diff --git a/crates/ailang-surface/tests/round_trip.rs b/crates/ailang-surface/tests/round_trip.rs
index 81caefd..2447525 100644
--- a/crates/ailang-surface/tests/round_trip.rs
+++ b/crates/ailang-surface/tests/round_trip.rs
@@ -1,21 +1,27 @@
 //! Round-trip gate for the form-(A) projection.
 //!
-//! Two complementary checks over `examples/`:
+//! Three complementary checks over `examples/`, each gathering
+//! fixtures dynamically via `read_dir` (no hardcoded lists). The
+//! tests are pure readers — they do not write into the working
+//! tree.
 //!
-//! 1. `print_then_parse_round_trips_every_fixture`: for every
-//!    `examples/*.ail.json` fixture, load → `print` → `parse` →
-//!    canonical bytes; assert byte-equal to original.
+//! 1. `print_then_parse_round_trips_every_fixture`: Direction 1 of
+//!    the Roundtrip Invariant (DESIGN.md §"Roundtrip Invariant").
+//!    For every `examples/*.ail.json` fixture, load → `print` →
+//!    `parse` → canonical bytes; assert byte-equal to original.
 //!
-//! 2. `every_ailx_fixture_matches_its_json_counterpart`: for every
-//!    `examples/*.ailx` fixture, parse → canonical bytes; if a
-//!    same-stem `.ail.json` counterpart exists, assert canonical-byte
-//!    equality against it. The `.ailx` side is the human/AI authoring
-//!    ground-truth — fixtures must be writeable without going through
-//!    the printer and still match the JSON-AST.
+//! 2. `every_ailx_fixture_matches_its_json_counterpart`: hand-
+//!    authored ground-truth check. For every `examples/*.ailx`
+//!    fixture, parse → canonical bytes; if a same-stem `.ail.json`
+//!    counterpart exists, assert canonical-byte equality against
+//!    it. Pins the `.ailx` corpus against semantic drift between
+//!    the two forms at the fixture level.
 //!
-//! Both tests gather fixtures dynamically via `read_dir`; no hardcoded
-//! lists. The tests are pure readers — they do not write into the
-//! working tree.
+//! 3. `parse_then_print_then_parse_is_idempotent_on_every_ailx_fixture`:
+//!    Direction 2 of the Roundtrip Invariant. For every well-formed
+//!    `.ailx` text `t`, asserts `canonical_bytes(parse(t))` equals
+//!    `canonical_bytes(parse(print(parse(t))))`. Robust against
+//!    future `.ailx` fixtures without a JSON counterpart.
 
 use std::path::{Path, PathBuf};
 
@@ -196,3 +202,76 @@ fn every_ailx_fixture_matches_its_json_counterpart() {
         paired, parse_only
     );
 }
+
+/// Direction 2 of the Roundtrip Invariant (DESIGN.md §"Roundtrip
+/// Invariant"): for every well-formed `.ailx` text `t`, the
+/// composition `parse → print → parse` is idempotent on the AST.
+///
+/// For the 57 `.ailx` fixtures that have a JSON counterpart this
+/// follows logically from `print_then_parse_round_trips_every_fixture`
+/// + `every_ailx_fixture_matches_its_json_counterpart`. This test
+/// asserts the property directly so it stays robust for future
+/// `.ailx` fixtures without a JSON counterpart, and so the spec's
+/// Direction-2 claim has a dedicated enforcement point.
