diff --git a/AGENTS.md b/AGENTS.md
index f7ebeb9d3..dd56245ab 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -273,7 +273,7 @@ stops startup instead of leaving a healthy-looking partial schema, and
 application code must not compensate for a missing table.
 
 Period leftover pairs (ADR 0017 / 0018 / 0048 / 0049 / 0119 / 0158 / 0162 /
-0163 / 0164 / 0182 / 0185 / 0201 / 0233 / 0266 / 0267 / 0268 / 0269 / 0270 / 0271 / 0272 / 0273 / 0274 / 0275 / 0276 / 0277 / 0278 / 0279 / 0280 / 0281 / 0282 / 0283 / 0284 / 0285 / 0286 / 0287 / 0288 / 0289 / 0290 / 0291 / 0292 / 0293 / 0294 / 0295 / 0296 / 0297 / 0298 / 0299 / 0300 / 0301 / 0302 / 0303 / 0304 / 0305 / 0306 / 0307 / 0308 / 0309 / 0310 / 0311 / 0312 / 0313 / 0314 / 0315 / 0316 / 0317 / 0318 / 0319 / 0320 / 0321 / 0322 / 0323) are computed in `lineageweave/leftover_pairs.py` from the
+0163 / 0164 / 0182 / 0185 / 0201 / 0233 / 0266 / 0267 / 0268 / 0269 / 0270 / 0271 / 0272 / 0273 / 0274 / 0275 / 0276 / 0277 / 0278 / 0279 / 0280 / 0281 / 0282 / 0283 / 0284 / 0285 / 0286 / 0287 / 0288 / 0289 / 0290 / 0291 / 0292 / 0293 / 0294 / 0295 / 0296 / 0297 / 0298 / 0299 / 0300 / 0301 / 0302 / 0303 / 0304 / 0305 / 0306 / 0307 / 0308 / 0309 / 0310 / 0311 / 0312 / 0313 / 0314 / 0315 / 0316 / 0317 / 0318 / 0319 / 0320 / 0321 / 0322 / 0323 / 0324) are computed in `lineageweave/leftover_pairs.py` from the
 residual after a real GRM/GPCM score, never invented. Distances are
 Euclidean on the two-dimensional Gabriel leftover map; missing cells stay
 out of the factorization. Closest and farthest post–criterion pairs
@@ -656,6 +656,11 @@ leftoverMapCompareAxisBadge returns a usable leftover-axis caption. Distinct acc
 name `leftover map comparison leftover axis {axis} σ {value}`. Share and singular value
 omit independently. Rank-0 unused axes still name `σ 0.00`. Do not invent leftover-map
 singular values from leftover-map axis share.
+ADR 0324 captions leftover-map graphic-display axes with persisted leftover-map singular
+values `σ_k` when leftoverMapPlotAxisBadge returns a usable leftover-map axis caption.
+Distinct accessible name `leftover-map axis {axis} σ {value} ({share}%)`. Share and
+singular value omit independently. Rank-0 unused axes still name leftover-map axis
+`σ 0.00`. Do not invent leftover-map singular values from leftover-map axis share.
 When `R`, `R̂`, `U`, `x`,
 `s`, and `e` are finite, `e + s + x = 1`. When `Y`, `E`, and `R` are
 finite, `Y − E = R`. When `R`, `R̂`, and `U` are
@@ -760,6 +765,9 @@ returns a usable finite non-negative value.
 Grouping comparison leftover-axis report badge leftover-map singular values (ADR 0323) captions
 leftover-axis report badges on the grouping comparison strip with persisted leftover-map
 singular values `σ_k` when leftoverMapCompareAxisBadge returns a usable leftover-axis caption.
+Leftover-map graphic-display leftover-map singular values (ADR 0324) captions leftover-map
+graphic-display axes with persisted leftover-map singular values `σ_k` when leftoverMapPlotAxisBadge
+returns a usable leftover-map axis caption.
 Item complete-case coverage
 (ADR 0282) captions the leftover-map graphic with how many scored criteria
 entered the map. Item complete-case coverage on the pair list (ADR 0285)
diff --git a/ARCHITECTURE.md b/ARCHITECTURE.md
index 8321c5d25..84746aa4a 100644
--- a/ARCHITECTURE.md
+++ b/ARCHITECTURE.md
@@ -754,6 +754,8 @@ ADR 0322 captions leftover-axis report badges with persisted leftover-map
 singular values `σ_k`.
 ADR 0323 captions leftover-axis report badges on the grouping comparison strip
 with persisted leftover-map singular values `σ_k`.
+ADR 0324 captions leftover-map graphic-display axes with persisted leftover-map
+singular values `σ_k`.
 Click a post marker or a pair button
 opens that post. Those ADRs are the normative mathematical, storage, and
 display contracts. Leftover-map axis share
@@ -806,7 +808,8 @@ graphic (ADR 0319), leftover-map coordinate ticks on the grouping comparison lef
 graphic (ADR 0320), leftover-map singular values on the grouping comparison leftover-map
 graphic (ADR 0321), leftover-map singular values on leftover-axis report badges
 (ADR 0322), leftover-map singular values on leftover-axis report badges on the
-grouping comparison strip (ADR 0323);
+grouping comparison strip (ADR 0323), leftover-map singular values on leftover-map
+graphic-display axes (ADR 0324);
 `POST .../rebuild` scores every grouping kind (post_admin). `make seed`
 folds A-100/B-200 Event Lineage fixtures (and the Riverbend calendar
 post) that already have constructed IRT cells into the same shared
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..a15f4858e
--- /dev/null
+++ b/CHANGELOG.d/2.81.0-leftover-map-plot-axis-singular.md
@@ -0,0 +1,18 @@
+## 2.81.0 — Leftover-map singular values on leftover-map graphic-display axes
+
+- Caption leftover-map graphic-display axes with persisted leftover-map singular
+  values `σ_k` (ADR 0324). After `make seed`, leftover-map graphic-display axes
+  name persisted leftover-map singular values when finite together with persisted
+  leftover-map axis share; click a leftover pair opens that post. A missing,
+  non-finite, or negative singular value omits that `σ` caption and keeps
+  `leftover-map axis {k} ({share}%)`. Rank-0 unused axes still name `σ 0.00`.
+  Leftover-map graphic-display axes stay `leftover-map axis {k} σ {value} ({share}%)`
+  so they stay distinct from leftover-axis `leftover axis {k} σ {value} {share}%`,
+  from comparison leftover-axis `leftover map comparison leftover axis {k} σ {value} {share}%`,
+  and from comparison graphic
+  `leftover map comparison graphic leftover-map axis {k} σ {value} ({share}%)`.
+  Do not invent `σ_k` from leftover-map axis share. This increment does not
+  change leftover-map singular values on leftover-axis report badges or on
+  leftover-axis report badges on the grouping comparison strip. A finite negative
+  leftover is shown, never clamped. Never invent a leftover score. Never invent a
+  theta. No new columns.
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9a0d1cec3..f0ab37f05 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -8,6 +8,21 @@ All notable changes to this project are documented here. Format follows
 
