diff --git a/CHANGELOG.d/2.81.0-leftover-map-plot-axis-singular.md b/CHANGELOG.d/2.81.0-leftover-map-plot-axis-singular.md
new file mode 100644
index 000000000..6e39642a5
--- /dev/null
+++ b/CHANGELOG.d/2.81.0-leftover-map-plot-axis-singular.md
@@ -0,0 +1,3 @@
+### Added
+
+- Report leftover-map graphic axes now expose persisted Gabriel singular values independently of persisted axis share, preserving finite `σ=0` and omitting invalid evidence without deriving one measure from the other.
diff --git a/CHANGELOG.d/2.82.0-leftover-map-axis-singular-only.md b/CHANGELOG.d/2.82.0-leftover-map-axis-singular-only.md
new file mode 100644
index 000000000..e8b7973de
--- /dev/null
+++ b/CHANGELOG.d/2.82.0-leftover-map-axis-singular-only.md
@@ -0,0 +1,3 @@
+### Fixed
+
+- Report leftover-axis evidence now has an explicit singular-only state so a valid persisted Gabriel `σ` remains visible when axis share is unavailable; share-only, combined, and empty states remain independent and missing evidence is not rendered as `NaN%`.
diff --git a/docs/adr/0324-leftover-map-report-graphic-axis-singular.md b/docs/adr/0324-leftover-map-report-graphic-axis-singular.md
new file mode 100644
index 000000000..c40c6d946
--- /dev/null
+++ b/docs/adr/0324-leftover-map-report-graphic-axis-singular.md
@@ -0,0 +1,31 @@
+# ADR 0324 — Name persisted singular values on report leftover-map graphic axes
+
+**Decision status:** Proposed
+**Date:** 2026-08-31
+
+## Context
+
+LineageWeave persists leftover-map axis share and Gabriel singular value `σ_k`. Comparison graphics and comparison-strip evidence can already expose persisted `σ_k`; the report graphic still shows share only. That hides scale evidence on the report graphic and creates inconsistent semantics for the same persisted axes.
+
+Missingness is independent. A valid finite, non-negative `σ_k`, including `0`, must remain visible when share is absent; valid share must remain visible when `σ_k` is absent or invalid. Neither value is reconstructed from the other.
+
+## Decision
+
+Report graphic axes use distinct copy:
+
+- singular only: `leftover-map axis {axis} σ {value}`;
+- singular plus share: `leftover-map axis {axis} σ {value} ({share}%)`;
+- share only: the existing `leftover-map axis {axis} ({share}%)`;
+- neither usable: the existing axis name without invented evidence.
+
+No square root, normalization, SQL, migration, or owner duplication is introduced. The rendering consumes LineageWeave-owned persisted evidence and leaves comparison copy distinct.
+
+## Consequences
+
+Report and comparison graphics now preserve the same evidence semantics while keeping surface-specific labels. This ADR remains **Proposed** until fresh exact-head frontend, browser/accessibility, security, and independent-review evidence is current.
+
+## References
+
+Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. *Biometrika, 58*(3), 453–467. https://doi.org/10.1093/biomet/58.3.453
+
+Jeon, M., Jin, I. H., Schweinberger, M., & Baugh, S. (2021). Mapping unobserved item–respondent interactions: A latent space item response model with interaction map. *Psychometrika, 86*(2), 378–403. https://doi.org/10.1007/s11336-021-09762-5
diff --git a/docs/adr/0325-leftover-map-report-axis-singular-only.md b/docs/adr/0325-leftover-map-report-axis-singular-only.md
new file mode 100644
index 000000000..1ddc3f8ac
--- /dev/null
+++ b/docs/adr/0325-leftover-map-report-axis-singular-only.md
@@ -0,0 +1,35 @@
+# ADR 0325 — Preserve singular-only and share-only report-axis evidence
+
+**Decision status:** Proposed
+**Date:** 2026-08-31
+
+## Context
+
+LineageWeave persists two different measurements for a leftover-map axis: Gabriel singular value `σ_k` and axis share. They have independent missingness. The report badge path previously chose its rendering branch from `σ_k` alone and formatted a missing share through numeric arithmetic, which can surface `NaN%` and erase the distinction between unavailable evidence and a measured value.
+
+A finite, non-negative persisted `σ_k`, including `0`, must remain buyer-visible when share is unavailable. A finite persisted share must remain visible when `σ_k` is unavailable. Neither measurement may be reconstructed, normalized, clamped, or inferred from the other.
+
+## Decision
+
+Define one LineageWeave-owned report-axis badge projection with four states:
+
+- combined: `leftover axis {axis} σ {value} {share}%`;
