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 - [ ] **[B-0712](backlog/P2/B-0712-soraya-round45-witnessdurable-commit-protocol-tla-z3-fscheck-triple-2026-05-23.md)** Soraya round-45 hand-off — WitnessDurable commit protocol (TLA+ spec + Z3 quorum-arithmetic lemma + FsCheck cross-check)
 - [ ] **[B-0713](backlog/P2/B-0713-soraya-round50-imaginary-stack-toy-model-registry-gap-lean-2026-05-23.md)** Soraya round-50 hand-off — register Lean ImaginaryStack/ToyModel in verification-registry.md (sorry-bearing artifact with HaPPY-paper fidelity claim)
 - [ ] **[B-0714](backlog/P2/B-0714-soraya-round51-tla-cfg-runnability-gap-3-specs-2026-05-23.md)** Soraya round-51 hand-off — author 3 missing TLA+ `.cfg` files (AsyncStreamEnumerator / ConsistentHashRebalance / DictionaryStripedCAS) — runnability gap distinct from B-0709 registry gap
+- [ ] **[B-0715](backlog/P2/B-0715-soraya-round52-istimeinvariant-axiom-registry-gap-dbsp-chain-rule-2026-05-23.md)** Soraya round-52 hand-off — register `IsTimeInvariant` axiom in verification-registry (Class 1/2 statement+paper-drift on a load-bearing axiom that BOTH registered DBSP theorems depend on)
 
 ## P3 — convenience / deferred
 
diff --git a/docs/backlog/P2/B-0715-soraya-round52-istimeinvariant-axiom-registry-gap-dbsp-chain-rule-2026-05-23.md b/docs/backlog/P2/B-0715-soraya-round52-istimeinvariant-axiom-registry-gap-dbsp-chain-rule-2026-05-23.md
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+---
+id: B-0715
+priority: P2
+status: open
+title: "Soraya round-52 hand-off — register `IsTimeInvariant` axiom in verification-registry (Class 1/2 statement+paper-drift on a load-bearing axiom that BOTH registered DBSP theorems depend on)"
+created: 2026-05-23
+last_updated: 2026-05-23
+classification: buildable-now
+decomposition: atomic
+assignee: kenji
+discovered_by: soraya
+owners: [kenji, formal-verification-expert]
+type: drift-cleanup
+composes_with:
+  - tools/lean4/Lean4/DbspChainRule.lean
+  - docs/research/verification-registry.md
+  - docs/research/chain-rule-proof-log.md
+---
+
+# B-0715 — Register `IsTimeInvariant` axiom (Soraya round-52 hand-off)
+
+## Origin
+
+Soraya's seventh autonomous routing tick (2026-05-23 — round 52, post-PR #4789 merge of B-0714). Distinct axis from B-0709 (portfolio coverage), B-0713 (Lean exploratory artifact), B-0714 (TLA+ runnability).
+
+## Finding
+
+`tools/lean4/Lean4/DbspChainRule.lean:272` defines:
+
+```lean
+structure IsTimeInvariant (f : ...) where
+  commute_zInv : ∀ s n, f (zInv s) n = zInv (f s) n
+```
+
+This is a **de facto axiom** (no proof obligation; callers discharge per-operator). Both registered theorems in `verification-registry.md` (`chain_rule_proposition_3_2` row + `Dop_LTI_commute` row) take `IsTimeInvariant` as hypothesis — but the axiom itself has **no registry row**.
+
+The artifact's own header (lines 50-51, 201-203) carries **strikethrough revision history**: `~~Prop 3.5 unspoken premise~~ → Theorem 3.3 explicit` (corrected round 35, 2026-05-05). **The drift class this row is designed to catch already empirically fired on THIS exact axiom** — registry rows are the structural prevention mechanism, currently missing for the axiom.