 ### Added
 
+- Period leftover pairs now caption leftover-map graphic-display axes with persisted
+  leftover-map singular values `σ_k` (ADR 0324 / v2.81.0). After `make seed`, leftover-map
+  graphic-display axes name persisted leftover-map singular values when finite together
+  with persisted leftover-map axis share; click a leftover pair opens that post. A
+  missing, non-finite, or negative singular value omits that `σ` caption and keeps
+  `leftover-map axis {k} ({share}%)`. Rank-0 unused axes still name `σ 0.00`. Leftover-map
+  graphic-display axes stay `leftover-map axis {k} σ {value} ({share}%)` so they stay
+  distinct from leftover-axis `leftover axis {k} σ {value} {share}%`, from comparison
+  leftover-axis `leftover map comparison leftover axis {k} σ {value} {share}%`, and from
+  comparison graphic `leftover map comparison graphic leftover-map axis {k} σ {value} ({share}%)`.
+  Do not invent `σ_k` from leftover-map axis share. This increment does not change
+  leftover-map singular values on leftover-axis report badges or on leftover-axis
+  report badges on the grouping comparison strip. A finite negative leftover is shown,
+  never clamped. Never invent a leftover score or a theta. No new columns.
+
 - Period leftover pairs now caption leftover-axis report badges on the grouping
   comparison strip with persisted leftover-map singular values `σ_k`
   (ADR 0323 / v2.80.0). After `make seed`, grouping comparison leftover-axis
diff --git a/CLAUDE.md b/CLAUDE.md
index 4546003e0..f29361dc8 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -49,7 +49,7 @@ cutoff. Global Ask optional `knowledge_cutoff` uses the same cover
 
 Create/start endpoint rules (ADR 0017 / 0021), tie-vs-miss similarity
 (ADR 0026), R&R catalog ids (ADR 0019 / 0027), leftover pairs
-(ADR 0048–0164 / 0182 / 0185 / 0201 / 0233 / 0266 / 0267 / 0268 / 0269 / 0270 / 0271 / 0272 / 0273 / 0274 / 0275 / 0276 / 0277 / 0278 / 0279 / 0280 / 0281 / 0282 / 0283 / 0284 / 0285 / 0286 / 0287 / 0288 / 0289 / 0290 / 0291 / 0292 / 0293 / 0294 / 0295 / 0296 / 0297 / 0298 / 0299 / 0300 / 0301 / 0302 / 0303 / 0304 / 0305 / 0306 / 0307 / 0308 / 0309 / 0310 / 0311 / 0312 / 0313 / 0314 / 0315 / 0316 / 0317 / 0318 / 0319 / 0320 / 0321 / 0322 / 0323), occupational construct catalog search
+(ADR 0048–0164 / 0182 / 0185 / 0201 / 0233 / 0266 / 0267 / 0268 / 0269 / 0270 / 0271 / 0272 / 0273 / 0274 / 0275 / 0276 / 0277 / 0278 / 0279 / 0280 / 0281 / 0282 / 0283 / 0284 / 0285 / 0286 / 0287 / 0288 / 0289 / 0290 / 0291 / 0292 / 0293 / 0294 / 0295 / 0296 / 0297 / 0298 / 0299 / 0300 / 0301 / 0302 / 0303 / 0304 / 0305 / 0306 / 0307 / 0308 / 0309 / 0310 / 0311 / 0312 / 0313 / 0314 / 0315 / 0316 / 0317 / 0318 / 0319 / 0320 / 0321 / 0322 / 0323 / 0324), occupational construct catalog search
 (ADR 0257), the text-channel embedding swap and cosine
 clamp (ADR 0190), per-edge channel-score persistence (ADR 0195),
 token-backed status notices (ADR 0220),
diff --git a/docs/adr/0148-leftover-map-axis-share.md b/docs/adr/0148-leftover-map-axis-share.md
index 74728c994..7b5f55843 100644
--- a/docs/adr/0148-leftover-map-axis-share.md
+++ b/docs/adr/0148-leftover-map-axis-share.md
@@ -7,7 +7,9 @@
 [ADR 0322](0322-leftover-map-axis-singular.md)
 (leftover-map singular values on leftover-axis report badges);
 [ADR 0323](0323-leftover-map-compare-axis-singular.md)
-(leftover-map singular values on leftover-axis report badges on the grouping comparison strip)
+(leftover-map singular values on leftover-axis report badges on the grouping comparison strip);
+[ADR 0324](0324-leftover-map-plot-axis-singular.md)
+(leftover-map singular values on leftover-map graphic-display axes)
 
 ## Context
 
diff --git a/docs/adr/0322-leftover-map-axis-singular.md b/docs/adr/0322-leftover-map-axis-singular.md
index bf1183f72..e098a7567 100644
--- a/docs/adr/0322-leftover-map-axis-singular.md
+++ b/docs/adr/0322-leftover-map-axis-singular.md
@@ -83,7 +83,9 @@ Independent of leftover-map singular values on the grouping comparison
 leftover-map graphic. This increment does not caption leftover-map singular
 values on leftover-axis badges on the grouping comparison strip with a
 distinct name
-([ADR 0323](0323-leftover-map-compare-axis-singular.md)).
+([ADR 0323](0323-leftover-map-compare-axis-singular.md)). This increment does
+not caption leftover-map singular values on leftover-map graphic-display axes
+([ADR 0324](0324-leftover-map-plot-axis-singular.md)).
 
 ## References
 
diff --git a/docs/adr/0323-leftover-map-compare-axis-singular.md b/docs/adr/0323-leftover-map-compare-axis-singular.md
index 6d294a869..8c2c28d56 100644
--- a/docs/adr/0323-leftover-map-compare-axis-singular.md
+++ b/docs/adr/0323-leftover-map-compare-axis-singular.md
@@ -103,6 +103,8 @@ leftover-map axis share are finite, leftover-map axis share is
 
 Independent of leftover-map singular values on leftover-axis report badges
 in the period-report panel ([ADR 0322](0322-leftover-map-axis-singular.md)).
+Independent of leftover-map singular values on leftover-map graphic-display
+axes ([ADR 0324](0324-leftover-map-plot-axis-singular.md)).
 