+- singular only: `leftover axis {axis} σ {value}`;
+- share only: `leftover axis {axis} {share}%`;
+- neither usable: omit the badge.
+
+The projection consumes persisted axis values only. `σ_k` is accepted only when finite and non-negative; `σ=0` remains explicit. Share uses the existing finite-value formatter. Missing or invalid evidence fails closed independently.
+
+This decision changes presentation composition only. It does not add persistence, cross-service SQL, psychometric estimation, or source copies from fast-mlsirm, TEPP, or another canonical owner.
+
+## Consequences
+
+The report no longer needs to represent missing share as `NaN%`, and a singular-only axis remains inspectable. Existing combined and share-only buyer copy remains unchanged. The helper is a deterministic projection that can be unit-tested without synthetic domain data.
+
+This ADR remains **Proposed** until the exact-head buyer path actually consumes the projection and fresh frontend, browser/accessibility, security, and independent-review evidence is current.
+
+## References
+
+Gabriel, K. R. (1971). The biplot graphic display of matrices with application to principal component analysis. *Biometrika, 58*(3), 453–467. https://doi.org/10.1093/biomet/58.3.453
+
+Jeon, M., Jin, I. H., Schweinberger, M., & Baugh, S. (2021). Mapping unobserved item–respondent interactions: A latent space item response model with interaction map. *Psychometrika, 86*(2), 378–403. https://doi.org/10.1007/s11336-021-09762-5
diff --git a/frontend/src/App.tsx b/frontend/src/App.tsx
index ecd927785..ce2842434 100644
--- a/frontend/src/App.tsx
+++ b/frontend/src/App.tsx
@@ -137,12 +137,7 @@ import {
   LEFTOVER_MAP_PLOT_INCOMPLETE_POST,
   LEFTOVER_MAP_PLOT_ITEM_COVERAGE,
 } from "./leftoverMapCoverage";
-import {
-  leftoverMapAxisBadgeShare,
-  leftoverMapAxisBadgeSingular,
-  LEFTOVER_MAP_AXIS_BADGE_SHARE,
-  LEFTOVER_MAP_AXIS_BADGE_SINGULAR,
-} from "./leftoverMapAxisBadge";
+import { leftoverMapAxisBadge } from "./leftoverMapAxisBadge";
 import {
   formatLeftoverMapReconstruction,
   LEFTOVER_MAP_COMPARE_RECONSTRUCTION_LABEL,
@@ -3930,17 +3925,10 @@ function ReportsPanel({
               </p>
             ) : null}
             {report.leftover_map_axes?.map((axis) => {
-              const singular = leftoverMapAxisBadgeSingular(axis);
-              const share = leftoverMapAxisBadgeShare(axis.leftover_share);
-              return (
+              const badge = leftoverMapAxisBadge(axis);
+              return badge === null ? null : (
                 <span key={axis.axis_index} className="post-badge">
-                  {singular === null
-                    ? tf(LEFTOVER_MAP_AXIS_BADGE_SHARE, { axis: axis.axis_index, share })
-                    : tf(LEFTOVER_MAP_AXIS_BADGE_SINGULAR, {
-                        axis: axis.axis_index,
-                        value: singular,
-                        share,
-                      })}
+                  {tf(badge.template, badge.values)}
                 </span>
               );
             })}
diff --git a/frontend/src/components/LeftoverMapPlot.tsx b/frontend/src/components/LeftoverMapPlot.tsx
index a09c0ee0e..9e36987ae 100644
--- a/frontend/src/components/LeftoverMapPlot.tsx
+++ b/frontend/src/components/LeftoverMapPlot.tsx
@@ -33,6 +33,8 @@ import {
   leftoverSingularForAxis,
   LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR,
   LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR_SHARE,
+  LEFTOVER_MAP_PLOT_AXIS_SINGULAR,
+  LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE,
 } from "../leftoverMapPlotAxisSingular";
 import {
   firstPlottablePairForPost,
@@ -106,10 +108,20 @@ function leftoverMapPlotAxisText(
       share: percent,
     });
   }
+  if (singular === null) {
+    if (percent === null) {
+      return t(axisIndex === 1 ? "leftover-map axis 1" : "leftover-map axis 2");
+    }
+    return tf(LEFTOVER_MAP_PLOT_AXIS_SHARE, { axis: axisIndex, share: percent });
+  }
   if (percent === null) {
-    return t(axisIndex === 1 ? "leftover-map axis 1" : "leftover-map axis 2");
+    return tf(LEFTOVER_MAP_PLOT_AXIS_SINGULAR, { axis: axisIndex, value: singular });
   }
-  return tf(LEFTOVER_MAP_PLOT_AXIS_SHARE, { axis: axisIndex, share: percent });
+  return tf(LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE, {
+    axis: axisIndex,
+    value: singular,
+    share: percent,
+  });
 }
 
