diff --git a/docs/thesis-claim-coverage.md b/docs/thesis-claim-coverage.md
index d81b6ab84a1..28334da1d10 100644
--- a/docs/thesis-claim-coverage.md
+++ b/docs/thesis-claim-coverage.md
@@ -2,7 +2,7 @@
**Status:** PROPOSAL pre-R1-close. Promotes to ACTIVE on R1 closure → R2 promotion transition per [`docs/r2-structure.md` §"Open calls" item 1](r2-structure.md). Authoritative **union receipt + disposition map** for THESIS claims; source-of-truth for each claim remains the cited gate / lane / authority doc.
-**Last refresh:** 2026-04-26 against main HEAD `407a8bcb1`. Refresh discipline below.
+**Last refresh:** 2026-04-27 against main HEAD `242c65d0`. Refresh discipline below.
## Purpose
@@ -15,17 +15,17 @@ This doc is that audit. Every thesis claim in `THESIS.md §"Thesis claims — co
## How to use
- **R2 promotion gate:** Director reviews this doc before promoting `docs/r2-structure.md` to ROADMAP `## Release R2 Program` per Transition mechanics step 5. **Zero GAP rows** is the promotion bar; partial-status rows are notes, not blockers.
-- **R1 close declaration:** R1 Closure Manager cross-references this doc when declaring all-gates-green; the 52 R1-closed claims should map 1:1 to lane gate green status.
-- **R2 manager dispatch:** R2 managers reference this doc when scoping work; the 18 R2-gated claims should map to one of the 6 R2 manager programs.
+- **R1 close declaration:** R1 Closure Manager cross-references this doc when declaring all-gates-green; the 55 R1-closed claims should map 1:1 to lane gate green status.
+- **R2 manager dispatch:** R2 managers reference this doc when scoping work; the 13 R2-gated claims should map to one of the 6 R2 manager programs.
- **Refresh:** at every release transition + on demand when THESIS claims author or change.
## Coverage statistics
| Disposition | Count |
|---|---|
-| **R1-closed** | 52 |
-| **R2-gated** | 18 |
-| **post-R2-external** | 4 |
+| **R1-closed** | 55 |
+| **R2-gated** | 13 |
+| **post-R2-external** | 6 |
| **GAP (no disposition)** | **0** ✓ |
| **TOTAL CLAIMS** | 74 |
@@ -35,10 +35,12 @@ This doc is that audit. Every thesis claim in `THESIS.md §"Thesis claims — co
| Tier/Category | R1-closed | R2-gated | post-R2-external | Total |
|---|---|---|---|---|
-| Tier 1 (Structural correctness) | 9 | 1 | 0 | 10 |
-| Tier 2 (Runtime safety) | 0 | 0 | 1 | 1 |
+| Core abstraction | 1 | 0 | 0 | 1 |
+| Correctness is structural — meta-claim | 4 | 0 | 0 | 4 |
+| Tier 1 (Structural correctness) | 3 | 2 | 0 | 5 |
+| Tier 2 (Runtime safety) | 0 | 1 | 0 | 1 |
| Tier 3 (Verification) | 1 | 3 | 0 | 4 |
-| Concept unifications | 3 | 1 | 0 | 4 |
+| Concept unifications | 2 | 2 | 0 | 4 |
| Epistemic stacking | 6 | 0 | 0 | 6 |
| Substrate shape | 4 | 0 | 1 | 5 |
| Free consequences | 3 | 1 | 0 | 4 |
@@ -74,23 +76,23 @@ This doc is that audit. Every thesis claim in `THESIS.md §"Thesis claims — co
|---|---|---|---|---|
| 6 | Type mismatches, field typos, non-exhaustive, bare containers, circular deps, stale imports, cross-target drift caught at compile | R1-closed | T-Emit `emit_omni_demo_fixtures_green` + T-Demo fixtures | green |
| 7 | CX gate: every recursive function terminates with proven bound | R1-closed | T-LaneE `complexity_merge_sort_is_nlogn`, `complexity_merge_sort_v3_matches_v2_oracle` | green |
-| 8 | Coercion = emission: compiler reads target spec, translates; no separate coercion engine | R2-gated | ROADMAP §"Post-R1 Program — Grounding Completeness" T-Ground-Dissolve lane | not-started |
+| 8 | Coercion = emission: compiler reads target spec, translates; no separate coercion engine | R2-gated | ROADMAP §"Post-R1 Program — Grounding Completeness" T-Ground-Dissolve lane | blocked on T-Ground critical path |
| 9 | Ownership: compiler proves no aliased mutation in emitted code | R1-closed | T-LaneE E-family carrier port (ownership substrate) | partial |
-| 10 | Grounding completeness: target primitives structurally modeled, inhabits-search coercion, fail-closed | R2-gated | ROADMAP §"Post-R1 Program — Grounding Completeness" T-Ground-Pilot through T-Ground-Dissolve | not-started |
+| 10 | Grounding completeness: target primitives structurally modeled, inhabits-search coercion, fail-closed | R2-gated | ROADMAP §"Post-R1 Program — Grounding Completeness" T-Ground-Pilot through T-Ground-Dissolve | in-flight (pilot closed; Rust/Engine/Tests/Dissolve remain) |
### Tier 2 — Runtime safety
| # | Claim | Disposition | Evidence | Status |
|---|---|---|---|---|
-| 11 | Division by zero, overflow, OOB, force-unwrap, partial functions proven safe or made total | R2-gated | `docs/r2-structure.md` Goal 4 (T-ImpossibleBugs unhandled-diagnostic-paths class); Tier 2 substrate | not-started |
+| 11 | Division by zero, overflow, OOB, force-unwrap, partial functions proven safe or made total | R2-gated | `docs/r2-structure.md` Goal 4 (T-ImpossibleBugs unhandled-diagnostic-paths class); Tier 2 substrate | in-flight (Int division Result carrier PR tail active) |
### Tier 3 — Verification from structure
| # | Claim | Disposition | Evidence | Status |
|---|---|---|---|---|