 ## References
 
diff --git a/docs/adr/0324-leftover-map-plot-axis-singular.md b/docs/adr/0324-leftover-map-plot-axis-singular.md
new file mode 100644
index 000000000..02616597e
--- /dev/null
+++ b/docs/adr/0324-leftover-map-plot-axis-singular.md
@@ -0,0 +1,129 @@
+# ADR 0324 — Name leftover-map singular values on leftover-map graphic-display axes
+
+**Decision status:** Accepted
+**Date:** 2026-08-31
+
+Amends leftover-map axis share on the graphic display
+([ADR 0269](0269-leftover-map-axis-share-plot.md)), leftover-map axis share
+persistence ([ADR 0148](0148-leftover-map-axis-share.md)). Independent of leftover-map
+singular values on leftover-axis report badges
+([ADR 0322](0322-leftover-map-axis-singular.md)), leftover-map singular
+values on leftover-axis report badges on the grouping comparison strip
+([ADR 0323](0323-leftover-map-compare-axis-singular.md)), leftover-map
+singular values on the grouping comparison leftover-map graphic
+([ADR 0321](0321-leftover-map-compare-plot-singular.md)), leftover-map
+coordinate ticks on that comparison graphic
+([ADR 0320](0320-leftover-map-compare-plot-ticks.md)), leftover-map
+axis share on that comparison graphic
+([ADR 0305](0305-leftover-map-compare-plot-axis-share.md)), leftover-map
+graphic display on the grouping comparison strip
+([ADR 0304](0304-leftover-map-compare-graphic.md)), leftover-map
+coordinates ([ADR 0267](0267-leftover-map-coordinates.md)), leftover-map
+graphic display ([ADR 0268](0268-leftover-map-graphic-display.md)), and
+leftover-map coordinate ticks on the graphic display
+([ADR 0270](0270-leftover-map-coordinate-ticks.md)).
+
+## Context
+
+ADR 0148 already persists leftover-map singular values `σ_k` and leftover-map
+axis share `σ_k² / Σ_j σ_j²`. ADR 0269 captions leftover-map graphic-display
+axes with share only as `leftover-map axis {k} ({share}%)`. ADR 0321 already
+captions the grouping comparison leftover-map graphic with persisted `σ_k`.
+ADR 0322 already captions leftover-axis report badges with persisted `σ_k`.
+ADR 0323 already captions grouping comparison leftover-axis report badges
+with persisted `σ_k`. Period leftover-map graphic axes still hide `σ_k`, so
+Gabriel (1971) singular values appear on leftover-axis badges and on the
+comparison graphic and never on the leftover-map graphic-display axes that
+name the same axes. Hiding `σ_k` on leftover-map graphic-display axes lets
+leftover-map axis share be read as leftover-map structure even when the buyer
+cannot tell whether axis 1 is large because `σ_1` is large or because axis 2
+collapsed. A missing, non-finite, or negative singular value is not a leftover
+score and must omit independently of leftover-map axis share. Rank-0 unused
+axes still persist `σ_k = 0`. A finite negative leftover is shown, never
+clamped. Do not invent `σ_k` from leftover-map axis share.
+
+This increment captions leftover-map graphic-display axes with already persisted
+leftover-map singular values. Leftover-map graphic-display axes stay
+`leftover-map axis {k} σ {value} ({share}%)` so they stay distinct from
+leftover-axis badges `leftover axis {k} σ {value} {share}%`, from comparison
+leftover-axis `leftover map comparison leftover axis {k} σ {value} {share}%`,
+and from comparison graphic
+`leftover map comparison graphic leftover-map axis {k} σ {value} ({share}%)`.
+It does not add columns. Do not invent a leftover score. Do not invent a
+theta.
+
+This protected increment uses **0324** so it does not collide with leftover-map
+singular values on leftover-axis report badges on the grouping comparison
+strip (0323), leftover-map singular values on leftover-axis report badges
+(0322), leftover-map singular values on the grouping comparison leftover-map
+graphic (0321), leftover-map coordinate ticks on that graphic (0320), leftover-map
+axis share on that graphic (0305), leftover-map graphic display on the grouping
+comparison strip (0304), leftover-map axis share persistence (0148), leftover-map
+axis share on the graphic display (0269), or the dashboard stacks.
+
+## Decision
+
+On leftover-map graphic-display axes, caption leftover-map axis `k` with
+persisted leftover-map singular value `σ_k` when that singular value is
+finite and non-negative, including rank-0 zero singular values. Share and
+singular value omit independently: no share and no `σ_k` keeps
+`leftover-map axis {k}`; share only is `leftover-map axis {k} ({share}%)`;
+`σ_k` only is `leftover-map axis {k} σ {value}`; both is
+`leftover-map axis {k} σ {value} ({share}%)`. A missing, non-finite, or
+negative singular value omits that `σ` caption and keeps the existing
+`leftover-map axis {k} ({share}%)` text. Do not invent `σ_k` from leftover-map
+axis share. Axis 1 and axis 2 stay independently named. Click a leftover pair
+to open that post.
+
+Leftover-map graphic-display singular values omit independently of leftover-map
+comparison graphic leftover-map axis singular values and leftover-axis report
+badges. A missing singular value omits that leftover-map graphic-display `σ`
+caption and keeps a usable leftover-map axis share caption, leftover-map
+comparison graphic leftover-map axis `σ` caption, leftover-axis report badge
+`σ` caption, leftover-map comparison leftover-axis `σ` caption, leftover-map
+graphic leftover-map axis ticks, leftover-map distance caption, leftover-map
+rank caption, leftover expected `E`, leftover observed `Y`, leftover residual
+`R`, leftover-map unexplained leftover `U`, leftover-map reconstruction `R̂`,
+and leftover-map graphic coverage notes.
+
+This increment does not change leftover-map singular values on leftover-axis
+report badges. Those leftover-axis badges stay
+`leftover axis {axis} σ {value} {share}%` (ADR 0322). This increment does
+not change leftover-map singular values on leftover-axis report badges on the
+grouping comparison strip (ADR 0323). This increment does not persist leftover-map
+inner product, cosine, or length.
+
+Do not add SQL. Do not edit shipped migrations. Do not invent a leftover
+score. Do not invent a theta.
+
+## Consequences
+
+After `make seed`, leftover-map graphic-display axes name persisted leftover-map
+singular values when finite together with persisted leftover-map axis share;
+click a leftover pair opens that post. Hidden posts stay hidden. Rank-0 unused
+axes still name leftover-map axis `σ 0.00`. Grouping comparison leftover-map
+graphic leftover-map singular values (ADR 0321), leftover-axis report badge
+leftover-map singular values (ADR 0322), and grouping comparison leftover-axis
+report badge leftover-map singular values (ADR 0323) remain.
+
+## Related
+
+Independent of leftover-map singular values on leftover-axis report badges
+([ADR 0322](0322-leftover-map-axis-singular.md)). Independent of leftover-map
+singular values on leftover-axis report badges on the grouping comparison
+strip ([ADR 0323](0323-leftover-map-compare-axis-singular.md)). Independent of
+leftover-map singular values on the grouping comparison leftover-map graphic
+([ADR 0321](0321-leftover-map-compare-plot-singular.md)).
+
+## 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
+(LSIRM interaction `−γ‖ξ_j − ζ_i‖` after main effects
+`α_j − β_i`; typically `p = 2` for the interaction map.)
diff --git a/docs/product-technical-gap-baseline.md b/docs/product-technical-gap-baseline.md
index 19515f547..3c8aa6d5d 100644
--- a/docs/product-technical-gap-baseline.md
+++ b/docs/product-technical-gap-baseline.md
@@ -1,5 +1,23 @@
 # Product & Technical Gap Baseline
 
