diff --git a/frontend/src/leftoverMapAxisBadge.ts b/frontend/src/leftoverMapAxisBadge.ts
index 4a00d425f..84941caa9 100644
--- a/frontend/src/leftoverMapAxisBadge.ts
+++ b/frontend/src/leftoverMapAxisBadge.ts
@@ -13,6 +13,9 @@ export const LEFTOVER_MAP_AXIS_BADGE_SINGULAR = "leftover axis {axis} σ {value}
 
 export const LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY = "leftover axis {axis} σ {value}";
 
+export const LEFTOVER_MAP_AXIS_TICK_SINGULAR =
+  "leftover axis {axis} tick {value} σ {singular}";
+
 export type LeftoverMapAxisBadge = {
   template: string;
   values: Record<string, string | number>;
@@ -70,3 +73,19 @@ export function leftoverMapAxisBadge(
     values: { axis: axis.axis_index, value: singular, share },
   };
 }
+
+/** Project finite persisted σ onto one report-axis tick without inventing share evidence. */
+export function leftoverMapAxisTickBadge(
+  axisIndex: number,
+  tickLabel: string,
+  leftoverSingular: number | null | undefined,
+): LeftoverMapAxisBadge | null {
+  const singular = formatLeftoverMapPlotAxisSingular(leftoverSingular);
+  if (singular === null) {
+    return null;
+  }
+  return {
+    template: LEFTOVER_MAP_AXIS_TICK_SINGULAR,
+    values: { axis: axisIndex, value: tickLabel, singular },
+  };
+}
diff --git a/tests/test_leftover_axis_tick_singular_contract.py b/tests/test_leftover_axis_tick_singular_contract.py
new file mode 100644
index 000000000..e13c8f657
--- /dev/null
+++ b/tests/test_leftover_axis_tick_singular_contract.py
@@ -0,0 +1,27 @@
+"""Executable contract for period/report leftover-axis tick singular captions."""
+
+from pathlib import Path
+
+
+ROOT = Path(__file__).resolve().parents[1]
+BADGE_SOURCE = ROOT / "frontend" / "src" / "leftoverMapAxisBadge.ts"
+
+
+def test_report_leftover_axis_tick_keeps_persisted_singular_without_share() -> None:
+    """A report leftover-axis tick may name valid persisted σ with no axis share."""
+    assert BADGE_SOURCE.exists(), "report-axis badge helper is missing"
+    source = BADGE_SOURCE.read_text(encoding="utf-8")
+
+    assert "leftoverMapAxisTickBadge" in source
+    assert "leftover axis {axis} tick {value} σ {singular}" in source
+
+
+def test_report_leftover_axis_tick_never_infers_sigma_or_share() -> None:
+    """Invalid σ falls back to an ordinary leftover-axis tick; share is never synthesized."""
+    assert BADGE_SOURCE.exists(), "report-axis badge helper is missing"
+    source = BADGE_SOURCE.read_text(encoding="utf-8")
+
+    assert "formatLeftoverMapPlotAxisSingular" in source
+    assert "Math.sqrt" not in source
+    tail = source.split("leftoverMapAxisTickBadge", 1)[-1][:1600]
+    assert "leftover_share" not in tail