-| 12 | L4: emitted code executes and matches `.dag` evaluation | R2-gated | T-Ground-Tests lane | not-started |
-| 13 | L5: same `.dag` produces same behavior in Rust/Python/Go | R2-gated | T-Ground-Rust / T-Ground-Python / T-Ground-Go lanes | not-started |
-| 14 | L6: every structural form compiles to every target | R2-gated | T-Ground-Engine (inhabitance-search walker) | not-started |
+| 12 | L4: emitted code executes and matches `.dag` evaluation | R2-gated | T-Ground-Tests lane | blocked on earlier T-Ground lanes |
+| 13 | L5: same `.dag` produces same behavior in Rust/Python/Go | R2-gated | T-Ground-Rust / T-Ground-Python / T-Ground-Go lanes | pending/fill queue per T-Ground; Rust/Engine tails remain |
+| 14 | L6: every structural form compiles to every target | R2-gated | T-Ground-Engine (inhabitance-search walker) | in-flight (ValueBody list/sum producer landed; Engine consumer active) |
| 15 | L7: operations obey declared algebraic laws | R1-closed | T-LensAPI `lens_composition_associative` | green |
### Concept unifications
@@ -98,8 +100,8 @@ This doc is that audit. Every thesis claim in `THESIS.md §"Thesis claims — co
| # | Claim | Disposition | Evidence | Status |
|---|---|---|---|---|
| 16 | Coercion cost = complexity | R1-closed | T-LaneE complexity lens (realization costs compose with `.dag`-level CX) | green |
-| 17 | Coercion = emission | R2-gated | T-Ground-Dissolve dissolves coercion scaffolding | not-started |
-| 18 | Target language spec = transport spec = interpreter runtime | R2-gated | T-Ground lanes (Rust/Python/Go structural modeling) | not-started |
+| 17 | Coercion = emission | R2-gated | T-Ground-Dissolve dissolves coercion scaffolding | blocked on T-Ground critical path |
+| 18 | Target language spec = transport spec = interpreter runtime | R2-gated | T-Ground lanes (Rust/Python/Go structural modeling) | in-flight |
| 19 | Idempotency + cancellation + redundancy = algebraic simplification | R1-closed | T-Demo impossible-bugs idempotency-violation demo | green |
### Epistemic stacking
@@ -130,7 +132,7 @@ This doc is that audit. Every thesis claim in `THESIS.md §"Thesis claims — co
| 31 | Automatic parallelism from dependency graph | R1-closed | T-Demo `fixture_integration_canonical` parallelism demo | green |
| 32 | Automatic memoization from purity + cost | R1-closed | Purity structural; cost via T-LaneE complexity lens | green |
| 33 | Space bound proofs from CX | R1-closed | T-LaneE complexity dimension includes space tracking | green |
-| 34 | Cross-language optimization from shared cost algebra | R2-gated | T-Ground-Engine (inhabitance-search composing cost across targets) | not-started |
+| 34 | Cross-language optimization from shared cost algebra | R2-gated | T-Ground-Engine (inhabitance-search composing cost across targets) | in-flight (Engine prerequisite landed; consumer tail active) |
### Omni-emission
@@ -140,7 +142,7 @@ This doc is that audit. Every thesis claim in `THESIS.md §"Thesis claims — co
| 36 | Coherence structural, not checked; drift impossible (same Node tree source) | R1-closed | T-Emit multi-target structural coherence | green |
| 37 | Shape A — language targets (Rust/Python/Go/TypeScript/Swift/HDL); cost O(1) per spec | R1-closed | T-Emit Rust/Python/Go gates; TypeScript/Swift/HDL post-R1 | partial (3 of 6+ targets) |
| 38 | Shape B — user-program artifacts (YAML/Terraform/K8s/SQL/OpenAPI) via `.dag` emitter programs | post-R2-external | ROADMAP Track 16 (user code, not compiler targets); pressure-test via `../ctrl/` | not-started |
-| 39 | Target-level cost complexity composes with `.dag`-level CX statically | R2-gated | T-Ground-Engine (realization costs from language specs) | not-started |
+| 39 | Target-level cost complexity composes with `.dag`-level CX statically | R2-gated | T-Ground-Engine (realization costs from language specs) | in-flight |
| 40 | Distinction Shape A vs Shape B; compiler emits languages, user code emits other artifacts | post-R2-external | ROADMAP Track 16 design decision | unknown |
| 41 | Cost scaling O(1) per target, not O(N × M); effort scales with conceptual content | R1-closed | Structural property of substrate (emit pass per target, not per layer count) | green |
| 42 | Emission independent of intent (what ≠ how) | R1-closed | Separation of program declaration from realization specs | green |
@@ -198,9 +200,9 @@ This doc is that audit. Every thesis claim in `THESIS.md §"Thesis claims — co
| 64 | (R1) Suboptimal-complexity contract violation: function annotated bound errors at compile | R1-closed | T-Demo `impossible_bug_class_suite_r1` includes suboptimal-complexity demo | partial (CostBounded receipt is runner-fail) |
| 65 | (R1) Idempotency-contract violation: marked `@idempotent` function structure errors | R1-closed | T-Demo impossible-bugs suite (`compose_effects` + `AppendEffect` violation) | green |
| 66 | (R1) Transport/type-drift: client/server cannot hold different types for same field | R1-closed | T-Demo impossible-bugs suite (`TypeMismatch` multi-target) | green |
-| 67 | (R2+) Nested-optional flatten: `Option