diff --git a/crates/ail/tests/typeclass_22b3.rs b/crates/ail/tests/typeclass_22b3.rs
index 39d3761..d6355eb 100644
--- a/crates/ail/tests/typeclass_22b3.rs
+++ b/crates/ail/tests/typeclass_22b3.rs
@@ -49,25 +49,21 @@ fn monomorphise_workspace_is_identity_on_class_free_workspace() {
     }
 }
 
-/// Property: the Task 1 skeleton's class-present branch is also a
-/// no-op. The fixture has a `Def::Class` and a `Def::Instance` (so
-/// the early-out does NOT fire) but no concrete class-method call
-/// sites yet wired through the pipeline; under the skeleton, the
-/// fall-through `Ok(ws.clone())` must preserve every module's
-/// canonical hash.
+/// Property: when a workspace has a class + instance but no concrete
+/// class-method call sites, the mono pass produces a hash-identical
+/// workspace — the early-out path is bypassed (typeclasses present)
+/// but the fixpoint loop terminates on round 1 with zero new targets,
+/// so no FnDefs are appended.
 ///
-/// NOTE: this test will need updating in Task 5 once the skeleton
-/// is replaced with the real fixpoint — at that point synth fns
-/// will be appended to the `defining_module`, breaking module-hash
-/// equality on that module by design. The test as written
-/// guarantees the Task 1 contract and catches accidental partial
-/// rewrites landed before Task 5.
+/// The fixture (`test_22b3_no_call_sites.ail.json`) declares
+/// `class Show` + `instance Show Int` with a Lam-shaped instance
+/// body, but `main` is a literal — there is no `show <x>` call at any
+/// type. Updated in Task 5 from `test_22b2_instance_present.ail.json`,
+/// which had a `show 42` call site that the real fixpoint now
+/// (correctly) materialises into `show#Int`.
 #[test]
 fn monomorphise_workspace_is_identity_when_no_concrete_call_sites() {
-    // `test_22b2_instance_present.ail.json` has `class Show` +
-    // `instance Show Int` and typechecks cleanly; reused across
-    // 22b.2 tests so its shape is stable.
-    let entry = examples_dir().join("test_22b2_instance_present.ail.json");
+    let entry = examples_dir().join("test_22b3_no_call_sites.ail.json");
     let ws = ailang_core::load_workspace(&entry).expect("load");
     let diags = ailang_check::check_workspace(&ws);
     assert!(diags.is_empty(), "fixture must typecheck: {:?}", diags);
@@ -82,14 +78,15 @@ fn monomorphise_workspace_is_identity_when_no_concrete_call_sites() {
         before.modules.keys().collect::<Vec<_>>(),
         "module set must be identical"
     );
-    // Each module hashes byte-identical (skeleton clones unchanged).
+    // Each module hashes byte-identical — no synth fns appended
+    // because no call site triggered a target.
     for (mname, m) in &ws_after.modules {
         let before_m = &before.modules[mname];
         let h_after = ailang_core::module_hash(m);
         let h_before = ailang_core::module_hash(before_m);
         assert_eq!(
             h_after, h_before,
-            "class-present module `{}` must hash-identical through Task 1 skeleton",
+            "class-present-but-no-call-site module `{}` must hash-identical",
             mname
         );
     }
@@ -366,3 +363,30 @@ fn synthesise_mono_fn_zero_arg_method_uses_body_verbatim() {
         f.body
     );
 }
+
+/// Property: when two call sites of `show` apply at the same concrete
+/// type (Int), the workspace fixpoint synthesises the matching FnDef
+/// (`show#Int`) exactly once across the whole workspace. Verifies the
+/// dedup contract — the pass must not emit one FnDef per call site.
+#[test]
+fn fixpoint_dedupes_repeated_calls_at_same_type() {
+    let entry = examples_dir().join("test_22b3_dup_call_sites.ail.json");
+    let ws = ailang_core::load_workspace(&entry).expect("load");
+    let diags = ailang_check::check_workspace(&ws);
+    assert!(diags.is_empty(), "fixture must typecheck: {:?}", diags);
+
+    let ws = ailang_check::monomorphise_workspace(&ws).expect("mono");
+
+    // Count `show#Int` fns workspace-wide.
+    let mut count = 0usize;
+    for m in ws.modules.values() {
+        for d in &m.defs {
+            if let ailang_core::ast::Def::Fn(f) = d {
+                if f.name == "show#Int" {
+                    count += 1;
+                }
+            }
+        }
+    }
+    assert_eq!(count, 1, "exactly one show#Int across the workspace");
+}
diff --git a/crates/ailang-check/src/mono.rs b/crates/ailang-check/src/mono.rs
index 34d593b..9a16276 100644
--- a/crates/ailang-check/src/mono.rs
+++ b/crates/ailang-check/src/mono.rs
@@ -74,10 +74,136 @@ pub fn monomorphise_workspace(ws: &Workspace) -> Result<Workspace> {
         return Ok(ws.clone());
     }
 
-    // Skeleton in Task 1: even with classes present, return the
-    // workspace clone unchanged. Subsequent tasks fill in collection,
-    // synthesis, and rewriting.