+> Exact-head loop overlay: 2026-08-31 11:05 KST. Protected `main` is
+> `cb187cadee5fb6c46d8a944815ccc154a1e028d1`. Writes work. Do not
+> self-approve. #863 leftover-map singular values on leftover-axis report badges
+> on the grouping comparison strip (v2.80.0 / ADR 0323) is `52b3597`, stacked on
+> #862 @ `f24b664`. Independent APPROVE is missing. Next buyer increment on this
+> cycle: leftover-map singular values on leftover-map graphic-display axes
+> (ADR 0324 / v2.81.0) delivered locally on
+> `feat/leftover-map-plot-axis-singular-v2810`. Caption persisted leftover-map
+> singular values `σ_k` on leftover-map graphic-display axes from already-named
+> leftover-map axes. Distinct accessible name `leftover-map axis {axis} σ {value} ({share}%)`.
+> Rank-0 unused axes still name `σ 0.00`. Share and singular value omit
+> independently. Do not invent `σ_k` from leftover-map axis share. Do not change
+> leftover-map singular values on leftover-axis report badges or on leftover-axis
+> report badges on the grouping comparison strip this increment. Stack onto #863.
+> Leave open for independent review. Do not squash-merge. Do not self-approve.
+> Issues #79 and #87 stay open. Do not merge #808 without independent APPROVE.
+> Never self-approve.
+
 > Exact-head loop overlay: 2026-08-31 10:40 KST. Protected `main` is
 > `cb187cadee5fb6c46d8a944815ccc154a1e028d1`. Writes work. Do not
 > self-approve. #862 leftover-map singular values on leftover-axis report badges
diff --git a/docs/storybook-inventory.md b/docs/storybook-inventory.md
index 6811f24df..d4c5f9fae 100644
--- a/docs/storybook-inventory.md
+++ b/docs/storybook-inventory.md
@@ -5,8 +5,8 @@ operator-facing control you can click before changing product CSS.
 
