbolic solver integration.
Context
- Target algorithm under verification: {{target_algorithm}}
- Core mathematical domain: {{mathematical_domain}}
- Automated solver and verification toolchain: {{verification_framework}}
- Discovered counterexample trace: {{counterexample_trace}}
- Downstream theoretical and operational impact: {{discrepancy_impact}}
- Recipient research and engineering squad: {{recipient_team}}
Task
Author an analytical, high-precision engineering email informing {{recipient_team}} of a formal proof violation in {{target_algorithm}}, isolating the symbolic counterexample, and detailing the exact mathematical remediation requirements.
Method
- Parse {{counterexample_trace}} to isolate the exact state invariant violated during verification execution.
- Cross-reference the violated invariant against the axiomatic foundations of {{mathematical_domain}}.
- Evaluate solver performance logs in {{verification_framework}} to eliminate timeout artifacts, unsound heuristics, or syntax errors.
- Quantify how {{discrepancy_impact}} degrades mathematical soundness across related algorithmic subsystems.
- Construct a minimal reproducible mathematical test case demonstrating state divergence under symbolic evaluation.
- Formulate formal patch hypotheses, such as inductive invariant strengthening, boundary clamping, or precondition adjustment.
- Synthesize findings into an email structured for clear technical triage and immediate verification reproduction.
Constraints
- MUST present the counterexample using rigorous mathematical notation and explicit state assignments.
- MUST prescribe precise mathematical boundary conditions rather than broad conceptual advice.
- MUST NOT suggest disabling solver assertions or loosening tolerance bounds to force verification pass rates.
- Keep the total email body between 400 and 650 words.
Output format
Subject line: [VERIFICATION FAILURE] {{target_algorithm}} - Axiom Violation in {{mathematical_domain}}
- Executive Summary: 2-3 sentences outlining the failing proof obligation and verification state.
- Minimal Counterexample Trace: Explicit variable assignments and the violated invariant condition.
- Mathematical Soundness Analysis: Impact assessment covering {{discrepancy_impact}}.
- Required Remediations: Numbered corrective steps for {{recipient_team}} before resubmission to {{verification_framework}}.
Self-review
- Did I isolate the exact mathematical boundary condition that triggered the proof failure?
- Does the email provide actionable steps without hand-waving solver mechanics?
- Are all 6 contextual variables referenced accurately and naturally in the text?
Explicit role, a named task, and discrete steps the model can follow.
Background, inputs and variables the model needs before it starts.
Hard boundaries — what the model must and must not do.
A named, field-level shape for the response.
Ordered work items that force analysis before an answer.
Length and structure that travel across frontier models.
Signal density — instruction weight without padding.
Documented variables so the scaffold adapts to new inputs.
Quality bar, assumptions and behaviour when inputs are thin.
How much real usage the template has behind it.