-    Ok(ws.clone())
+    // Take ownership of a mutable workspace clone; the pass
+    // appends synthesised defs to per-module def lists.
+    let mut ws_owned: Workspace = ws.clone();
+    let env = build_workspace_env(&ws_owned);
+
+    // Dedup set: every (class, method, type-hash) we have already
+    // synthesised. Once a key is here, future collection rounds
+    // skip it.
+    let mut synthesised: BTreeSet<(String, String, String)> = BTreeSet::new();
+
+    // Fixpoint: keep collecting until a round adds nothing new.
+    // Each round walks every fn body in every module — including
+    // bodies appended by the previous round, which is what makes
+    // the loop close on chained class-method calls (e.g.
+    // `Eq.ne x y = not (eq x y)`).
+    loop {
+        let new_targets = collect_targets_workspace_wide(&ws_owned, &env)?;
+        // Dedup within a round (multiple call sites of `show` at
+        // the same type produce N copies of the same MonoTarget)
+        // AND across rounds (already-synthesised keys filtered out).
+        // Stable iteration order — preserve first-seen target so
+        // any later debugging round-trips to a deterministic output.
+        let mut seen_this_round: BTreeSet<(String, String, String)> = BTreeSet::new();
+        let mut new: Vec<MonoTarget> = Vec::new();
+        for t in new_targets {
+            let k = mono_target_key(&t);
+            if synthesised.contains(&k) || !seen_this_round.insert(k) {
+                continue;
+            }
+            new.push(t);
+        }
+        if new.is_empty() {
+            break;
+        }
+
+        // Synthesise each new target; append its FnDef to the
+        // target's `defining_module`. Mark the key as synthesised
+        // so the next round won't re-collect.
+        //
+        // Iter 22b.3 uses ws_owned.registry as the source of
+        // truth for ClassDef + InstanceDef lookups. Both come
+        // from the un-modified workspace registry — synthesis
+        // never mutates the registry.
+        let class_index = build_class_index(&ws_owned);
+        for t in &new {
+            let key = mono_target_key(t);
+            let registry_key = (t.class.clone(), ailang_core::canonical::type_hash(&t.type_));
+            let entry = ws_owned
+                .registry
+                .entries
+                .get(&registry_key)
+                .ok_or_else(|| {
+                    crate::CheckError::Internal(format!(
+                        "monomorphise_workspace: target `{} {}` has no registry entry",
+                        t.class,
+                        ailang_core::pretty::type_to_string(&t.type_),
+                    ))
+                })?;
+            let class_def = class_index.get(&t.class).ok_or_else(|| {
+                crate::CheckError::Internal(format!(
+                    "monomorphise_workspace: class `{}` not found",
+                    t.class
+                ))
+            })?;
+            let f = synthesise_mono_fn(t, class_def, &entry.instance)?;
+            let target_module = ws_owned
+                .modules
+                .get_mut(&t.defining_module)
+                .ok_or_else(|| {
+                    crate::CheckError::Internal(format!(
+                        "monomorphise_workspace: defining module `{}` missing",
+                        t.defining_module
+                    ))
+                })?;
+            target_module.defs.push(Def::Fn(f));
+            synthesised.insert(key);
+        }
+    }
+
+    // Task 6 will splice the call-site rewrite here.
+    Ok(ws_owned)
+}
+
+/// Iter 22b.3: walk every fn / const body in the workspace,
+/// returning the union of [`collect_mono_targets`] outputs. Const
+/// bodies are wrapped in a synthetic zero-arg `FnDef` for the
+/// collection call — the residual gathering only depends on body
+/// shape, so the wrapping is harmless.
+fn collect_targets_workspace_wide(
+    ws: &Workspace,
+    env: &crate::Env,
+) -> Result<Vec<MonoTarget>> {
+    let mut out: Vec<MonoTarget> = Vec::new();
+    for (mname, m) in &ws.modules {
+        for d in &m.defs {
+            match d {
+                Def::Fn(f) => {
+                    out.extend(collect_mono_targets(f, mname, env)?);
+                }
+                Def::Const(c) => {
+                    let pseudo = AstFnDef {
+                        name: c.name.clone(),
+                        ty: c.ty.clone(),
+                        params: Vec::new(),
+                        body: c.value.clone(),
+                        doc: None,
+                        suppress: Vec::new(),
+                    };
+                    out.extend(collect_mono_targets(&pseudo, mname, env)?);
+                }
+                _ => {}
+            }
+        }
+    }
+    Ok(out)
+}
+
+/// Iter 22b.3: workspace-wide `class-name -> ClassDef` index.
+/// Used by the fixpoint to look up the matching class definition
+/// when synthesising a fn.
