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 - [ ] **[B-0180](backlog/P2/B-0180-fix-circuitregistration-tla-config-bug-safety-invariant-undefined-2026-05-03.md)** Fix CircuitRegistration.tla config bug — `.cfg` references invariant `Safety` not defined in `.tla` (blocks B1 → A CI registration)
 - [ ] **[B-0182](backlog/P2/B-0182-linux-only-formal-verification-tests-pure-math-no-os-difference-aaron-2026-05-03.md)** Filter formal-verification tests to standard Linux only — TLC + Alloy + Lean are pure-math computation; no OS-specific behavior
 - [ ] **[B-0183](backlog/P2/B-0183-tla-alloy-runners-as-ts-wrappers-not-fsharp-tests-aaron-2026-05-03.md)** TLA+ / Alloy runners should be TS wrappers under tools/, not F# xunit tests — pure-shell-out, no F# operator-algebra logic involved
+- [ ] **[B-0185](backlog/P2/B-0185-delta-crdt-property-tests-redesign-after-1426-close-2026-05-03.md)** Delta-CRDT property tests redesign — careful single-pass design after #1426 close
 
 ## P3 — convenience / deferred
 
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+---
+id: B-0185
+priority: P2
+status: open
+title: Delta-CRDT property tests redesign — careful single-pass design after #1426 close
+tier: formal-verification
+effort: M
+ask: Otto 2026-05-03 — closed PR #1426 after 5 reviewer threads surfaced distinct design issues; needs full-pass redesign rather than incremental property additions
+created: 2026-05-03
+last_updated: 2026-05-03
+depends_on: []
+composes_with:
+  - docs/research/2026-05-03-math-proofs-honest-assessment.md
+  - memory/feedback_under_specified_action_preconditions_recurring_class_in_formal_specs_aaron_2026_05_03.md
+tags: [c3, fscheck, delta-crdt, anti-entropy, redesign, math-proofs-assessment]
+---
+
+# B-0185 — Delta-CRDT property tests redesign
+
+## What happened
+
+PR #1426 attempted to add delta-CRDT anti-entropy property tests with 3 (then 5) properties for `GCounterDelta` + `PNCounterDelta`. After review, 5 unresolved threads surfaced distinct correctness issues. PR closed honestly rather than ship a flawed property suite.
+
+## Issues identified by reviewers
+
+1. **Same-replica deltas built from same `priorDvv` carry identical dots.** Doesn't exercise the out-of-order anti-entropy case (two distinct successive deltas from one replica that arrive reordered).
+2. **GCounter coverage misses within-replica path.** Successive causal-state deltas from one replica applied out of order — the genuinely interesting case for anti-entropy.
+3. **PN same-replica test with unconstrained `int` falls back to disjoint-component scenario.** When `d1` and `d2` have opposite signs, one lands in P-side and one in N-side — the test loses its within-component-merge intent.
+4. **Delta convergence checked on `Value` only, not full state.** Different internal states can have equal `Value`; full-state equality is the stronger invariant.
+5. **Description/test-plan drift.** After adding properties post-review, the PR description didn't reflect the actual property count.
+
+## Path forward (what the redesign should include)
+
+- **Causal-state tracking via DVV.Sync chains.** Build a sequence of deltas where each carries a different causality (`priorDvv = previousDelta.Causality`) so out-of-order anti-entropy is genuinely tested.
+- **Full-state equality, not just Value equality.** Compare on the underlying CRDT state representation directly (or convert both sides to a canonical form).
+- **Per-component sign constraints.** For PNCounter, generate same-sign deltas explicitly to exercise within-component merge; have a separate test for cross-component (different sign) deltas to exercise disjoint-component merge.
+- **Within-replica path coverage.** Two successive same-replica deltas with different dots, applied in different orders. Both for GCounter and PNCounter.
+- **Idempotence on full state.** `apply(apply(s, d), d) == apply(s, d)` on full state, not just Value.
+- **Single-pass design.** Land all properties together, not incrementally. Each property's domain constraints should be visible in the property name (mirrors LWW-Register's `under unique replica ids` pattern from #1424).
+
+## Effort
+
+M — 1-2 days of careful design + implementation. Worth doing properly because the layer-protected (DeltaCrdt's apply) is a foundational anti-entropy contract; partial coverage that misses within-replica path could mask future regressions.
+
+## Composes with
+
+- `feedback_under_specified_action_preconditions_recurring_class_in_formal_specs_aaron_2026_05_03.md` — same author-time class: missing precondition / domain constraint that lets a property "pass" without actually validating the law.
+- The 14+ already-merged C3 properties (PN-Counter, OR-Set, LWW-Register, MerkleTree) substantially close the C3 → B grade upgrade in the math-proofs assessment; this row tracks the residual delta-CRDT layer.
+
+## Why P2 (not P1)
+
+- The math is already proven via Z3 axioms (8 unbounded-Int theorems) + Lean Mathlib chain rule. Delta-CRDT property tests pin the F# wrapper layer; failures wouldn't invalidate the underlying math, only the wrapper's correctness.
+- C3 row in math-proofs assessment is substantially closed by the merged properties; this row is residual coverage, not a load-bearing gap.
+- 1-2 day effort with multi-axis constraints — worth doing right rather than rushed.
+
+## Acceptance criteria
+
+- [ ] DVV.Sync chain builds successive deltas with distinct causality
+- [ ] Full-state equality used (not just Value equality)
+- [ ] Per-component sign constraints for PNCounter same-replica properties
+- [ ] Within-replica out-of-order anti-entropy case covered for both GCounter and PNCounter
+- [ ] Idempotence checked on full state, not just Value
+- [ ] Single PR with all properties — no incremental additions
+- [ ] PR description matches the property set actually validated