Bounded Proof Signoff: What a Depth Actually Proves: Comparison Matrix

Comparison matrix

Proof counts, coverage views, and bounded-depth stats all need context to express true residual risk.

+------------------+----------------+----------------+----------------+
| Approach         | Strength       | Weakness       | Best when      |
+------------------+----------------+----------------+----------------+
| Strict model     | high trust     | longer runtime | signoff-critical logic |
| Balanced model   | faster closure | needs reviews  | daily regressions |
| Heavy abstraction | runtime gain   | confidence risk | exploratory triage |
| Property refactor | debug clarity  | rewrite effort | stalled proof sets |
+------------------+----------------+----------------+----------------+

When to choose each approach

• Use bounded results only with explicit temporal horizon rationale and documented residual risk.

• Escalate critical bounded-only properties to targeted unbounded or hybrid evidence plan.

Interview traps

• Applying one setup strategy to all property classes without intent review.

• Accepting waivers before replaying first divergence with owners.

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.

Principal formal review addendum

Bounded Proof Signoff: What a Depth Actually Proves should be reviewed as a requirement-evidence workflow, not a single status report.

Use non-vacuous closure rate, counterexample turnaround time, and requirement-level residual risk trend as the monitoring lens and formal closure packet: assumptions audit, proof status matrix, counterexample classification, and requirement traceability as closure proof.

Signoff is requirement-centric evidence synthesis, not a single dashboard percentage. Strong teams preserve legal reachability while improving convergence.