Formal Coverage Metrics: Beyond Green Proof Counts: Mechanism

Mechanism to understand

Mechanism for Formal Coverage Metrics: Beyond Green Proof Counts is anchored on non-vacuous closure rate, counterexample turnaround, and residual-risk trend by requirement class. Convert outcomes into assumption-aware, evidence-backed actions.

Formal closure quality depends on metric meaning, not property pass volume.

• Name the first boundary where requirement intent diverges.

• Prove mechanism with one high-confidence evidence packet.

• Assign owner for smallest reversible mitigation.

Execution flow

FORMAL EXECUTION FLOW - Formal Coverage Metrics: Beyond Green Proof Counts

requirement intent and risk class
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property and assumption modeling
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proof engine exploration and trace extraction
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counterexample classification and fix hypothesis
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re-proof, coverage audit, and signoff decision

Formal deep dive

Signoff quality is requirement-centric and must integrate proof status, reachability, bounded limits, and waiver governance.

Concept diagram

FORMAL SIGNOFF PYRAMID

requirements -> properties and covers -> quality metrics -> waiver governance -> release decision

Metric graph

SIGNOFF CONFIDENCE TREND

fully proven critical    ███████
bounded-only critical    ████
unexplained cover gaps   ███

Metrics and artifacts to collect

• requirement-to-proof closure map

• critical cover reachability and gap aging

• bounded-only risk register

• waiver debt with owner and expiry

Mini case study

A release review blocked signoff until bounded-only properties were paired with explicit residual-risk and replay plans.

Debug branches

• Separate status color from proof quality dimensions.

• Treat unreachable critical covers as signoff blockers.

• Document bounded-horizon rationale with architecture limits.

Senior review question

Ask: which requirement intent is proven, under which assumptions, and what residual risk remains?

Key takeaways

• Tie each proof claim to assumption boundaries and reachability evidence.

• Prefer minimal reversible fixes and preserve legal behavior visibility.

Common pitfalls

• Treating runtime reduction as proof-quality improvement without audits.

• Declaring closure while critical covers remain unreachable.

• Using broad waivers instead of first-divergence root-cause ownership.

Mechanism deep dive

Mechanism detail: Formal closure quality depends on metric meaning, not property pass volume. Teams should separate assertion status (proven/falsified/inconclusive) from proof quality indicators such as vacuity, proof core relevance, assumption influence, and cone-of-influence footprint. A property can be proven yet deliver weak confidence if its antecedent is rarely reachable, its trigger is masked by over-constraint, or its proof relies on assumptions that are broader than the architecture contract allows. Proof coverage views are most useful when mapped to design intent: which requirements are mathematically guaranteed, which logic cones remain weakly exercised, and where assumptions carry non-trivial risk. Mature projects trend coverage by requirement class (safety, liveness, protocol progression, arbitration fairness) and perform periodic mutation-like perturbations to ensure proofs are sensitive to real defects rather than structurally immune artifacts.

Prefer requirement decomposition over monolithic assertions for debug clarity.