diff --git a/crates/rhei-cli/src/cli/agent_spawn_records.rs b/crates/rhei-cli/src/cli/agent_spawn_records.rs
index e9059c01..fac7d568 100644
--- a/crates/rhei-cli/src/cli/agent_spawn_records.rs
+++ b/crates/rhei-cli/src/cli/agent_spawn_records.rs
@@ -155,18 +155,31 @@ struct SpawnPlan {
 }
 
 impl SpawnPlan {
-    /// Whether this visit's budget is already spent, so the spawn must not
-    /// happen at all. §FS-rhei-agents.3.2.3
-    fn budget_spent(&self, budget: u64) -> bool {
-        self.charged >= budget
+    /// The budget spent, if this visit's is already gone and the spawn must
+    /// not happen at all. A poll state's own bound never spends here — its
+    /// exhaustion is `poll.max_attempts`, checked elsewhere. §FS-rhei-agents.3.2.3
+    fn budget_spent(&self, budget: AttemptBudget) -> Option<u64> {
+        match budget {
+            AttemptBudget::Visit(budget) if self.charged >= budget => Some(budget),
+            AttemptBudget::Visit(_) | AttemptBudget::Poll { .. } => None,
+        }
     }
 
     /// The line the run prints beside `Log:` when it is retrying rather than
     /// starting, naming the attempt, the budget it comes out of, what ended the
     /// attempt before it, and where that attempt's transcript is.
     // §FS-rhei-agents.3.2.1
-    fn respawn_note(&self, task_id: &str, state_name: &str, budget: u64) -> Option<String> {
+    fn respawn_note(
+        &self,
+        task_id: &str,
+        state_name: &str,
+        budget: AttemptBudget,
+    ) -> Option<String> {
         let previous = self.previous.as_ref()?;
+        let budget = match budget {
+            AttemptBudget::Visit(budget) => budget.to_string(),
+            AttemptBudget::Poll { max_attempts } => format!("{max_attempts} (poll.max_attempts)"),
+        };
         Some(format!(
             "  Re-spawning Task {task_id} in state '{state_name}': attempt {} of {budget}; \
              the previous attempt {} (previous log: {}).",
@@ -181,9 +194,13 @@ impl SpawnPlan {
     /// Asked *before* the spawn and answered about the state of the visit after
     /// it, because the message that needs it is printed when that spawn has
     /// already finished. An interrupted spawn never reaches that message, so the
-    /// charge this predicts is the charge that happens.
+    /// charge this predicts is the charge that happens. A poll state's own
+    /// exhaustion rule is its only bound, so it always has attempts left here.
     // §FS-rhei-agents.3.2.1 §FS-rhei-agents.3.2.3
-    fn retry_outlook(&self, budget: u64) -> RetryOutlook {
+    fn retry_outlook(&self, budget: AttemptBudget) -> RetryOutlook {
+        let AttemptBudget::Visit(budget) = budget else {
+            return RetryOutlook::AttemptsLeft;
+        };
         if self.charged.saturating_add(1) < budget {
             RetryOutlook::AttemptsLeft
         } else {
@@ -362,6 +379,21 @@ fn newest_spawn_record_for_state(
     newest.map(|(_, record)| record)
 }
 