 | Story | Operator next action | Token / module |
 |---|---|---|
-| `Reports/LeftoverMapPlot` | Read the leftover-map graphic display of persisted `ξ` (posts) and `ζ` (criteria), match axis ticks to those coordinates, pair-segment `d` to leftover-map distance, pair-segment `R̂` to leftover-map reconstruction, pair-segment `R̂²/R²` to leftover-map explained leftover share, pair-segment `U²/R²` to leftover-map unexplained leftover share, pair-segment `2R̂U/R²` to leftover-map cross share, pair-segment `U` to leftover-map unexplained leftover, pair-segment `R` to leftover residual, pair-segment `Y` to leftover observed, pair-segment `E` to leftover expected, and pair-segment leftover-map rank, then click a post marker to open that post. Leftover-map axes name persisted leftover-map axis share when finite. The plot names leftover-map complete-case coverage, leftover-map item complete-case coverage, leftover-map incomplete post coverage, and leftover-map incomplete item coverage when persisted. The comparison variant names leftover-map complete-case coverage under `Leftover map comparison graphic coverage` and leftover-map item complete-case coverage under `Leftover map comparison graphic item coverage` and leftover-map incomplete post coverage under `Leftover map comparison graphic incomplete posts` and leftover-map incomplete item coverage under `Leftover map comparison graphic incomplete items`. `ClosestAndFarthest`, `RankZeroOrigin`, `MissingCoordinates`, `MissingAxisShare`, `Comparison`, `ComparisonMissingCoverage`, `ComparisonMissingItemCoverage`, `ComparisonMissingIncompletePosts`, and `ComparisonMissingIncompleteItems` cover two-pair maps, rank-0 origin with 0% share, a `0` tick, `d 0.00`, `R̂ 0.00`, `R̂²/R² 0.00`, `U²/R² 0.00`, `2R̂U/R² 0.00`, `U 0.00`, `R 0.00`, `Y 0.00`, `E 0.00`, and `rank 0`, omitted plots, missing share that keeps existing leftover-map axis text, grouping comparison leftover-map graphic coverage that matches leftover map used N of M scored posts, omitted comparison graphic coverage when leftoverMapCoverageCounts fail-closes, grouping comparison leftover-map graphic item coverage that matches leftover map used N of M scored criteria, omitted comparison graphic item coverage when leftoverMapItemCoverageCounts fail-closes, grouping comparison leftover-map graphic incomplete posts that matches leftover map dropped N incomplete posts, omitted comparison graphic incomplete posts when leftoverMapIncompletePostCount fail-closes, grouping comparison leftover-map graphic incomplete items that matches leftover map dropped N incomplete criteria, and omitted comparison graphic incomplete items when leftoverMapIncompleteItemCount fail-closes. The plot does not invent a leftover score. | `LeftoverMapPlot`, `leftoverMapPlotLayout`, `leftoverMapPlotAxisShare`, `--color-primary`, `--color-palette-blue-mid` |
-| `Reports/LeftoverPairList` | Read closest/farthest leftover pairs with named `R`, `Y`/`E`, rank, `U`, `s`, `e`, `x`, `R̂`, `ξ`/`ζ`, and `d`, then open that post. The leftover-map graphic display sits above the pair buttons when coordinates are finite, leftover-map axes name persisted leftover-map axis share, leftover-map axis ticks name persisted coordinates, pair segments name persisted leftover-map distance, pair segments name persisted leftover-map reconstruction, pair segments name persisted leftover-map explained leftover share, pair segments name persisted leftover-map unexplained leftover share, pair segments name persisted leftover-map cross share, pair segments name persisted leftover-map unexplained leftover, pair segments name persisted leftover residual, pair segments name persisted leftover observed, pair segments name persisted leftover expected, and pair segments name persisted leftover-map rank. The pair-list note names leftover-map complete-case coverage only when leftoverMapCoverageCounts returns usable complete-case integers, leftover-map item complete-case coverage, leftover-map incomplete post coverage, and leftover-map incomplete item coverage when persisted. The grouping comparison strip names leftover-map complete-case coverage, leftover-map item complete-case coverage, leftover-map incomplete post coverage, leftover-map incomplete item coverage, and leftover-axis report badges with persisted leftover-map singular values under `leftover map comparison leftover axis {axis} σ {value}` with distinct comparison labels when leftoverMapCoverageCounts / leftoverMapItemCoverageCounts / leftoverMapIncompletePostCount / leftoverMapIncompleteItemCount / leftoverMapCompareAxisBadge return usable values. | `LeftoverPairList`, `LeftoverMapPlot`, `ticket-list`, `post-badge` |
+| `Reports/LeftoverMapPlot` | Read the leftover-map graphic display of persisted `ξ` (posts) and `ζ` (criteria), match axis ticks to those coordinates, pair-segment `d` to leftover-map distance, pair-segment `R̂` to leftover-map reconstruction, pair-segment `R̂²/R²` to leftover-map explained leftover share, pair-segment `U²/R²` to leftover-map unexplained leftover share, pair-segment `2R̂U/R²` to leftover-map cross share, pair-segment `U` to leftover-map unexplained leftover, pair-segment `R` to leftover residual, pair-segment `Y` to leftover observed, pair-segment `E` to leftover expected, and pair-segment leftover-map rank, then click a post marker to open that post. Leftover-map axes name persisted leftover-map singular values `σ_k` and leftover-map axis share when finite. The plot names leftover-map complete-case coverage, leftover-map item complete-case coverage, leftover-map incomplete post coverage, and leftover-map incomplete item coverage when persisted. The comparison variant names leftover-map complete-case coverage under `Leftover map comparison graphic coverage` and leftover-map item complete-case coverage under `Leftover map comparison graphic item coverage` and leftover-map incomplete post coverage under `Leftover map comparison graphic incomplete posts` and leftover-map incomplete item coverage under `Leftover map comparison graphic incomplete items`. `ClosestAndFarthest`, `RankZeroOrigin`, `MissingCoordinates`, `MissingAxisShare`, `Comparison`, `ComparisonMissingCoverage`, `ComparisonMissingItemCoverage`, `ComparisonMissingIncompletePosts`, and `ComparisonMissingIncompleteItems` cover two-pair maps, rank-0 origin with 0% share, a `0` tick, `d 0.00`, `R̂ 0.00`, `R̂²/R² 0.00`, `U²/R² 0.00`, `2R̂U/R² 0.00`, `U 0.00`, `R 0.00`, `Y 0.00`, `E 0.00`, and `rank 0`, omitted plots, missing share that keeps leftover-map axis `σ` without share, grouping comparison leftover-map graphic coverage that matches leftover map used N of M scored posts, omitted comparison graphic coverage when leftoverMapCoverageCounts fail-closes, grouping comparison leftover-map graphic item coverage that matches leftover map used N of M scored criteria, omitted comparison graphic item coverage when leftoverMapItemCoverageCounts fail-closes, grouping comparison leftover-map graphic incomplete posts that matches leftover map dropped N incomplete posts, omitted comparison graphic incomplete posts when leftoverMapIncompletePostCount fail-closes, grouping comparison leftover-map graphic incomplete items that matches leftover map dropped N incomplete criteria, and omitted comparison graphic incomplete items when leftoverMapIncompleteItemCount fail-closes. The plot does not invent a leftover score. | `LeftoverMapPlot`, `leftoverMapPlotLayout`, `leftoverMapPlotAxisShare`, `--color-primary`, `--color-palette-blue-mid` |
+| `Reports/LeftoverPairList` | Read closest/farthest leftover pairs with named `R`, `Y`/`E`, rank, `U`, `s`, `e`, `x`, `R̂`, `ξ`/`ζ`, and `d`, then open that post. The leftover-map graphic display sits above the pair buttons when coordinates are finite, leftover-map axes name persisted leftover-map singular values and leftover-map axis share, leftover-map axis ticks name persisted coordinates, pair segments name persisted leftover-map distance, pair segments name persisted leftover-map reconstruction, pair segments name persisted leftover-map explained leftover share, pair segments name persisted leftover-map unexplained leftover share, pair segments name persisted leftover-map cross share, pair segments name persisted leftover-map unexplained leftover, pair segments name persisted leftover residual, pair segments name persisted leftover observed, pair segments name persisted leftover expected, and pair segments name persisted leftover-map rank. The pair-list note names leftover-map complete-case coverage only when leftoverMapCoverageCounts returns usable complete-case integers, leftover-map item complete-case coverage, leftover-map incomplete post coverage, and leftover-map incomplete item coverage when persisted. The grouping comparison strip names leftover-map complete-case coverage, leftover-map item complete-case coverage, leftover-map incomplete post coverage, leftover-map incomplete item coverage, and leftover-axis report badges with persisted leftover-map singular values under `leftover map comparison leftover axis {axis} σ {value}` with distinct comparison labels when leftoverMapCoverageCounts / leftoverMapItemCoverageCounts / leftoverMapIncompletePostCount / leftoverMapIncompleteItemCount / leftoverMapCompareAxisBadge return usable values. | `LeftoverPairList`, `LeftoverMapPlot`, `ticket-list`, `post-badge` |
 | `Workspace/OperationsDashboard` | Compare Event and post counts, inspect external-information coverage, then open the cited source behind a claim, handover, or repeat-issue fact. `EvidenceReady`, `NarrowViewport`, `AnalysisPendingAndMissingEvidence`, `AnalysisFailed`, and `LoadError` cover populated, mobile, unavailable-evidence, analysis-pending, retryable failure, and transport-error states. | `--color-dashboard-*`, `OperationsDashboard` |
 | `Post/SimilarVocPanel` | Compare ontology/semantic similar VOC and prior action evidence, then open the source; unavailable states show no fabricated TEPP theta or weight. | `SimilarVocPanel.css`, `SimilarVocPanel` |
 | `Post/Recorded perspectives` | Read the imported primary and every evidence-connected additional Voice with its recorded truth state instead of flattening them into one compound category. `CombinedEvidence`, `RejectedEvidence`, and `NarrowViewport` cover desktop, rejected-evidence, and narrow layouts. | `VoicePerspectiveList`, `ticket-list`, `post-meta` |
diff --git a/frontend/package.json b/frontend/package.json
index 9b99eca3c..9750a7d2e 100644
--- a/frontend/package.json
+++ b/frontend/package.json
@@ -1,7 +1,7 @@
 {
   "name": "frontend",
   "private": true,
-  "version": "2.80.0",
+  "version": "2.81.0",
   "type": "module",
   "scripts": {
     "dev": "vite",
diff --git a/frontend/src/App.test.tsx b/frontend/src/App.test.tsx
index 085626a09..bbc95eac7 100644
--- a/frontend/src/App.test.tsx
+++ b/frontend/src/App.test.tsx
@@ -4200,8 +4200,8 @@ describe("App, authenticated", () => {
     expect(await screen.findByLabelText("Leftover pairs")).toBeInTheDocument();
     expect(screen.getByLabelText("Leftover-map graphic display")).toBeInTheDocument();
     expect(screen.getByLabelText("Leftover map comparison graphic")).toBeInTheDocument();
-    expect(screen.getByText("leftover-map axis 1 (82%)")).toBeInTheDocument();
-    expect(screen.getByText("leftover-map axis 2 (18%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 1 σ 1.84 (82%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 2 σ 0.86 (18%)")).toBeInTheDocument();
     expect(screen.getByText("leftover map comparison graphic leftover-map axis 1 σ 1.84 (82%)")).toBeInTheDocument();
     expect(screen.getByText("leftover map comparison graphic leftover-map axis 2 σ 0.86 (18%)")).toBeInTheDocument();
     expect(
@@ -4335,6 +4335,12 @@ describe("App, authenticated", () => {
         "leftover map comparison graphic leftover-map axis 2 σ 0.86 (18%)",
       ),
     ).toBeInTheDocument();
+    expect(
+      within(screen.getByLabelText("Grouping comparison")).queryByText("leftover-map axis 1 σ 1.84 (82%)"),
+    ).not.toBeInTheDocument();
+    expect(
+      within(screen.getByLabelText("Grouping comparison")).queryByText("leftover-map axis 2 σ 0.86 (18%)"),
+    ).not.toBeInTheDocument();
     expect(
       within(screen.getByLabelText("Grouping comparison")).queryByText("leftover-map axis 1 (82%)"),
     ).not.toBeInTheDocument();
diff --git a/frontend/src/components/LeftoverMapPlot.test.tsx b/frontend/src/components/LeftoverMapPlot.test.tsx
index ed9b89639..5adcea2ac 100644
--- a/frontend/src/components/LeftoverMapPlot.test.tsx
+++ b/frontend/src/components/LeftoverMapPlot.test.tsx
@@ -164,8 +164,8 @@ describe("LeftoverMapPlot", () => {
     expect(
       screen.getByRole("button", { name: "Open leftover-map post Public post at ξ (0.00, 0.00)" }),
     ).toBeInTheDocument();
-    expect(screen.getByText("leftover-map axis 1 (0%)")).toBeInTheDocument();
-    expect(screen.getByText("leftover-map axis 2 (0%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 1 σ 0.00 (0%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 2 σ 0.00 (0%)")).toBeInTheDocument();
     expect(screen.getAllByLabelText("leftover-map axis 1 tick 0.00").length).toBeGreaterThan(0);
     expect(screen.queryByLabelText("leftover-map axis 1 tick +1.00")).not.toBeInTheDocument();
     expect(screen.getByLabelText("leftover-map distance d 0.00")).toBeInTheDocument();
@@ -180,7 +180,7 @@ describe("LeftoverMapPlot", () => {
     expect(screen.getByLabelText("leftover-map rank rank 0")).toBeInTheDocument();
   });
 