+fn build_class_index(ws: &Workspace) -> BTreeMap<String, ClassDef> {
+    let mut idx = BTreeMap::new();
+    for m in ws.modules.values() {
+        for d in &m.defs {
+            if let Def::Class(c) = d {
+                idx.insert(c.name.clone(), c.clone());
+            }
+        }
+    }
+    idx
 }
 
 /// Iter 22b.3: returns `true` iff any module in `ws` declares at
diff --git a/crates/ailang-surface/tests/round_trip.rs b/crates/ailang-surface/tests/round_trip.rs
index 91922d9..ebd98ce 100644
--- a/crates/ailang-surface/tests/round_trip.rs
+++ b/crates/ailang-surface/tests/round_trip.rs
@@ -32,17 +32,19 @@ fn list_json_fixtures() -> Vec<PathBuf> {
             p.file_name()
                 .and_then(|n| n.to_str())
                 .map(|n| {
-                    // Iter 22b.1 / 22b.2: the `test_22b1_*` and
-                    // `test_22b2_*` fixtures exercise class/instance
-                    // defs at the workspace-load level, but the surface
-                    // (Form-B) parser/printer arms for those nodes are
-                    // deferred to 22b.4. Until that ships, including
-                    // these fixtures in the round-trip gate would block
-                    // 22b on a property the schema floor does not yet
+                    // Iter 22b.1 / 22b.2 / 22b.3: the `test_22b1_*`,
+                    // `test_22b2_*`, and `test_22b3_*` fixtures exercise
+                    // class/instance defs at the workspace-load and
+                    // monomorphisation levels, but the surface (Form-B)
+                    // parser/printer arms for those nodes are deferred
+                    // to 22b.4. Until that ships, including these
+                    // fixtures in the round-trip gate would block 22b
+                    // on a property the schema floor does not yet
                     // promise. Skip them.
                     n.ends_with(".ail.json")
                         && !n.starts_with("test_22b1_")
                         && !n.starts_with("test_22b2_")
+                        && !n.starts_with("test_22b3_")
                 })
                 .unwrap_or(false)
         })
diff --git a/examples/test_22b3_dup_call_sites.ail.json b/examples/test_22b3_dup_call_sites.ail.json
new file mode 100644
index 0000000..63a44444
--- /dev/null
+++ b/examples/test_22b3_dup_call_sites.ail.json
@@ -0,0 +1,55 @@
+{
+  "schema": "ailang/v0",
+  "name": "test_22b3_dup_call_sites",
+  "imports": [],
+  "defs": [
+    {
+      "kind": "class", "name": "Show", "param": "a",
+      "methods": [{
+        "name": "show",
+        "type": {
+          "k": "fn", "params": [{ "k": "var", "name": "a" }],
+          "ret": { "k": "con", "name": "Str" }, "effects": []
+        }
+      }]
+    },
+    {
+      "kind": "instance",
+      "class": "Show",
+      "type": { "k": "con", "name": "Int" },
+      "methods": [{
+        "name": "show",
+        "body": {
+          "t": "lam",
+          "params": ["x"],
+          "paramTypes": [{ "k": "var", "name": "a" }],
+          "retType": { "k": "con", "name": "Str" },
+          "body": { "t": "lit", "lit": { "kind": "str", "value": "n" } }
+        }
+      }]
+    },
+    {
+      "kind": "fn",
+      "name": "main",
+      "type": {
+        "k": "fn", "params": [], "ret": { "k": "con", "name": "Str" },
+        "effects": []
+      },
+      "params": [],
+      "body": {
+        "t": "let",
+        "name": "_a",
+        "value": {
+          "t": "app",
+          "fn": { "t": "var", "name": "show" },
+          "args": [{ "t": "lit", "lit": { "kind": "int", "value": 5 } }]
+        },
+        "body": {
+          "t": "app",
+          "fn": { "t": "var", "name": "show" },
+          "args": [{ "t": "lit", "lit": { "kind": "int", "value": 7 } }]
+        }
+      }
+    }
+  ]
+}
diff --git a/examples/test_22b3_no_call_sites.ail.json b/examples/test_22b3_no_call_sites.ail.json
new file mode 100644
index 0000000..b72d73f
--- /dev/null
+++ b/examples/test_22b3_no_call_sites.ail.json
@@ -0,0 +1,42 @@
+{
+  "schema": "ailang/v0",
+  "name": "test_22b3_no_call_sites",
+  "imports": [],
+  "defs": [
+    {
+      "kind": "class", "name": "Show", "param": "a",
+      "methods": [{
+        "name": "show",
+        "type": {
+          "k": "fn", "params": [{ "k": "var", "name": "a" }],
+          "ret": { "k": "con", "name": "Str" }, "effects": []
+        }
+      }]
+    },
+    {
+      "kind": "instance",
+      "class": "Show",
+      "type": { "k": "con", "name": "Int" },
+      "methods": [{
+        "name": "show",
+        "body": {
+          "t": "lam",
+          "params": ["x"],
+          "paramTypes": [{ "k": "var", "name": "a" }],
+          "retType": { "k": "con", "name": "Str" },
+          "body": { "t": "lit", "lit": { "kind": "str", "value": "n" } }
+        }
+      }]
+    },
+    {
+      "kind": "fn",
+      "name": "main",
+      "type": {
+        "k": "fn", "params": [], "ret": { "k": "con", "name": "Str" },
+        "effects": []
+      },
+      "params": [],
+      "body": { "t": "lit", "lit": { "kind": "str", "value": "no-call" } }
+    }
+  ]
+}