+#[test]
+fn parse_then_print_then_parse_is_idempotent_on_every_ailx_fixture() {
+    let fixtures = list_ailx_fixtures();
+    assert!(
+        !fixtures.is_empty(),
+        "no .ailx fixtures found under {}",
+        examples_dir().display()
+    );
+
+    let mut failures = Vec::<String>::new();
+    let mut passed = 0usize;
+    for path in &fixtures {
+        let text = match std::fs::read_to_string(path) {
+            Ok(t) => t,
+            Err(e) => {
+                failures.push(format!("{}: read failed: {e}", path.display()));
+                continue;
+            }
+        };
+        let parsed_once = match ailang_surface::parse(&text) {
+            Ok(m) => m,
+            Err(e) => {
+                failures.push(format!("{}: parse(t) failed: {e}", path.display()));
+                continue;
+            }
+        };
+        let printed = ailang_surface::print(&parsed_once);
+        let parsed_twice = match ailang_surface::parse(&printed) {
+            Ok(m) => m,
+            Err(e) => {
+                failures.push(format!(
+                    "{}: parse(print(parse(t))) failed: {e}\n--- printed ---\n{printed}",
+                    path.display()
+                ));
+                continue;
+            }
+        };
+        let bytes_a = ailang_core::canonical::to_bytes(&parsed_once);
+        let bytes_b = ailang_core::canonical::to_bytes(&parsed_twice);
+        if bytes_a != bytes_b {
+            let s_a = String::from_utf8_lossy(&bytes_a).into_owned();
+            let s_b = String::from_utf8_lossy(&bytes_b).into_owned();
+            failures.push(format!(
+                "{}: parse → print → parse is NOT idempotent.\nparse(t):              {s_a}\nparse(print(parse(t))): {s_b}",
+                path.display()
+            ));
+            continue;
+        }
+        passed += 1;
+    }
+
+    if !failures.is_empty() {
+        panic!(
+            "{} of {} .ailx fixture(s) failed idempotency check (passed: {}):\n{}",
+            failures.len(),
+            fixtures.len(),
+            passed,
+            failures.join("\n\n")
+        );
+    }
+    eprintln!("parse→print→parse idempotency ok for {passed} .ailx fixtures");
+}
diff --git a/docs/DESIGN.md b/docs/DESIGN.md
index 64190a8..64a6041 100644
--- a/docs/DESIGN.md
+++ b/docs/DESIGN.md
@@ -1781,8 +1781,8 @@ without changing the identity of the module it produces.
 
 Float literals carry an IEEE-754 bit pattern, not a decimal
 approximation. The canonical encoding is
-`{"kind":"float","bits":"<16-hex>"}` and the surface emits the
-same bits-hex string. NaN, ±Inf, signed zero, and subnormals all
+`{"kind":"float","bits":"<16-lowercase-hex>"}` and the surface
+emits the same bits-hex string. NaN, ±Inf, signed zero, and subnormals all
 round-trip exactly because the JSON-number path is bypassed (see
 §"Float semantics", "Form-A serialisation"). Floats are not an
 exception to the invariant — the bits-hex encoding is the
@@ -1790,7 +1790,7 @@ mechanism that keeps them *inside* it.
 
 ### Enforcement
 
-The invariant is workspace-CI-enforced by four tests, each
+The invariant is workspace-CI-enforced by five tests, each
 operating on the `examples/` corpus via dynamic `read_dir`
 collection (no hardcoded fixture list, so newly added fixtures
 inherit the gate automatically):
@@ -1798,6 +1798,9 @@ inherit the gate automatically):
 - `crates/ailang-surface/tests/round_trip.rs::print_then_parse_round_trips_every_fixture`
   — for every `.ail.json`, `print` then `parse` produces canonical-
   byte-equal output. Direction 1 above.
+- `crates/ailang-surface/tests/round_trip.rs::parse_then_print_then_parse_is_idempotent_on_every_ailx_fixture`
+  — for every `.ailx` text `t`, `parse(t)` and `parse(print(parse(t)))`
+  produce canonical-byte-equal AST. Direction 2 above.
 - `crates/ailang-surface/tests/round_trip.rs::every_ailx_fixture_matches_its_json_counterpart`
   — for every `.ailx` with a same-stem `.ail.json` counterpart,
   `parse` of the text yields canonical bytes equal to the JSON
diff --git a/docs/journals/2026-05-12-audit-rt.md b/docs/journals/2026-05-12-audit-rt.md
new file mode 100644
index 0000000..0137d64
--- /dev/null
+++ b/docs/journals/2026-05-12-audit-rt.md
@@ -0,0 +1,99 @@
+# audit-rt — Milestone close: Roundtrip Invariant
+
+**Date:** 2026-05-12
+**Milestone:** Roundtrip Invariant (rt.1 + rt.2)
+**Status:** Closed, clean (after rt.tidy fixes)
+
+## Architect drift review
+
+`ailang-architect` reported `drift_found` with four items over
+`daf9f4f..HEAD`:
+
+- `[high]` DESIGN.md §"Roundtrip Invariant" Direction 2 (text →
+  JSON → text idempotency) is stated as a property but not
+  directly enforced by any of the four listed tests. Test 1 covers
+  Direction 1; test 2 covers `.ailx` → JSON ≡ counterpart; test 4
+  covers CLI render → parse. None tests `parse → print → parse`
+  idempotency on a hand-authored `.ailx` text directly. Architect
+  recommendation: claim soften OR add a fifth test.