+
+## Distinct from prior session findings
+
+- B-0709 (round 42, expanded 49): TLA+/Alloy portfolio coverage — different tool stack
+- B-0713 (round 50): Lean ImaginaryStack/ToyModel exploratory artifact — different artifact, sorry-bearing
+- B-0714 (round 51): TLA+ `.cfg` runnability — different tool + axis (runnability vs registry)
+
+This row: registered THEOREMS depend on an UNREGISTERED axiom in the same artifact. New axis.
+
+## Routing decision (Soraya)
+
+- **Primary tool**: Lean 4 (axiom IS the right encoding — `structure` with a property field is the Mathlib-idiomatic representation of a class-with-axioms)
+- **Cross-check**: NONE today — the axiom is structural, not pointwise-algebraic. Z3/FsCheck don't apply. Paper-fidelity cross-check is human-grade (registry audit by `verification-drift-auditor`)
+- **Wrong-tool cost at TOOL axis**: zero. Cost lives at **REGISTRY axis** — without a row, paper-statement drift (the round-35 `Prop 3.5 → Theorem 3.3` correction class) goes uncaught next iteration. Strikethrough revision in the file header is empirical proof this drift class is real on THIS axiom.
+
+## TLA+-hammer guard
+
+N/A — finding is Lean axiom-registry hygiene, not state-machine vs algebraic routing.
+
+## Acceptance criteria
+
+1. New row in `docs/research/verification-registry.md` for `Dbsp.ChainRule.IsTimeInvariant`:
+   - Artifact path: `tools/lean4/Lean4/DbspChainRule.lean:272`
+   - Paper anchor: Budiu et al. 2023 ([arXiv:2203.16684](https://arxiv.org/abs/2203.16684)), Theorem 3.3 (Linear) — *"For an LTI operator Q we have Q^Δ = Q"*
+   - Axiom statement: `commute_zInv : ∀ s n, f (zInv s) n = zInv (f s) n`
+   - Preconditions diff vs paper: paper's "Linear Time-Invariant" condition is per-operator; Lean encodes as structure-field discharged at instance site
+   - Cross-reference back-pointers added to existing two theorem rows' Preconditions-diff sections (instead of inlining the same hypothesis prose twice)
+   - Last audit: None yet — registered 2026-05-23
+   - Drift history: round-35 paper-citation correction (Prop 3.5 → Theorem 3.3) — preserved as audit-cadence anchor
+2. Follow-up consideration (out of scope for this row): `IsCausal`, `IsLinear`, `IsPointwiseLinear` structures carry similar de-facto-axiom status; if this row lands cleanly, future Soraya round can extend to all four (separate B-NNNN)
+
+## Effort
+
+S (one registry row + 2 back-pointer cross-references). Assignee: kenji.
+
+## Composes with
+
+- [`tools/lean4/Lean4/DbspChainRule.lean`](../../../tools/lean4/Lean4/DbspChainRule.lean) — target artifact line 272
+- [`docs/research/verification-registry.md`](../../research/verification-registry.md) — substrate this row fills
+- [`docs/research/chain-rule-proof-log.md`](../../research/chain-rule-proof-log.md) — round-35 paper-drift audit trail (empirical anchor for why registry rows matter)
+- B-0709 (round 42, expanded 49) — different axis (portfolio coverage)
+- B-0713 (round 50) — different artifact (Lean ImaginaryStack/ToyModel)
+- B-0714 (round 51) — different tool (TLA+) + axis (runnability)
+- `memory/persona/soraya/NOTEBOOK.md` round-52 entry (pending append)
+
+## Substrate-honest framing
+
+The artifact is well-formed Lean (DbspChainRule is CI-type-checked, no `sorry`, no `admit`). The gap is purely registry-hygiene: a load-bearing axiom that both registered theorems depend on is itself unregistered. The fix is one row + two back-pointers; bounded engineering work that closes the auditor's blind spot on this specific axiom's paper-drift class (which has already fired empirically once, on this same axiom, per the round-35 strikethrough revision history).