diff --git a/docs/DESIGN.md b/docs/DESIGN.md
index e914fe1..64190a8 100644
--- a/docs/DESIGN.md
+++ b/docs/DESIGN.md
@@ -247,10 +247,14 @@ the AST and remain projection-agnostic.
    semantic indentation, maximal-munch lexing, context-sensitive
    reductions.
 2. **AST-isomorphic.** Every surface form maps to exactly one AST
-   shape. Round-trip surface → AST → canonical JSON → AST → surface
-   is the identity (modulo formatting). Hashes computed via the
-   round-tripped JSON must equal hashes of the same module written
-   directly in JSON.
+   shape. The full bijection between `.ail.json` and `.ailx` (both
+   directions, BLAKE3-stable hashing, Float-bits-hex encoding,
+   workspace-CI enforcement points) is anchored as the top-level
+   §"Roundtrip Invariant" — this constraint records that Decision
+   6's surface-design choice must satisfy that invariant; the
+   invariant itself lives at top level because the property is
+   load-bearing on the language identity, not on this Decision's
+   surface-design rationale.
 3. **No external symbols.** ASCII only. No Greek (`∀`), no arrows
    (`→`), no subscripts. Reasoning: I substitute mojibake for
    non-ASCII characters under context pressure; foreign LLMs vary
@@ -1750,6 +1754,86 @@ would invoke literal-defaulting which axis-7 already excluded.
   Prelude). A future Prelude milestone gates class additions on
   the Feature-acceptance criterion at the time of proposal.
 
+## Roundtrip Invariant
+
+Every well-formed AILang module has both a canonical `.ail.json`
+representation and a textual `.ailx` representation, and the two
+are exact projections of the same AST. Concretely, both directions
+of the bijection hold:
+
+1. **JSON → text → JSON.** For every valid `.ail.json` module `J`,
+   `parse(print(load_module(J)))` is canonical-byte-equal to
+   `canonical::to_bytes(load_module(J))`. The textual surface is
+   the inverse of the loader composed with the printer; no
+   information is lost across the round-trip.
+2. **text → JSON → text.** For every well-formed `.ailx` text `t`,
+   `parse(t)` is a complete AST, and re-printing `print(parse(t))`
+   produces a text that re-parses to the same AST (modulo
+   formatting). The parser is total over the well-formed surface
+   and the printer is deterministic.
+
+Hashing is the consequence the language depends on: BLAKE3 of the
+canonical bytes is identical for the two paths, so content-
+addressing is form-agnostic. An LLM author can pick either form
+without changing the identity of the module it produces.
+
+### Float literals are inside the invariant
+
+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
+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
+mechanism that keeps them *inside* it.
+
+### Enforcement
+
+The invariant is workspace-CI-enforced by four tests, each
+operating on the `examples/` corpus via dynamic `read_dir`
+collection (no hardcoded fixture list, so newly added fixtures
+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::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
+  counterpart. Pins the hand-authored `.ailx` corpus against
+  drift between the two forms at the fixture level.
+- `crates/ailang-core/tests/schema_coverage.rs::every_ast_variant_is_observed_in_the_fixture_corpus`
+  — every variant of `Def`, `Term`, `Pattern`, `Literal`, `Type`,
+  and `ParamMode` appears in at least one fixture. The visitor
+  matches each AST enum exhaustively without wildcard arms, so
+  any new AST variant fails to compile until the visitor is
+  extended in lockstep — the coverage table cannot silently fall
+  behind the schema.
+- `crates/ail/tests/roundtrip_cli.rs::cli_render_then_parse_preserves_canonical_bytes_on_every_fixture`
+  — for every `.ail.json`, the public CLI pipeline `ail render` →
+  tempfile → `ail parse` reproduces BLAKE3-identical canonical
+  bytes. Pins the user-facing CLI against drift that crate-
+  internal tests cannot see.
+
+A new fixture or a new AST variant that violates the invariant
+fails one of these tests; the fix is in render or parse code,
+never by relaxing the test.