+/// Which rule bounds one visit's spawns, and by how much. `Poll` is carried
+/// only to be named in the respawn note, never as a second bound alongside
+/// the poll's own exhaustion rule.
+// §FS-rhei-agents.3.2.1 §FS-rhei-agents.3.2.3
+#[derive(Clone, Copy)]
+enum AttemptBudget {
+    /// The state's own `attempts:`, `defaults.attempts`, or the built-in.
+    /// `SpawnPlan::budget_spent` and `SpawnPlan::retry_outlook` bound spawns
+    /// at this count.
+    Visit(u64),
+    /// A poll state's `poll.max_attempts`. Never bounds a spawn — the poll's
+    /// own exhaustion path (`ready_auto_advance.rs`) does that.
+    Poll { max_attempts: u64 },
+}
+
 /// How many spawns one visit to this state may have.
 ///
 /// The chain a timeout resolves through, one level shorter because a budget has
@@ -373,20 +405,22 @@ fn newest_spawn_record_for_state(
 /// does, and it already carries its own bound in `poll.max_attempts`; a second
 /// bound over the same spawns would stop the loop before its own cap and
 /// silently change what the machine's author declared.
-// §FS-rhei-agents.3.2.3 §FS-rhei-agents.7.1 §FS-rhei-states.2
+// §FS-rhei-agents.3.2.1 §FS-rhei-agents.3.2.3 §FS-rhei-agents.7.1 §FS-rhei-states.2
 fn resolve_attempt_budget(
     state_def: Option<&rhei_validator::StateDef>,
     settings: &RheiSettings,
-) -> u64 {
-    if state_def.is_some_and(|def| def.poll.is_some()) {
-        return u64::MAX;
+) -> AttemptBudget {
+    if let Some(max_attempts) = state_def.and_then(|def| def.poll.as_ref()) {
+        return AttemptBudget::Poll { max_attempts: u64::from(max_attempts.max_attempts) };
     }
-    state_def
-        .and_then(|def| def.attempts)
-        .or(settings.defaults.attempts)
-        .map(u64::from)
-        .unwrap_or(DEFAULT_ATTEMPT_BUDGET)
-        .max(1)
+    AttemptBudget::Visit(
+        state_def
+            .and_then(|def| def.attempts)
+            .or(settings.defaults.attempts)
+            .map(u64::from)
+            .unwrap_or(DEFAULT_ATTEMPT_BUDGET)
+            .max(1),
+    )
 }
 