+- `[high]` `docs/roadmap.md` P1 entry "Round-trip completeness
+  invariant" still `- [ ]` (open) after the milestone closed.
+  Stale per roadmap convention (finished entries → `[x]` then
+  removal with one-line journal mirror).
+- `[low]` DESIGN.md wording: `<16-hex>` in new section vs
+  `<16-lowercase-hex>` in §"Data model". Casing constraint is
+  load-bearing for canonical-byte equality; should be stated
+  identically.
+- `[low]` rt.1 plan errata note (planner emitted ast.rs-mismatching
+  destructure scaffold). Single occurrence absorbed cleanly by the
+  Step-3.4 escape hatch. Not a deeper drift pattern; informational.
+
+## Bench-regression check
+
+`bench/check.py && bench/compile_check.py && bench/cross_lang.py`:
+
+- `check.py`: exit 0; 63 metrics; 0 regressed, 0 improved beyond
+  tolerance, 63 stable.
+- `compile_check.py`: exit 0; 24 metrics; 0 regressed, 0 improved
+  beyond tolerance, 24 stable.
+- `cross_lang.py`: exit 0; 25 metrics; 0 regressed, 0 improved
+  beyond tolerance, 25 stable.
+
+All three bench gates green. Bench was the most plausible source
+of a regression given rt.1 added three new tests but the tests
+are pure readers and are not exercised by the bench harness; the
+green signal matches that expectation.
+
+## Resolution (rt.tidy, boss-direct edits)
+
+Three fixes, mechanical, no plan/implement dispatch:
+
+1. **Direction-2 enforcement** —
+   `crates/ailang-surface/tests/round_trip.rs` gains a third test
+   `parse_then_print_then_parse_is_idempotent_on_every_ailx_fixture`.
+   For every `.ailx` fixture asserts
+   `canonical_bytes(parse(t)) == canonical_bytes(parse(print(parse(t))))`.
+   For the 57 fixtures with a JSON counterpart this is logically
+   derivable from tests 1 + 2; the dedicated test stays robust for
+   future `.ailx` fixtures without a counterpart. DESIGN.md
+   §"Roundtrip Invariant" "Enforcement" list updated from four to
+   five tests; module doc-comment updated from "two complementary
+   checks" to "three complementary checks". Test PASS first-shot
+   across all 57 fixtures.
+
+2. **Roadmap P1 entry removed.** The "Round-trip completeness
+   invariant" milestone entry deleted; this journal entry is the
+   one-line mirror per roadmap convention. The P1 todo "Brainstorm
+   Step 7.5" remains; the P1 Show + print-rewire milestone remains.
+
+3. **Wording fix.** DESIGN.md §"Roundtrip Invariant" Float-bits-hex
+   description changed from `<16-hex>` to `<16-lowercase-hex>` to
+   match §"Data model".
+
+The `[low]` planner-errata carry-on item is retained in the rt.1
+journal "Concerns" section; it will surface again only if a future
+tests-against-AST iteration repeats the pattern.
+
+## Spec acceptance criteria — final check
+
+1. ✓ Top-level `## Roundtrip Invariant` section in DESIGN.md;
+   Decision 6 Constraint 2 carries upward cross-reference. (rt.2)
+2. ✓ `every_ailx_fixture_matches_its_json_counterpart` dynamic in
+   `crates/ailang-surface/tests/round_trip.rs`. (rt.1)
+3. ✓ `crates/ailang-core/tests/schema_coverage.rs` with
+   exhaustive-match visitor; 34/34 variants observed. (rt.1)
+4. ✓ `crates/ail/tests/roundtrip_cli.rs` with BLAKE3 identity
+   over `ail render` → tempfile → `ail parse`. (rt.1)
+5. ✓ `cargo test --workspace` green with all four (now five) tests.