 /**
@@ -118,9 +130,9 @@ function leftoverMapPlotAxisText(
  * Person markers are posts; item markers are leftover criteria. Click a
  * post marker to open that post. Caption leftover-map axes with persisted
  * Gabriel inertia share when finite, including rank-0 zero-share axes.
- * Comparison graphic axes additionally name finite, non-negative persisted
- * Gabriel singular values independently of axis share; never derive one
- * measurement from the other. The comparison strip also exposes these two
+ * Report and comparison graphic axes additionally name finite, non-negative
+ * persisted Gabriel singular values independently of axis share; never derive
+ * one measurement from the other. The comparison strip also exposes these two
  * persisted measures as independent badges so a missing share does not erase
  * usable σ evidence and a missing σ does not erase usable share evidence.
  * Axis ticks name persisted leftover-map coordinates so ξ / ζ on the
diff --git a/frontend/src/leftoverMapAxisBadge.test.ts b/frontend/src/leftoverMapAxisBadge.test.ts
index 579273f88..66d5d099c 100644
--- a/frontend/src/leftoverMapAxisBadge.test.ts
+++ b/frontend/src/leftoverMapAxisBadge.test.ts
@@ -1,9 +1,11 @@
 import { describe, expect, it } from "vitest";
 import {
+  leftoverMapAxisBadge,
   leftoverMapAxisBadgeShare,
   leftoverMapAxisBadgeSingular,
   LEFTOVER_MAP_AXIS_BADGE_SHARE,
   LEFTOVER_MAP_AXIS_BADGE_SINGULAR,
+  LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY,
 } from "./leftoverMapAxisBadge";
 import {
   leftoverMapCompareAxisBadge,
@@ -17,10 +19,13 @@ import {
 } from "./leftoverMapPlotAxisSingular";
 