-  it("captions leftover-map axes with persisted leftover-map axis share", () => {
+  it("captions leftover-map axes with persisted leftover-map singular values and leftover-map axis share", () => {
     render(
       <LeftoverMapPlot
         pairs={PAIRS}
@@ -192,11 +192,11 @@ describe("LeftoverMapPlot", () => {
         onSelectPost={vi.fn()}
       />,
     );
-    expect(screen.getByText("leftover-map axis 1 (82%)")).toBeInTheDocument();
-    expect(screen.getByText("leftover-map axis 2 (18%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 1 σ 1.84 (82%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 2 σ 0.86 (18%)")).toBeInTheDocument();
   });
 
-  it("keeps existing leftover-map axis text when share is missing or non-finite", () => {
+  it("captions leftover-map graphic-display singular values when share is missing or non-finite", () => {
     render(
       <LeftoverMapPlot
         pairs={PAIRS}
@@ -207,12 +207,30 @@ describe("LeftoverMapPlot", () => {
         onSelectPost={vi.fn()}
       />,
     );
-    expect(screen.getByText("leftover-map axis 1")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 1 σ 1.84")).toBeInTheDocument();
     expect(screen.getByText("leftover-map axis 2")).toBeInTheDocument();
     expect(screen.queryByText(/leftover-map axis 1 \(/)).not.toBeInTheDocument();
     expect(screen.queryByText(/leftover-map axis 2 \(/)).not.toBeInTheDocument();
   });
 
+  it("omits leftover-map graphic-display singular values independently of leftover-map axis share", () => {
+    render(
+      <LeftoverMapPlot
+        pairs={PAIRS}
+        leftoverMapAxes={[
+          { axis_index: 1, leftover_singular_value: Number.NaN, leftover_share: 0.82 },
+          { axis_index: 2, leftover_singular_value: -0.01, leftover_share: 0.18 },
+        ]}
+        criterionLabel={criterionLabel}
+        onSelectPost={vi.fn()}
+      />,
+    );
+    expect(screen.getByText("leftover-map axis 1 (82%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 2 (18%)")).toBeInTheDocument();
+    expect(screen.queryByText("leftover-map axis 1 σ 1.84 (82%)")).not.toBeInTheDocument();
+    expect(screen.queryByText("leftover-map axis 2 σ 0.86 (18%)")).not.toBeInTheDocument();
+  });
+
   it("omits leftover-map distance on a pair segment when d is missing", () => {
     render(
       <LeftoverMapPlot
@@ -845,6 +863,8 @@ describe("LeftoverMapPlot", () => {
     ).toBeInTheDocument();
     expect(screen.getByText("leftover map comparison graphic leftover-map axis 1 σ 1.84 (82%)")).toBeInTheDocument();
     expect(screen.getByText("leftover map comparison graphic leftover-map axis 2 σ 0.86 (18%)")).toBeInTheDocument();
+    expect(screen.queryByText("leftover-map axis 1 σ 1.84 (82%)")).not.toBeInTheDocument();
+    expect(screen.queryByText("leftover-map axis 2 σ 0.86 (18%)")).not.toBeInTheDocument();
     expect(screen.queryByText("leftover-map axis 1 (82%)")).not.toBeInTheDocument();
     expect(screen.queryByText("leftover-map axis 2 (18%)")).not.toBeInTheDocument();
   });
diff --git a/frontend/src/components/LeftoverMapPlot.tsx b/frontend/src/components/LeftoverMapPlot.tsx
index a888a56e1..cad1f961d 100644
--- a/frontend/src/components/LeftoverMapPlot.tsx
+++ b/frontend/src/components/LeftoverMapPlot.tsx
@@ -25,10 +25,10 @@ import {
   LEFTOVER_MAP_COMPARE_PLOT_AXIS_1,
   LEFTOVER_MAP_COMPARE_PLOT_AXIS_2,
   LEFTOVER_MAP_COMPARE_PLOT_AXIS_SHARE,
-  LEFTOVER_MAP_PLOT_AXIS_SHARE,
 } from "../leftoverMapPlotAxisShare";
 import {
   formatLeftoverMapPlotAxisSingular,
+  leftoverMapPlotAxisBadge,
   leftoverSingularForAxis,
   LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR,
   LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR_SHARE,
@@ -86,13 +86,11 @@ function leftoverMapPlotAxisText(
   leftoverMapAxes: LeftoverMapAxis[] | undefined,
   variant: LeftoverMapPlotVariant,
 ): string {
-  const percent = formatLeftoverMapPlotAxisShare(
-    leftoverShareForAxis(leftoverMapAxes, axisIndex),
-  );
+  const leftoverShare = leftoverShareForAxis(leftoverMapAxes, axisIndex);
+  const leftoverSingular = leftoverSingularForAxis(leftoverMapAxes, axisIndex);
   if (variant === "comparison") {
-    const singular = formatLeftoverMapPlotAxisSingular(
-      leftoverSingularForAxis(leftoverMapAxes, axisIndex),
-    );
+    const percent = formatLeftoverMapPlotAxisShare(leftoverShare);
+    const singular = formatLeftoverMapPlotAxisSingular(leftoverSingular);
     if (singular === null && percent === null) {
       return t(axisIndex === 1 ? LEFTOVER_MAP_COMPARE_PLOT_AXIS_1 : LEFTOVER_MAP_COMPARE_PLOT_AXIS_2);
     }
@@ -108,10 +106,11 @@ function leftoverMapPlotAxisText(
       share: percent as string,
     });
   }
-  if (percent === null) {
+  const badge = leftoverMapPlotAxisBadge(axisIndex, leftoverSingular, leftoverShare);
+  if (badge === null) {
     return t(axisIndex === 1 ? "leftover-map axis 1" : "leftover-map axis 2");
   }
-  return tf(LEFTOVER_MAP_PLOT_AXIS_SHARE, { axis: axisIndex, share: percent });
+  return tf(badge.key, badge.values);
 }
 