 /// A plan for a unit test that only cares about the transcript a spawn writes:
diff --git a/crates/rhei-cli/src/cli/run_agent_sequential.rs b/crates/rhei-cli/src/cli/run_agent_sequential.rs
index c914ffcb..859ff3a3 100644
--- a/crates/rhei-cli/src/cli/run_agent_sequential.rs
+++ b/crates/rhei-cli/src/cli/run_agent_sequential.rs
@@ -128,7 +128,7 @@ fn run_sequential_agent_invocation(
         resolved_agent_log_suffix(resolved, Some(visit_count)).as_deref(),
     );
     let budget = resolve_attempt_budget(machine.states.get(current_state), settings);
-    if plan.budget_spent(budget) {
+    if let Some(spent_budget) = plan.budget_spent(budget) {
         // The same stall step 5 gives any unmet completion condition: the ticket
         // keeps its state, no transition fires, and the pass moves on.
         // §FS-rhei-run.3 §FS-rhei-agents.3.2.3
@@ -146,7 +146,7 @@ fn run_sequential_agent_invocation(
             budget_spent_halt_line(
                 task_id_str,
                 current_state,
-                budget,
+                spent_budget,
                 &completion_debt_label(&owed)
             )
         );
diff --git a/crates/rhei-cli/src/cli/run_parallel_program_spawn.rs b/crates/rhei-cli/src/cli/run_parallel_program_spawn.rs
index e8a6743a..c8645342 100644
--- a/crates/rhei-cli/src/cli/run_parallel_program_spawn.rs
+++ b/crates/rhei-cli/src/cli/run_parallel_program_spawn.rs
@@ -46,7 +46,7 @@ fn spawn_parallel_program_work_item(
     );
     let budget =
         resolve_attempt_budget(machine.states.get(item.current_state.as_str()), settings);
-    if plan.budget_spent(budget) {
+    if let Some(spent_budget) = plan.budget_spent(budget) {
         let owed = collect_missing_required_outputs(
             workspace_root,
             &task_workspace_root,
@@ -63,7 +63,7 @@ fn spawn_parallel_program_work_item(
             budget_spent_halt_line(
                 &item.task_id_str,
                 &item.current_state,
-                budget,
+                spent_budget,
                 &completion_debt_label(&owed),
             ),
         );
diff --git a/crates/rhei-cli/src/cli/run_parallel_spawn.rs b/crates/rhei-cli/src/cli/run_parallel_spawn.rs
index 75a2d9a1..f3a9e40f 100644
--- a/crates/rhei-cli/src/cli/run_parallel_spawn.rs
+++ b/crates/rhei-cli/src/cli/run_parallel_spawn.rs
@@ -74,7 +74,7 @@ fn spawn_parallel_agent_work_item(
     );
     let budget =
         resolve_attempt_budget(machine.states.get(item.current_state.as_str()), settings);
-    if plan.budget_spent(budget) {
+    if let Some(spent_budget) = plan.budget_spent(budget) {
         // `Skipped` is the pool's stall: the scheduler records it in
         // `stalled_tasks`, so the ticket keeps its state and is out of the
         // running for the rest of the run. §FS-rhei-run.3 §FS-rhei-agents.3.2.3
@@ -93,7 +93,7 @@ fn spawn_parallel_agent_work_item(
             budget_spent_halt_line(
                 &item.task_id_str,
                 &item.current_state,
-                budget,
+                spent_budget,
                 &completion_debt_label(&owed),
             ),
         );
diff --git a/crates/rhei-cli/src/cli/run_program_sequential.rs b/crates/rhei-cli/src/cli/run_program_sequential.rs
index f0b28ea0..24909950 100644
--- a/crates/rhei-cli/src/cli/run_program_sequential.rs
+++ b/crates/rhei-cli/src/cli/run_program_sequential.rs
@@ -79,7 +79,7 @@ fn run_sequential_program_work_items(
             None,
         );
         let budget = resolve_attempt_budget(machine.states.get(current_state.as_str()), settings);
-        if plan.budget_spent(budget) {
+        if let Some(spent_budget) = plan.budget_spent(budget) {
             let owed = collect_missing_required_outputs(
                 workspace_root,
                 &task_workspace_root,
@@ -94,7 +94,7 @@ fn run_sequential_program_work_items(
                 budget_spent_halt_line(
                     task_id_str,
                     current_state,
-                    budget,
+                    spent_budget,
                     &completion_debt_label(&owed)
                 )
             );
diff --git a/crates/rhei-cli/src/cli/tests_spawn_records.rs b/crates/rhei-cli/src/cli/tests_spawn_records.rs
index 82fe604f..e2c3d5a4 100644
--- a/crates/rhei-cli/src/cli/tests_spawn_records.rs
+++ b/crates/rhei-cli/src/cli/tests_spawn_records.rs
@@ -70,8 +70,9 @@ mod spawn_records {
         ended(&first, "exited", 0);
         let second = plan_for(dir.path());
         ended(&second, "exited", 0);
-        assert!(
-            plan_for(dir.path()).budget_spent(2),
+        assert_eq!(
+            plan_for(dir.path()).budget_spent(AttemptBudget::Visit(2)),
+            Some(2),
             "two recorded attempts spend a budget of two"
         );
 
@@ -82,7 +83,10 @@ mod spawn_records {
         assert_eq!(after.attempt, 1, "a fresh entry is not a third attempt at the last one");
         assert!(after.previous.is_none(), "and has nothing to narrate as a retry");
         assert!(after.log.ends_with("task-plan.1-implement.log"));
-        assert!(!after.budget_spent(2), "the budget came back with the visit");
+        assert!(
+            after.budget_spent(AttemptBudget::Visit(2)).is_none(),
+            "the budget came back with the visit"
+        );
     }
 
