Convergence Tactics for Hard Properties: Step-by-Step Walkthrough

Step-by-step analysis walkthrough

Use this sequence when owning Convergence Tactics for Hard Properties in a formal review.

1. Cluster failures by structure and requirement domain.

2. Inspect proof cores for missing invariants or noisy dependencies.

3. Apply one tactic: helper lemma, case split, or abstraction boundary.

4. Re-run cluster and compare convergence slope, not single status.

5. Audit legal reachability after every major constraint change.

Artifacts to collect

• Convergence playbook with stalled-property taxonomy, tactic decisions, and over-constraint audit log.

• counterexample replay package

• assumption traceability matrix

• vacuity and cover dashboard snapshot

• post-fix closure trend report

Decision memo template

FORMAL DECISION MEMO - Convergence Tactics for Hard Properties
symptom:
classification:
root cause:
fix:
validation:
owners: formal verification owner, rtl owner, tool expert, verification lead

Formal deep dive

Convergence requires engine strategy, invariant quality, and model realism to move together with measurable progress.

Concept diagram

CONVERGENCE DECISION FLOW

property bucket -> engine strategy -> helper invariants -> convergence audit -> closure

Metric graph

CONVERGENCE BURNDOWN

open hard properties    ███████
inconclusive aging      █████
closed with audit       ████████

Metrics and artifacts to collect

• engine effectiveness by property class

• induction and helper-lemma success ratio

• stalled-property aging dashboard

• runtime vs closure-quality movement

Mini case study

A stalled set closed only after case-splitting by mode and auditing fairness assumptions for realism.

Debug branches

• Bucket properties by structure and intent before tuning.

• Inspect proof core stability, not runtime alone.

• Reject speed gains that reduce legal reachability.

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

Convergence Tactics for Hard Properties should be reviewed as a requirement-evidence workflow, not a single status report.

Use Percentage of stalled properties recovered through helper assertions, case splits, and assumption refinement. as the monitoring lens and Convergence playbook with stalled-property taxonomy, tactic decisions, and over-constraint audit log. as closure proof.

Convergence is an engineering loop: classify hard properties, tune engines, strengthen invariants, and audit constraints continuously. Strong teams preserve legal reachability while improving convergence.