 /**
@@ -119,7 +118,8 @@ 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.
+ * leftover-map singular values ``σ_k`` and Gabriel inertia share when finite,
+ * including rank-0 zero-share axes.
  * Axis ticks name persisted leftover-map coordinates so ξ / ζ on the
  * pair row match the plot. Pair segments name persisted leftover-map
  * distance ``d``, leftover-map reconstruction ``R̂``, leftover-map
@@ -208,7 +208,8 @@ function leftoverMapPlotAxisText(
  * labels. ADR 0322 captions leftover-axis report badges with persisted
  * leftover-map singular values, not this graphic. ADR 0323 captions leftover-axis
  * report badges on the grouping comparison strip with persisted leftover-map
- * singular values, not this graphic.
+ * singular values, not this graphic. ADR 0324 captions leftover-map
+ * graphic-display axes with persisted leftover-map singular values.
  * Never invent a leftover score.
  */
 export function LeftoverMapPlot({
diff --git a/frontend/src/components/LeftoverPairList.test.tsx b/frontend/src/components/LeftoverPairList.test.tsx
index 230f10de2..6972dd29b 100644
--- a/frontend/src/components/LeftoverPairList.test.tsx
+++ b/frontend/src/components/LeftoverPairList.test.tsx
@@ -204,8 +204,8 @@ describe("LeftoverPairList", () => {
         name: "Open leftover-map post Public post at ξ (+0.50, +0.10)",
       }),
     );
-    expect(screen.getByText("leftover-map axis 1 (82%)")).toBeInTheDocument();
-    expect(screen.getByText("leftover-map axis 2 (18%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 1 σ 1.84 (82%)")).toBeInTheDocument();
+    expect(screen.getByText("leftover-map axis 2 σ 0.86 (18%)")).toBeInTheDocument();
     expect(screen.getByLabelText("Leftover-map graphic coverage")).toHaveTextContent(
       "Leftover map used 2 of 3 scored posts (complete-case)",
     );
diff --git a/frontend/src/i18n.test.ts b/frontend/src/i18n.test.ts
index ecfc52183..c67c890cd 100644
--- a/frontend/src/i18n.test.ts
+++ b/frontend/src/i18n.test.ts
@@ -66,6 +66,8 @@ describe("i18n", () => {
     "leftover-map axis 1",
     "leftover-map axis 2",
     "leftover-map axis {axis} ({share}%)",
+    "leftover-map axis {axis} σ {value}",
+    "leftover-map axis {axis} σ {value} ({share}%)",
     "leftover-map axis {axis} tick {value}",
     "leftover-map distance {label}",
     "leftover-map reconstruction {label}",
@@ -1111,6 +1113,28 @@ describe("i18n", () => {
     expect(tf("leftover-map axis {axis} ({share}%)", { axis: 1, share: "82" })).toBe(expected);
   });
 