     /// An interrupted invocation keeps its transcript — it ran — but the run
@@ -98,15 +102,25 @@ mod spawn_records {
         ended(&first, "interrupted", -1);
         let second = plan_for(dir.path());
         assert_eq!(second.attempt, 2, "the interrupted transcript is kept beside the retry");
-        assert!(!second.budget_spent(1), "but it did not spend the visit's only attempt");
+        assert!(
+            second.budget_spent(AttemptBudget::Visit(1)).is_none(),
+            "but it did not spend the visit's only attempt"
+        );
 
         ended(&second, "interrupted", -1);
         let third = plan_for(dir.path());
-        assert!(!third.budget_spent(1), "and neither did the next interruption");
+        assert!(
+            third.budget_spent(AttemptBudget::Visit(1)).is_none(),
+            "and neither did the next interruption"
+        );
 
         ended(&third, "timed out", -1);
         let fourth = plan_for(dir.path());
-        assert!(fourth.budget_spent(1), "a timeout is the ticket's own attempt, and spends it");
+        assert_eq!(
+            fourth.budget_spent(AttemptBudget::Visit(1)),
+            Some(1),
+            "a timeout is the ticket's own attempt, and spends it"
+        );
         assert_eq!(
             fourth.previous.as_ref().map(SpawnRecord::ending_sentence).as_deref(),
             Some("timed out after 1s")
diff --git a/crates/rhei-cli/tests/integration_markdown_plans.rs b/crates/rhei-cli/tests/integration_markdown_plans.rs
index d4ce96af..ef87de68 100644
--- a/crates/rhei-cli/tests/integration_markdown_plans.rs
+++ b/crates/rhei-cli/tests/integration_markdown_plans.rs
@@ -8,6 +8,7 @@ include!("integration_markdown_plans/callbacks_execution.rs");
 include!("integration_markdown_plans/callbacks_redirect_context.rs");
 include!("integration_markdown_plans/run_basic.rs");
 include!("integration_markdown_plans/run_programs_callbacks.rs");
+include!("integration_markdown_plans/run_poll_respawn_budget.rs");
 include!("integration_markdown_plans/run_agent_regressions.rs");
 include!("integration_markdown_plans/release.rs");
 include!("integration_markdown_plans/reset.rs");
diff --git a/crates/rhei-cli/tests/integration_markdown_plans/run_poll_respawn_budget.rs b/crates/rhei-cli/tests/integration_markdown_plans/run_poll_respawn_budget.rs
new file mode 100644
index 00000000..87750311
--- /dev/null
+++ b/crates/rhei-cli/tests/integration_markdown_plans/run_poll_respawn_budget.rs
@@ -0,0 +1,71 @@
+// §FS-rhei-agents.3.2.1: a poll state's re-spawn note names `poll.max_attempts`,
+// not the internal sentinel that marks it exempt from the visit budget.
+
+#[test]
+fn run_poll_respawn_note_names_poll_max_attempts_not_the_sentinel() {
+    let dir = unique_temp_dir("run-poll-respawn-budget");
+    let script = write_python_agent(
+        &dir,
+        "poll.py",
+        r#"append(pathlib.Path('runtime') / 'attempts.txt', 'attempt\n')
+sys.exit(75)
+"#,
+    );
+    let machine = format!(
+        r#"name: run-poll-respawn-budget-test
+version: 1
+states:
+  waiting:
+    description: Poll until attempts are exhausted
+    program:
+      command: {command}
+    poll:
+      interval: 0s
+      max_attempts: 3
+  exhausted:
+    description: Polling exhausted
+    final: true
+transitions:
+  - from: waiting
+    to: waiting
+    exit_code: 75
+  - from: waiting
+    to: exhausted
+    exit_code: 75
+"#,
+        command = fixture_command(&script)
+    );
+    let plan = r#"# Rhei: Poll Respawn Budget
+
+## Tasks
+
+### Task 1: Wait for external status
+**State:** waiting
+"#;
+
+    let plan_path = write_fixture_file(&dir, "plan.rhei.md", plan);
+    let machine_path = write_fixture_file(&dir, "states.yaml", &machine);
+
+    let result = run_run_command(&plan_path, &machine_path, &["--no-callbacks"]);
+    assert!(
+        result.status.success(),
+        "poll run should route to exhaustion after three attempts\nstdout:\n{}\nstderr:\n{}",
+        result.stdout,
+        result.stderr
+    );
+    assert!(
+        result.stdout.contains("attempt 2 of 3 (poll.max_attempts)"),
+        "respawn note should name poll.max_attempts\nstdout:\n{}",
+        result.stdout
+    );
+    assert!(
+        result.stdout.contains("attempt 3 of 3 (poll.max_attempts)"),
+        "respawn note should name poll.max_attempts\nstdout:\n{}",
+        result.stdout
+    );
+    assert!(
+        !result.stdout.contains("18446744073709551615"),
+        "respawn note must never print the internal exempt sentinel\nstdout:\n{}",
+        result.stdout
+    );
+}
diff --git a/docs/changelog.md b/docs/changelog.md
index 793decb9..8b571377 100644
--- a/docs/changelog.md
+++ b/docs/changelog.md
@@ -2,6 +2,13 @@
 