 describe("leftoverMapAxisBadgeShare", () => {
-  it("formats leftover-axis share percent without inventing a leftover score", () => {
-    expect(leftoverMapAxisBadgeShare(0.82)).toBe("82");
-    expect(leftoverMapAxisBadgeShare(0.18)).toBe("18");
-    expect(leftoverMapAxisBadgeShare(0)).toBe("0");
+  it("formats report-axis share as an optional suffix", () => {
+    expect(leftoverMapAxisBadgeShare(0.82)).toBe(" 82%");
+    expect(leftoverMapAxisBadgeShare(0.18)).toBe(" 18%");
+    expect(leftoverMapAxisBadgeShare(0)).toBe(" 0%");
+    expect(leftoverMapAxisBadgeShare(undefined)).toBe("");
+    expect(leftoverMapAxisBadgeShare(Number.NaN)).toBe("");
+    expect(leftoverMapAxisBadgeShare(Number.POSITIVE_INFINITY)).toBe("");
   });
 });
 
@@ -55,16 +60,58 @@ describe("leftoverMapAxisBadgeSingular", () => {
     expect(leftoverMapAxisBadgeSingular({ axis_index: 1 })).toBeNull();
   });
 
-  it("stays distinct from leftover-map graphic and comparison graphic leftover-map axis σ copy", () => {
-    expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR).toBe("leftover axis {axis} σ {value} {share}%");
-    expect(LEFTOVER_MAP_AXIS_BADGE_SHARE).toBe("leftover axis {axis} {share}%");
+  it("keeps report copy distinct from plot and comparison copy", () => {
+    expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR).toBe("leftover axis {axis} σ {value}{share}");
+    expect(LEFTOVER_MAP_AXIS_BADGE_SHARE).toBe("leftover axis {axis}{share}");
+    expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY).toBe("leftover axis {axis} σ {value}");
     expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR).not.toBe(LEFTOVER_MAP_PLOT_AXIS_SINGULAR);
     expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR).not.toBe(LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE);
     expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR).not.toBe(LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR);
     expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR).not.toBe(
       LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR_SHARE,
     );
-    expect(LEFTOVER_MAP_AXIS_BADGE_SINGULAR).not.toBe("leftover axis {axis} σ {value}");
+  });
+});
+
+describe("leftoverMapAxisBadge", () => {
+  it("keeps singular-only, share-only, combined, and empty states independent", () => {
+    expect(
+      leftoverMapAxisBadge({
+        axis_index: 1,
+        leftover_singular_value: 1.24,
+        leftover_share: 0.42,
+      }),
+    ).toEqual({
+      template: LEFTOVER_MAP_AXIS_BADGE_SINGULAR,
+      values: { axis: 1, value: "1.24", share: " 42%" },
+    });
+    expect(
+      leftoverMapAxisBadge({
+        axis_index: 1,
+        leftover_singular_value: 0,
+        leftover_share: null,
+      }),
+    ).toEqual({
+      template: LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY,
+      values: { axis: 1, value: "0.00" },
+    });
+    expect(
+      leftoverMapAxisBadge({
+        axis_index: 2,
+        leftover_singular_value: null,
+        leftover_share: 0.18,
+      }),
+    ).toEqual({
+      template: LEFTOVER_MAP_AXIS_BADGE_SHARE,
+      values: { axis: 2, share: " 18%" },
+    });
+    expect(
+      leftoverMapAxisBadge({
+        axis_index: 2,
+        leftover_singular_value: Number.NaN,
+        leftover_share: Number.POSITIVE_INFINITY,
+      }),
+    ).toBeNull();
   });
 });
 
diff --git a/frontend/src/leftoverMapAxisBadge.ts b/frontend/src/leftoverMapAxisBadge.ts
index 7d2b377df..4a00d425f 100644
--- a/frontend/src/leftoverMapAxisBadge.ts
+++ b/frontend/src/leftoverMapAxisBadge.ts
@@ -1,19 +1,33 @@
 /** Caption leftover-axis report badges with persisted Gabriel singular values. */
 
 import type { LeftoverMapAxis } from "./api";
+import { formatLeftoverMapPlotAxisShare } from "./leftoverMapPlotAxisShare";
 import {
   formatLeftoverMapPlotAxisSingular,
   leftoverSingularForAxis,
 } from "./leftoverMapPlotAxisSingular";
 
-export const LEFTOVER_MAP_AXIS_BADGE_SHARE = "leftover axis {axis} {share}%";
+export const LEFTOVER_MAP_AXIS_BADGE_SHARE = "leftover axis {axis}{share}";
 
-export const LEFTOVER_MAP_AXIS_BADGE_SINGULAR = "leftover axis {axis} σ {value} {share}%";
+export const LEFTOVER_MAP_AXIS_BADGE_SINGULAR = "leftover axis {axis} σ {value}{share}";
 
+export const LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY = "leftover axis {axis} σ {value}";
+
+export type LeftoverMapAxisBadge = {
+  template: string;
+  values: Record<string, string | number>;
+};
+
+/**
+ * Format report-axis share as an optional suffix consumed directly by the
+ * report template. Missing or non-finite share stays absent instead of
+ * leaking a synthetic `NaN%` value into buyer-visible evidence.
+ */
 export function leftoverMapAxisBadgeShare(
   leftoverShare: LeftoverMapAxis["leftover_share"] | null | undefined,
 ): string {
-  return ((leftoverShare ?? Number.NaN) * 100).toFixed(0);
+  const share = formatLeftoverMapPlotAxisShare(leftoverShare);
+  return share === null ? "" : ` ${share}%`;
 }
 
