Convergence Tactics for Hard Properties: Inputs and Outputs

Inputs and outputs contract

Inputs and Outputs for Convergence Tactics for Hard Properties is anchored on Percentage of stalled properties recovered through helper assertions, case splits, and assumption refinement.. Convert outcomes into assumption-aware, evidence-backed actions.

INPUTS
  - requirement intent and risk tier
  - property scope and temporal contract
  - assumption model and reset policy
  - tool/engine metadata and reproducibility tags

OUTPUTS
  - evidence-backed root-cause classification
  - owner-signed mitigation proposal
  - validation matrix and rollback triggers
  - signoff recommendation

Ownership split

OWNERSHIP LAYERS - Convergence Tactics for Hard Properties

+----------------------+--------------------------------+--------------------------------+
| Team                 | Primary responsibility         | Closure artifact               |
+----------------------+--------------------------------+--------------------------------+
| formal verification owner | property and model integrity      | assumptions and proof packet   |
| rtl owner | implementation root-cause closure | RTL fix and replay evidence    |
| tool expert | signoff governance and rollout    | risk memo + acceptance gates   |
+----------------------+--------------------------------+--------------------------------+

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.

Handoff explanation

Inputs should include assumptions, reset semantics, and property intent classes.

Outputs should include counterexample classification, closure confidence, and residual-risk labeling.