Bounded Proof Signoff: What a Depth Actually Proves: Theory Deep Dive

Foundational theory

Bounded Proof Signoff: What a Depth Actually Proves is a core topic in Formal Coverage & Signoff. Treat each proof result as evidence under a modeled world, not a context-free truth statement.

Core concepts explained

• Bounded model checking proves properties for executions up to a finite depth, which is valuable but fundamentally different from unbounded inductive closure. A depth N result guarantees no counterexample shorter than or equal to N cycles under the given assumptions; it does not prove behavior beyond that horizon unless strengthened by induction or decomposition arguments. Signoff use of bounded results therefore requires explicit rationale: depth justification tied to worst-case protocol latency, retry bounds, queue draining limits, and watchdog time constants. When properties remain bounded-only, teams should classify residual risk by escape potential and pair with targeted simulation or emulation stress that extends temporal coverage beyond the formal depth frontier. Credible reporting distinguishes fully proven, bounded-proven, and undetermined properties so decision makers do not mistake partial temporal guarantees for complete correctness.

• Primary metric: non-vacuous closure rate, counterexample turnaround time, and requirement-level residual risk trend

• Primary artifact: formal closure packet: assumptions audit, proof status matrix, counterexample classification, and requirement traceability

• Owners: formal verification owner, rtl owner, verification lead

• Proof quality includes vacuity and reachability, not pass/fail status only.

• Assumption discipline is part of design correctness, not tool setup.

Why this matters in formal signoff

Signoff is requirement-centric evidence synthesis, not a single dashboard percentage. Teams that formalize this posture reduce false passes and late-stage surprises.

Mental model

COVERAGE / SIGNOFF PYRAMID

          [Signoff criteria met]
        [Formal coverage closure]
      [Property quality + assumptions]
    [Assertion plan vs spec intent]
  [Requirements and risk inventory]

Top quality depends on bottom-layer completeness.

Worked intuition

1. Define requirement slice and property intent class (safety, liveness, or reachability).

2. Audit assumptions and reset model before trusting any status outcome.

3. Track movement in non-vacuous closure rate, counterexample turnaround time, and requirement-level residual risk trend with requirement-level ownership.

4. Collect formal closure packet: assumptions audit, proof status matrix, counterexample classification, and requirement traceability before signoff or waiver decisions.

5. Apply one bounded model or RTL change per debug hypothesis.

6. Publish closure with residual risk and rollback conditions.

Common misconceptions

• Green proof status always means silicon-safe behavior.

• Faster convergence always means better model quality.

• Unreachable cover goals are acceptable if safety assertions pass.

• Bounded depth is equivalent to full proof unless a failure appears.

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.

Theory reinforcement

Theory matters only when it predicts observed traces and closure movement.

Use precise terminology for safety, liveness, boundedness, and vacuity.