 export function leftoverMapAxisBadgeSingular(
@@ -25,3 +39,34 @@ export function leftoverMapAxisBadgeSingular(
     leftoverSingularForAxis([axis], axis.axis_index),
   );
 }
+
+/** Keep report-axis singular and share evidence independently observable. */
+export function leftoverMapAxisBadge(
+  axis: Pick<LeftoverMapAxis, "axis_index"> & {
+    leftover_share?: LeftoverMapAxis["leftover_share"] | null;
+    leftover_singular_value?: LeftoverMapAxis["leftover_singular_value"] | null;
+  },
+): LeftoverMapAxisBadge | null {
+  const singular = leftoverMapAxisBadgeSingular(axis);
+  const share = leftoverMapAxisBadgeShare(axis.leftover_share);
+
+  if (singular === null && share === "") {
+    return null;
+  }
+  if (singular === null) {
+    return {
+      template: LEFTOVER_MAP_AXIS_BADGE_SHARE,
+      values: { axis: axis.axis_index, share },
+    };
+  }
+  if (share === "") {
+    return {
+      template: LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY,
+      values: { axis: axis.axis_index, value: singular },
+    };
+  }
+  return {
+    template: LEFTOVER_MAP_AXIS_BADGE_SINGULAR,
+    values: { axis: axis.axis_index, value: singular, share },
+  };
+}
diff --git a/frontend/src/leftoverMapPlotAxisSingular.ts b/frontend/src/leftoverMapPlotAxisSingular.ts
index 14fa82bde..aed961ef0 100644
--- a/frontend/src/leftoverMapPlotAxisSingular.ts
+++ b/frontend/src/leftoverMapPlotAxisSingular.ts
@@ -3,6 +3,12 @@
 import type { LeftoverMapAxis } from "./api";
 import { formatLeftoverMapPlotAxisShare } from "./leftoverMapPlotAxisShare";
 
+export const LEFTOVER_MAP_PLOT_AXIS_SINGULAR =
+  "leftover-map axis {axis} σ {value}";
+
+export const LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE =
+  "leftover-map axis {axis} σ {value} ({share}%)";
+
 export const LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR =
   "leftover map comparison graphic leftover-map axis {axis} σ {value}";
 
diff --git a/tests/test_leftover_axis_report_singular_contract.py b/tests/test_leftover_axis_report_singular_contract.py
index 5319a7113..192efc04f 100644
--- a/tests/test_leftover_axis_report_singular_contract.py
+++ b/tests/test_leftover_axis_report_singular_contract.py
@@ -13,13 +13,12 @@ def test_report_axis_badge_keeps_singular_value_and_share_semantically_distinct(
     assert BADGE_SOURCE.exists(), "report-axis singular-value badge helper is missing"
     badge_source = BADGE_SOURCE.read_text(encoding="utf-8")
 
-    assert 'LEFTOVER_MAP_AXIS_BADGE_SHARE = "leftover axis {axis} {share}%"' in badge_source
-    assert (
-        'LEFTOVER_MAP_AXIS_BADGE_SINGULAR = "leftover axis {axis} σ {value} {share}%"'
-        in badge_source
-    )
+    assert 'LEFTOVER_MAP_AXIS_BADGE_SHARE = "leftover axis {axis}{share}"' in badge_source
+    assert 'LEFTOVER_MAP_AXIS_BADGE_SINGULAR = "leftover axis {axis} σ {value}{share}"' in badge_source
+    assert 'LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY = "leftover axis {axis} σ {value}"' in badge_source
     assert "leftoverSingularForAxis" in badge_source
     assert "formatLeftoverMapPlotAxisSingular" in badge_source
+    assert "formatLeftoverMapPlotAxisShare" in badge_source
     assert "leftover map comparison graphic" not in badge_source
 
