diff --git a/src/graph/llm.rs b/src/graph/llm.rs
index 4be1ef2..a409469 100644
--- a/src/graph/llm.rs
+++ b/src/graph/llm.rs
@@ -262,7 +262,7 @@ async fn run_with_retries(
 
 /// Whether `turn` (0-based) is the final turn the node's cap allows. A cap of 0 means no cap.
 pub(crate) fn is_last_turn(turn: u32, max_iterations: u32) -> bool {
-    max_iterations > 0 && turn + 1 == max_iterations
+    max_iterations > 0 && turn == max_iterations - 1
 }
 
 async fn run_chat_loop(
@@ -768,6 +768,12 @@ mod tests {
         assert!(!is_last_turn(u32::MAX, 0));
     }
 
+    #[test]
+    fn is_last_turn_at_u32_max_does_not_overflow() {
+        assert!(is_last_turn(u32::MAX - 1, u32::MAX));
+        assert!(!is_last_turn(u32::MAX, u32::MAX));
+    }
+
     /// The turn-top abort check runs before any client is created, so an
     /// already-aborted graph never issues a model call and the node fails
     /// with the abort reason rather than a connection error.
diff --git a/src/graph/map.rs b/src/graph/map.rs
index 7c15f9d..16651a5 100644
--- a/src/graph/map.rs
+++ b/src/graph/map.rs
@@ -1,5 +1,5 @@
 use super::executor::{PeerRetireGuard, StepContext, StepResult, TaskCancelGuard, step};
-use super::state::StateManager;
+use super::state::{StateManager, is_lone_template};
 use super::types::{ConcurrencyCap, Graph, MapNode, Node, NodeType};
 use super::validator::branch_subgraph;
 use crate::config::{RenderMode, RequestContext};
@@ -324,7 +324,8 @@ fn wants_peer_identity(node: &Node) -> bool {
 /// accepted; anything else is the author's bug and surfaces as an error
 /// rather than being clamped. A literal 0 is rejected the same way, so a
 /// graph loaded with validation off fails here instead of silently running
-/// one item at a time. Only the absent-cap default is clamped.
+/// one item at a time, and a string that is not exactly one `{{key}}` is
+/// rejected before interpolation for the same reason. Only the absent-cap default is clamped.
 fn resolve_max_concurrency(
     node: &MapNode,
     state: &StateManager,
@@ -340,6 +341,13 @@ fn resolve_max_concurrency(
         Some(ConcurrencyCap::Template(t)) => t,
     };
 
+    if !is_lone_template(template) {
+        bail!(
+            "map node '{node_id}': max_concurrency \"{template}\" is a string but not a template; \
+             write an integer or exactly one `{{{{key}}}}` with nothing around it"
+        );
+    }
+
     let value = state
         .interpolate_raw(template)
         .with_context(|| format!("map node '{node_id}': evaluating `max_concurrency` template"))?;
@@ -662,6 +670,28 @@ mod tests {
         );
         assert!(chain.contains("budget"), "{chain}");
     }
+
+    #[test]
+    fn resolve_max_concurrency_rejects_non_template_string() {
+        let state = state_with("budget", Value::from(3));
+        let cap = Some(ConcurrencyCap::Template("4".into()));
+        let msg = resolve(cap, &state).unwrap_err().to_string();
+        assert!(
+            msg.contains(
+                "is a string but not a template; write an integer or exactly one `{{key}}` \
+                 with nothing around it"
+            ),
+            "{msg}"
+        );
+        assert!(msg.contains("map node 'm': max_concurrency \"4\""), "{msg}");
+    }
+
+    #[test]
+    fn resolve_max_concurrency_accepts_padded_template() {
+        let state = state_with("budget", Value::from(3));
+        let cap = Some(ConcurrencyCap::Template("  {{budget}}  ".into()));
+        assert_eq!(resolve(cap, &state).unwrap(), 3);
+    }
 }
 