 ## Unreleased
 
+- **The re-spawn note on a poll state names its own `poll.max_attempts`
+  instead of an internal sentinel.** A poll state is exempt from the visit
+  attempt budget — `poll.max_attempts` already bounds it — and that exemption
+  was encoded internally as `u64::MAX`, which `rhei run` then printed verbatim:
+  `attempt 4 of 18446744073709551615`. The exemption was correct; only the
+  rendering was wrong. The note now reads `attempt 4 of 96 (poll.max_attempts)`
+  for a poll state, and is unchanged for every other state. (PR #119)
 - **The root `CHANGELOG.md` no longer claims the release maintains it.** It
   opened by saying this file's `Unreleased` section is what "release automation
   promotes into a numbered section here at release time", citing
diff --git a/docs/functional-spec/rhei-agents.spec.md b/docs/functional-spec/rhei-agents.spec.md
index 3d24bc5b..a0245b07 100644
--- a/docs/functional-spec/rhei-agents.spec.md
+++ b/docs/functional-spec/rhei-agents.spec.md
@@ -840,7 +840,12 @@ Under `orchestrator` authority, `rhei run`:
      previous attempt {ending} (previous log: {path})` — one line, naming the
      attempt being spent, the budget it comes out of, and the transcript it is
      retrying, so a re-spawn is not read as a state being started for the first
-     time. `{ending}` is read from that attempt's spawn record (§8.4) and says
+     time. On a poll state (§FS-rhei-states.2) the budget named is the state's
+     own `poll.max_attempts`, and the line says which mechanism it is:
+     `attempt {n} of {max_attempts} (poll.max_attempts)` — that is the bound
+     that actually applies, since §3.2.3 exempts a poll state from `attempts:`.
+     The engine never prints its internal "no budget applies" sentinel as a
+     count. `{ending}` is read from that attempt's spawn record (§8.4) and says
      what actually happened to it — `timed out after 30m`, `was interrupted by
      a run shutdown`, `exited 3`, or `exited 0 without meeting this state's
      completion condition`. The engine never reports one ending as another: a
@@ -937,7 +942,9 @@ that makes it a visit.
 A **poll state** (§FS-rhei-states.2) is exempt from the budget. Re-spawning
 without moving is what a poll state is for, and it already declares its own
 bound in `poll.max_attempts`; a second bound over the same spawns would end the
-loop earlier than the machine's author said it should.
+loop earlier than the machine's author said it should. The re-spawn note of
+§3.2.1 still names a budget on a poll state — `poll.max_attempts` itself, not
+this exemption's internal encoding of "no budget applies here".
 
 ## 4. Environment Variables