 
diff --git a/tests/test_leftover_axis_report_singular_only_contract.py b/tests/test_leftover_axis_report_singular_only_contract.py
new file mode 100644
index 000000000..2232a8d8c
--- /dev/null
+++ b/tests/test_leftover_axis_report_singular_only_contract.py
@@ -0,0 +1,50 @@
+"""Executable contract for the report-axis singular-only state."""
+
+from pathlib import Path
+
+
+ROOT = Path(__file__).resolve().parents[1]
+BADGE_SOURCE = ROOT / "frontend" / "src" / "leftoverMapAxisBadge.ts"
+APP_SOURCE = ROOT / "frontend" / "src" / "App.tsx"
+
+
+def test_report_axis_badge_preserves_singular_when_share_is_missing() -> None:
+    """A valid persisted σ remains visible when axis share is absent."""
+    assert BADGE_SOURCE.exists(), "report-axis singular-value badge helper is missing"
+    source = BADGE_SOURCE.read_text(encoding="utf-8")
+
+    assert (
+        'LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY = "leftover axis {axis} σ {value}"'
+        in source
+    )
+    assert 'LEFTOVER_MAP_AXIS_BADGE_SINGULAR = "leftover axis {axis} σ {value}{share}"' in source
+    assert "formatLeftoverMapPlotAxisShare" in source
+    assert 'return share === null ? "" : ` ${share}%`;' in source
+    assert "Number.NaN" not in source
+
+
+def test_report_axis_badge_keeps_sigma_and_share_missingness_independent() -> None:
+    """σ-only, share-only, combined, and empty states must remain data-driven."""
+    assert BADGE_SOURCE.exists(), "report-axis singular-value badge helper is missing"
+    source = BADGE_SOURCE.read_text(encoding="utf-8")
+
+    assert "formatLeftoverMapPlotAxisSingular" in source
+    assert "leftoverMapAxisBadgeShare" in source
+    assert "LEFTOVER_MAP_AXIS_BADGE_SINGULAR" in source
+    assert "LEFTOVER_MAP_AXIS_BADGE_SHARE" in source
+    assert "LEFTOVER_MAP_AXIS_BADGE_SINGULAR_ONLY" in source
+    assert 'singular === null && share === ""' in source
+    assert 'share === ""' in source
+    assert "Math.sqrt" not in source
+
+
+def test_report_axis_rendering_consumes_the_four_state_projection() -> None:
+    """The report path must omit a badge when neither persisted axis datum is usable."""
+    app_source = APP_SOURCE.read_text(encoding="utf-8")
+
+    assert "leftoverMapAxisBadge" in app_source
+    assert "const badge = leftoverMapAxisBadge(axis);" in app_source
+    assert "badge === null ? null" in app_source
+    assert "tf(badge.template, badge.values)" in app_source
+    assert "leftoverMapAxisBadgeShare" not in app_source
+    assert "leftoverMapAxisBadgeSingular" not in app_source
diff --git a/tests/test_leftover_map_report_graphic_axis_singular_contract.py b/tests/test_leftover_map_report_graphic_axis_singular_contract.py
new file mode 100644
index 000000000..10ecc77f2
--- /dev/null
+++ b/tests/test_leftover_map_report_graphic_axis_singular_contract.py
@@ -0,0 +1,33 @@
+"""Executable contract for persisted singular values on report-graphic axes."""
+
+from pathlib import Path
+
+
+ROOT = Path(__file__).resolve().parents[1]
+SINGULAR_SOURCE = ROOT / "frontend" / "src" / "leftoverMapPlotAxisSingular.ts"
+PLOT_SOURCE = ROOT / "frontend" / "src" / "components" / "LeftoverMapPlot.tsx"
+
+
+def test_report_graphic_axis_has_distinct_singular_and_singular_share_copy() -> None:
+    """Report-graphic σ copy must stay distinct from pair badges and comparison variants."""
+    assert SINGULAR_SOURCE.exists(), "persisted singular-value projection helper is missing"
+    source = SINGULAR_SOURCE.read_text(encoding="utf-8")
+    plot_source = PLOT_SOURCE.read_text(encoding="utf-8")
+
+    assert '"leftover-map axis {axis} σ {value}"' in source
+    assert '"leftover-map axis {axis} σ {value} ({share}%)"' in source
+    assert "LEFTOVER_MAP_PLOT_AXIS_SINGULAR" in plot_source
+    assert "LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE" in plot_source
+
+
+def test_report_graphic_singular_value_comes_from_persisted_axis_evidence() -> None:
+    """Invalid σ omits independently of share; finite σ=0 remains explicit."""
+    assert SINGULAR_SOURCE.exists(), "persisted singular-value projection helper is missing"
+    source = SINGULAR_SOURCE.read_text(encoding="utf-8")
+
+    assert "leftover_singular_value" in source
+    assert "Number.isFinite" in source
+    assert "< 0" in source
+    assert ".toFixed(2)" in source
+    assert "Math.sqrt" not in source
+    assert "Math.max" not in source