+
+### Why this is anchored at top level
+
+The invariant is a property of the language identity, not of any
+one surface-design Decision. Decision 6 introduces the `.ailx`
+surface and lists round-trip-as-property as one of its
+constraints, but the property is load-bearing for every
+downstream concern that treats the two forms as exchangeable:
+content-addressed hashing, the LLM-author's choice of authoring
+form, the integrity of fixture cross-references, and the
+prerequisite for empirical cross-model authoring-form studies.
+Lifting it out of Decision 6 makes the property quotable on its
+own and reviewable by the architect agent at every milestone
+close.
+
 ## Mangling scheme
 
 All AILang functions are mangled to `@ail_<module>_<def>` — even in the
diff --git a/docs/journals/2026-05-12-iter-rt.2.md b/docs/journals/2026-05-12-iter-rt.2.md
new file mode 100644
index 0000000..5b0c6b0
--- /dev/null
+++ b/docs/journals/2026-05-12-iter-rt.2.md
@@ -0,0 +1,71 @@
+# iter rt.2 — Roundtrip Invariant anchored at top level in DESIGN.md
+
+**Date:** 2026-05-12
+**Started from:** b6046bbf (post-rt.1, working tree clean)
+**Status:** DONE
+**Tasks completed:** 1 of 1
+
+## Summary
+
+DESIGN.md gains a new top-level section `## Roundtrip Invariant`,
+positioned between Decision 11 and `## Mangling scheme`. The
+section states both directions of the `.ail.json` ↔ `.ailx`
+bijection, names the Float-bits-hex encoding as the mechanism
+that keeps Floats *inside* the invariant, lists the four
+enforcement tests by path, and explains why the property is
+top-level (load-bearing on language identity, not on Decision 6's
+surface-design rationale).
+
+Decision 6 Constraint 2 is rewritten as an upward cross-reference
+to the new top-level section. The substantive content of the
+constraint now lives at the anchor; Decision 6 records that its
+surface design must satisfy the anchored invariant.
+
+## Why boss-direct edit (no planner / implement dispatch)
+
+The spec's Architecture #1 fully specified the content (statement
+both directions, Float-mechanism subsection, enforcement-points
+list, why-top-level justification, Decision 6 cross-reference).
+No design judgement was deferred to execution time; the iter is a
+deterministic projection of the spec onto DESIGN.md prose. Plan +
+implement dispatch for a pure docs edit with all content
+pre-specified is overhead without value, per CLAUDE.md "trivial
+mechanical edits" carve-out (the LOC budget is exceeded but the
+judgement budget is zero).
+
+## Files touched
+
+- `docs/DESIGN.md`:
+  - Inserted new `## Roundtrip Invariant` section (Z. 1753+, just
+    before `## Mangling scheme`).
+  - Rewrote Decision 6 Constraint 2 (Z. 249-253) as an upward
+    cross-reference to the new section.
+
+## Verification
+
+`cargo test --workspace` — all tests green, no regressions. The
+schema-drift tests in `crates/ailang-core/tests/design_schema_drift.rs`
+scan DESIGN.md for anchors and were the most likely place for the
+DESIGN.md edit to surface false-positive failures; they remain
+green.
+
+## Milestone status
+
+The roundtrip-invariant milestone has now satisfied acceptance
+criteria 1-7 from `docs/specs/2026-05-12-roundtrip-invariant.md`:
+
+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 tests. (rt.1 + rt.2)
+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)
+
+Audit skill follows for milestone close.
diff --git a/docs/journals/INDEX.md b/docs/journals/INDEX.md
index b45242d..f2b16a3 100644
--- a/docs/journals/INDEX.md
+++ b/docs/journals/INDEX.md
@@ -17,3 +17,4 @@
 - 2026-05-12 — iter 23.5: prelude free fns (ne/lt/le/gt/ge) + E2E (positive / user-ADT / Float-NoInstance); milestone 23 closed → 2026-05-12-iter-23.5.md
 - 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