 #[cfg(test)]
diff --git a/src/graph/state.rs b/src/graph/state.rs
index 824a8fe..6a1c21d 100644
--- a/src/graph/state.rs
+++ b/src/graph/state.rs
@@ -320,14 +320,24 @@ pub(super) fn template_root_keys(template: &str) -> Vec<String> {
         .collect()
 }
 
-// Whether `s` is exactly one `{{key}}` reference and nothing else, after the
-// same trim `interpolate_raw` applies, so this accepts exactly the strings the
-// runtime resolves as a pure reference.
+// Whether `s` is exactly one `{{key}}` reference and nothing else (after the
+// same trim `interpolate_raw` applies) whose path parses with the grammar
+// `get_nested_value` uses, so this accepts exactly the strings the runtime
+// can resolve as a pure reference.
 pub(super) fn is_lone_template(s: &str) -> bool {
     let s = s.trim();
-    TEMPLATE_VAR_RE
-        .find(s)
-        .is_ok_and(|m| m.is_some_and(|m| m.start() == 0 && m.end() == s.len()))
+    let Ok(Some(m)) = TEMPLATE_VAR_RE.captures(s) else {
+        return false;
+    };
+    let whole = m.get(0).expect("group 0 always present");
+    if whole.start() != 0 || whole.end() != s.len() {
+        return false;
+    }
+    let path = m.get(1).expect("template regex has one group").as_str();
+    let mut parts = path.split('.');
+    let first = parts.next().and_then(split_indices);
+    first.is_some_and(|(name, _)| !name.is_empty())
+        && parts.all(|part| split_indices(part).is_some())
 }
 
 fn value_to_string(value: &Value) -> String {
@@ -973,6 +983,28 @@ mod tests {
         }
     }
 
+    #[test]
+    fn is_lone_template_matches_runtime_path_grammar() {
+        for accepted in [
+            "{{a.b[0][1].c}}",
+            "{{a[0][1]}}",
+            "{{a.}}",
+            "{{a..b}}",
+            "{{a.[0]}}",
+        ] {
+            assert!(
+                is_lone_template(accepted),
+                "{accepted:?} resolves at run time and must be accepted"
+            );
+        }
+        for rejected in ["{{limits[foo]}}", "{{a[]}}", "{{a[0}}", "{{.a}}"] {
+            assert!(
+                !is_lone_template(rejected),
+                "{rejected:?} never resolves at run time and must be rejected"
+            );
+        }
+    }
+
     #[test]
     fn interpolate_raw_inner_spaces_treated_as_mixed() {
         let manager = manager_with(&[("k", json!("v"))]);
diff --git a/src/graph/validator.rs b/src/graph/validator.rs
index c6e5097..c19c855 100644
--- a/src/graph/validator.rs
+++ b/src/graph/validator.rs
@@ -3647,6 +3647,27 @@ mod tests {
         }
     }
 
+    #[test]
+    fn map_max_concurrency_non_numeric_index_errors() {
+        let map = map_with_cap("m", "br", Some("end"), "{{limits[foo]}}");
+        let branch = llm_with_state_updates("br", &[("output", "{{output}}")], None);
+        let graph = graph_with(
+            vec![("m", map), ("br", branch), ("end", end_node("end"))],
+            "m",
+        );
+
+        let result = validator().validate(&graph);
+
+        assert!(
+            result.errors.iter().any(|e| e.message
+                == "map node's `max_concurrency` is a string but not a template; write \
+                    an integer or exactly one `{{key}}` with nothing around it"
+                && e.node_id.as_deref() == Some("m")),
+            "a non-numeric index can never resolve and must fail at load: {:?}",
+            result.errors
+        );
+    }
+
     #[test]
     fn map_max_concurrency_lone_template_forms_pass() {
         for cap in ["{{budget}}", "{{cfg.limits[0]}}", "  {{budget}}  "] {