+   (rt.1 + rt.2 + rt.tidy)
+6. ✓ No roundtrip gaps surfaced; no render/parse code changes
+   needed in this milestone. (rt.1)
+7. ✓ Tests are pure readers; the CLI test's only filesystem side
+   effect is `tempfile::TempDir`. (rt.1)
+
+## Outcome
+
+Milestone closed clean. Five workspace-wide tests now anchor the
+`.ail.json` ↔ `.ailx` bijection plus AST-variant coverage; the
+property has a dedicated top-level section in DESIGN.md. No
+follow-up iterations queued in this milestone.
diff --git a/docs/journals/INDEX.md b/docs/journals/INDEX.md
index f2b16a3..a5dca1d 100644
--- a/docs/journals/INDEX.md
+++ b/docs/journals/INDEX.md
@@ -18,3 +18,4 @@
 - 2026-05-12 — audit-23: milestone 23 close (architect clean, compile_check ratified per H2 / 5-fn workload), DESIGN.md stub-fix tidy → 2026-05-12-audit-23.md
 - 2026-05-12 — iter rt.1: roundtrip invariant audit tests (3 new tests + ailx-pair dynamic); all PASS first-shot, no gaps surfaced → 2026-05-12-iter-rt.1.md
 - 2026-05-12 — iter rt.2: DESIGN.md anchor for Roundtrip Invariant (top-level section + Decision 6 Constraint 2 upward cross-reference) → 2026-05-12-iter-rt.2.md
+- 2026-05-12 — audit-rt: milestone close (Roundtrip Invariant) — architect drift fixed in rt.tidy (3 items: Direction-2 5th test, roadmap P1 removed, wording sync); bench all-green → 2026-05-12-audit-rt.md
diff --git a/docs/roadmap.md b/docs/roadmap.md
index a5d17c7..34e4251 100644
--- a/docs/roadmap.md
+++ b/docs/roadmap.md
@@ -49,34 +49,6 @@ context. Pick the next milestone from P1.)_
   has neither instance by design; polymorphic helpers at Float fire
   Float-aware `NoInstance` per DESIGN.md §"Float semantics".
 
-- [ ] **\[milestone\]** Round-trip completeness invariant — `.ail.json`
-  ↔ `.ailx` must be a structurally lossless bijection. For every
-  valid module: `ail parse` followed by `ail render` yields the
-  original `.ailx` (modulo formatting), and `ail render` followed by
-  `ail parse` yields the original `.ail.json` (canonical key order).
-  Decision 6 mentions round-trip-as-property in passing, and
-  `crates/ailang-surface/tests/round_trip.rs` checks the `.ailx`
-  direction over the fixture corpus, but the invariant is not
-  prominently anchored as a non-negotiable language property and
-  the symmetric direction (every `.ail.json` has a printable, re-
-  parseable `.ailx` form) is not workspace-wide enforced. This
-  milestone (a) audits the existing fixture corpus for structural
-  gaps in either direction, (b) closes any render / parse gaps
-  surfaced, (c) lifts the round-trip property to a named, prominent
-  invariant in DESIGN.md (likely as a dedicated subsection of
-  Decision 6, or as its own decision-level entry), (d) adds a
-  workspace-wide check (E2E or unit, in addition to the existing
-  surface-side fixture test) that the invariant holds over every
-  fixture on every build.
-  - context: brainstorm 2026-05-12 — surfaced while scoping the
-    cross-model authoring-form test (see P2 entry below). The test
-    requires both forms to be exactly equipotent in expressive
-    power; otherwise measured form-preference is contaminated by
-    expressive-power gaps rather than authoring ergonomics. The
-    invariant is also load-bearing on its own: if `.ailx` is the
-    "AI authoring projection" per Decision 6, programs expressible
-    in one form but not the other are a first-class bug class.
-
 - [ ] **\[todo\]** Brainstorm Step 7.5 — Grounding-check is the *last*
   step before the spec is committed. Any post-PASS edit to the spec
   (Boss-side polish, user-requested change, anything) must