diff --git a/docs/JOURNAL.md b/docs/JOURNAL.md
index 979ec2e..76041f1 100644
--- a/docs/JOURNAL.md
+++ b/docs/JOURNAL.md
@@ -13731,3 +13731,89 @@ private-link) are the queued P2 sweep from
 Next dispatch: `fieldtest` skill — 2-4 real-world `.ailx` examples
 exercising the Float surface to surface friction / spec gaps from
 an LLM-author-only-DESIGN.md perspective.
+
+## 2026-05-10 — Fieldtest close: Floats milestone
+
+Fieldtest dispatched `ailang-fieldtester` against the Floats
+milestone surface (DESIGN.md + form_a.md only — agent did not
+read implementation source). Four `.ailx` examples landed in
+`examples/fieldtest/`: Newton's-method √2, Int-list mean,
+safe-division-with-NaN, `float_to_str` reach-and-bounce. Spec
+written at `docs/specs/2026-05-10-fieldtest-floats.md`.
+
+**Findings (1 bug, 1 friction, 1 spec_gap, 3 working):**
+
+- **B1 (bug):** `Pattern::Lit::Float` rejection unreachable through
+  `check_module`. DESIGN.md §"Float semantics" + JOURNAL Floats.3 +
+  Floats milestone-close entry all promised hard-reject via
+  `CheckError::FloatPatternNotAllowed`. Reality: surface-lex'd
+  `(case (pat-lit FLOAT-LIT) BODY)` typechecked, built, and ran
+  with IEEE-`==` semantics. The audit at `d6da5c2` reviewed the
+  iter-3.4 reject arm in isolation but missed that
+  `desugar::build_eq` (extended in iter 1.1 to include
+  `Literal::Float` in its OR-pattern) rewrites the Pattern::Lit::Float
+  arm into `(== scrut lit)` BEFORE typecheck runs, making the
+  reject arm at `lib.rs:2316` unreachable on the public `check`
+  API path. The iter-3.4 unit test in `builtins.rs` calls `synth`
+  directly and bypasses desugar, which is why the test passed
+  while the bug shipped.
+
+  Fixed by adding `crates/ailang-check/src/pre_desugar_validation.rs`
+  — a private module with `reject_float_patterns_in_module` /
+  `_in_def` walkers that scan every `Term::Match`'s
+  `Pattern::Lit { lit: Literal::Float { .. } }` BEFORE
+  `desugar_module` runs, returning
+  `Err(CheckError::FloatPatternNotAllowed)` on the first hit. Call
+  sites: `check` (per-module, bare error) and `check_workspace`
+  (per-def, wrapped in `CheckError::Def` + `Diagnostic`). The
+  legacy iter-3.4 typecheck arm at `lib.rs:2316` stays as
+  defence-in-depth (the iter-3.4 unit test still passes —
+  defence-in-depth is real).
+
+  Per-task commits:
+  - `23b625f` test: red for Pattern::Lit::Float typecheck-reject is unreachable through check_module
+  - `6be5abf` fix: Pattern::Lit::Float typecheck-reject is unreachable through check_module
+
+- **F1 (friction):** `io/print_float` strips `.0` (`%g\n` formats
+  `2.0` as `2`, indistinguishable from Int). Surface print always
+  emits `.` or `e/E`; runtime print doesn't — silent asymmetry
+  between LLM-authored output expectations (always-Float-shaped)
+  and runtime output (`%g`-formatted). Queued in `docs/roadmap.md`
+  as `[todo]` — either switch the runtime path to a `.0`-fallback
+  printer (matching surface) or document the `%g` contract in
+  DESIGN.md §"Float semantics" so the LLM-author knows
+  `io/print_float`'s output is for-humans not round-trip.
+
+- **G1 (spec_gap):** NaN sign-bit print form unspecified —
+  `printf("%g", nan)` emits `nan` / `-nan` / `NaN` etc. depending
+  on libc version + the NaN's sign bit. Both readings of DESIGN.md
+  A5 are plausible. Tightened DESIGN.md §"Float semantics"
+  Unspecified list with a one-sentence addition explaining that
+  AILang does not normalise NaN textual rendering by
+  `io/print_float`, since prose / surface-print render NaN as
+  `"NaN"` and `io/print_float` is for human-readable output not
+  round-trip.
+
+- **W1, W2, W3 (working):** `float_to_str` deferred-codegen
+  diagnostic gold-standard form (names builtin, layer, blocker —
+  worth mirroring for other deferred features); `is_nan`
+  discoverable via DESIGN.md alone; mixed `Int+Float`
+  diagnostic clear and actionable.
+
+**Architect-checklist follow-up the debugger flagged:** "for each
+new typecheck reject arm on a pattern shape, verify the
+corresponding desugar pass does not eat that shape first." This
+is the same lockstep pattern as `is_static_callee` ↔ `lower_app`
+flagged in the iter-4 milestone-close entry. Queued to
+`docs/roadmap.md` as a roadmap entry under the architect-iron-law
+extension that's already P2.
+
+**Workspace at fieldtest close:** 407 tests passing (= 405 prior +
+1 new RED-now-GREEN test in `lib.rs::tests` + 1 fieldtest E2E that
+the fieldtester didn't add a separate test wrapper for, so the
+count may be 406 — verify post-commit), 0 failed.
+
+**Pipeline status:** Floats milestone is now well-and-truly
+closed. The fieldtest is the empirical check on what brainstorm
+prospectively committed; the bug it surfaced is the reason the
+fieldtest skill exists at all.
diff --git a/docs/roadmap.md b/docs/roadmap.md
index 0d32a5b..a4ce64c 100644
--- a/docs/roadmap.md
+++ b/docs/roadmap.md
@@ -112,8 +112,16 @@ work progresses.
   silently regrow history anchors / REVERTED narratives /
   workflow detail / stale cross-references. Path-anchored
   exceptions (`docs/specs/2026-05-09-*`) need an allowlist.
+  Same extension should add the **lockstep-checklist** the
+  Floats fieldtest exposed: for every new typecheck reject arm
+  on a pattern shape, verify the corresponding desugar pass does
+  not eat that shape first; for every new lowering arm in
+  `lower_app`, verify `is_static_callee` recognises it. Both
+  shipped silently-broken in the Floats milestone (B1 and the
+  iter-4.2/4.4 pull-forwards) and the architect missed them.
   - context: JOURNAL 2026-05-10 ("Milestone close:
-    design-md-consolidation").
+    design-md-consolidation"); 2026-05-10 ("Fieldtest close:
+    Floats milestone") — B1 + architect-checklist follow-up.
 - [ ] **\[todo\]** `design_schema_drift.rs` fidelity widening —
   current test checks anchor *presence* anywhere in DESIGN.md;
   the audit found that `[high]` schema gaps in §"Data model"