+  it.each([
+    ["ko", "잔여 지도 축 1 σ 1.84"],
+    ["zh", "残差图轴 1 σ 1.84"],
+    ["ja", "残差マップ軸 1 σ 1.84"],
+    ["vi", "trục bản đồ phần dư 1 σ 1.84"],
+  ] as const)("formats leftover-map plot axis singular values in %s", (locale, expected) => {
+    setLocale(locale);
+    expect(tf("leftover-map axis {axis} σ {value}", { axis: 1, value: "1.84" })).toBe(expected);
+  });
+
+  it.each([
+    ["ko", "잔여 지도 축 1 σ 1.84 (82%)"],
+    ["zh", "残差图轴 1 σ 1.84 (82%)"],
+    ["ja", "残差マップ軸 1 σ 1.84 (82%)"],
+    ["vi", "trục bản đồ phần dư 1 σ 1.84 (82%)"],
+  ] as const)("formats leftover-map plot axis singular share in %s", (locale, expected) => {
+    setLocale(locale);
+    expect(
+      tf("leftover-map axis {axis} σ {value} ({share}%)", { axis: 1, value: "1.84", share: "82" }),
+    ).toBe(expected);
+  });
+
   it.each([
     ["ko", "IRT 주효과 이후 관측 Y 2.40와 기대 E 2.00를 읽은 다음, 이 글을 여세요."],
     ["zh", "阅读 IRT 主效应后的观测 Y 2.40 与期望 E 2.00，然后打开这篇帖子。"],
diff --git a/frontend/src/i18n.ts b/frontend/src/i18n.ts
index 52cf6a35e..ec4b31d06 100644
--- a/frontend/src/i18n.ts
+++ b/frontend/src/i18n.ts
@@ -647,6 +647,8 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
     "leftover-map axis 1": "잔여 지도 축 1",
     "leftover-map axis 2": "잔여 지도 축 2",
     "leftover-map axis {axis} ({share}%)": "잔여 지도 축 {axis} ({share}%)",
+    "leftover-map axis {axis} σ {value}": "잔여 지도 축 {axis} σ {value}",
+    "leftover-map axis {axis} σ {value} ({share}%)": "잔여 지도 축 {axis} σ {value} ({share}%)",
     "leftover-map axis {axis} tick {value}": "잔여 지도 축 {axis} 눈금 {value}",
     "leftover-map distance {label}": "잔여 지도 거리 {label}",
     "leftover-map reconstruction {label}": "잔여 지도 재구성 {label}",
@@ -1297,6 +1299,8 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
     "leftover-map axis 1": "残差图轴 1",
     "leftover-map axis 2": "残差图轴 2",
     "leftover-map axis {axis} ({share}%)": "残差图轴 {axis} ({share}%)",
+    "leftover-map axis {axis} σ {value}": "残差图轴 {axis} σ {value}",
+    "leftover-map axis {axis} σ {value} ({share}%)": "残差图轴 {axis} σ {value} ({share}%)",
     "leftover-map axis {axis} tick {value}": "残差图轴 {axis} 刻度 {value}",
     "leftover-map distance {label}": "残差图距离 {label}",
     "leftover-map reconstruction {label}": "残差图重建 {label}",
@@ -1951,6 +1955,8 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
     "leftover-map axis 1": "残差マップ軸 1",
     "leftover-map axis 2": "残差マップ軸 2",
     "leftover-map axis {axis} ({share}%)": "残差マップ軸 {axis} ({share}%)",
+    "leftover-map axis {axis} σ {value}": "残差マップ軸 {axis} σ {value}",
+    "leftover-map axis {axis} σ {value} ({share}%)": "残差マップ軸 {axis} σ {value} ({share}%)",
     "leftover-map axis {axis} tick {value}": "残差マップ軸 {axis} 目盛 {value}",
     "leftover-map distance {label}": "残差マップ距離 {label}",
     "leftover-map reconstruction {label}": "残差マップ再構成 {label}",
@@ -2608,6 +2614,8 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
     "leftover-map axis 1": "trục bản đồ phần dư 1",
     "leftover-map axis 2": "trục bản đồ phần dư 2",
     "leftover-map axis {axis} ({share}%)": "trục bản đồ phần dư {axis} ({share}%)",
+    "leftover-map axis {axis} σ {value}": "trục bản đồ phần dư {axis} σ {value}",
+    "leftover-map axis {axis} σ {value} ({share}%)": "trục bản đồ phần dư {axis} σ {value} ({share}%)",
     "leftover-map axis {axis} tick {value}": "vạch trục bản đồ phần dư {axis} {value}",
     "leftover-map distance {label}": "khoảng cách bản đồ phần dư {label}",
     "leftover-map reconstruction {label}": "tái dựng bản đồ phần dư {label}",
diff --git a/frontend/src/leftoverMapPlotAxisSingular.test.ts b/frontend/src/leftoverMapPlotAxisSingular.test.ts
index bd36ce16a..4e47cfb21 100644
--- a/frontend/src/leftoverMapPlotAxisSingular.test.ts
+++ b/frontend/src/leftoverMapPlotAxisSingular.test.ts
@@ -2,6 +2,7 @@ import { describe, expect, it } from "vitest";
 import {
   formatLeftoverMapPlotAxisSingular,
   leftoverMapCompareAxisBadge,
+  leftoverMapPlotAxisBadge,
   leftoverSingularForAxis,
   LEFTOVER_MAP_COMPARE_AXIS_CAPTION,
   LEFTOVER_MAP_COMPARE_AXIS_LABEL,
@@ -13,7 +14,10 @@ import {
   LEFTOVER_MAP_PLOT_AXIS_SINGULAR,
   LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE,
 } from "./leftoverMapPlotAxisSingular";
-import { LEFTOVER_MAP_COMPARE_PLOT_AXIS_SHARE } from "./leftoverMapPlotAxisShare";
+import {
+  LEFTOVER_MAP_COMPARE_PLOT_AXIS_SHARE,
+  LEFTOVER_MAP_PLOT_AXIS_SHARE,
+} from "./leftoverMapPlotAxisShare";
 import { LEFTOVER_MAP_COMPARE_PLOT_TICK } from "./leftoverMapPlotLayout";
 import { LEFTOVER_MAP_AXIS_BADGE_SINGULAR } from "./leftoverMapAxisBadge";
 
@@ -168,3 +172,58 @@ describe("leftover map comparison leftover-axis report badges", () => {
     expect(LEFTOVER_MAP_COMPARE_AXIS_CAPTION).toContain("Open a leftover pair");
   });
 });
+
+describe("leftover-map graphic-display axis singular badges", () => {
+  it("names persisted leftover-map singular values on leftover-map graphic-display axes", () => {
+    expect(leftoverMapPlotAxisBadge(1, 1.84, 0.82)).toEqual({
+      key: LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE,
+      values: { axis: 1, value: "1.84", share: "82" },
+    });
+    expect(leftoverMapPlotAxisBadge(2, 0.86, 0.18)).toEqual({
+      key: LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE,
+      values: { axis: 2, value: "0.86", share: "18" },
+    });
+  });
+
+  it("names rank-0 zero leftover-map singular values on leftover-map graphic-display axes", () => {
+    expect(leftoverMapPlotAxisBadge(1, 0, 0)).toEqual({
+      key: LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE,
+      values: { axis: 1, value: "0.00", share: "0" },
+    });
+  });
+
+  it("omits leftover-map singular values independently of leftover-map axis share", () => {
+    expect(leftoverMapPlotAxisBadge(1, Number.NaN, 0.82)).toEqual({
+      key: LEFTOVER_MAP_PLOT_AXIS_SHARE,
+      values: { axis: 1, share: "82" },
+    });
+    expect(leftoverMapPlotAxisBadge(2, -0.01, 0.18)).toEqual({
+      key: LEFTOVER_MAP_PLOT_AXIS_SHARE,
+      values: { axis: 2, share: "18" },
+    });
+    expect(leftoverMapPlotAxisBadge(1, 1.84, Number.NaN)).toEqual({
+      key: LEFTOVER_MAP_PLOT_AXIS_SINGULAR,
+      values: { axis: 1, value: "1.84" },
+    });
+    expect(leftoverMapPlotAxisBadge(1, null, null)).toBeNull();
+  });
+
+  it("does not invent leftover-map singular values from leftover-map axis share", () => {
+    expect(leftoverMapPlotAxisBadge(1, undefined, 0.82)?.key).toBe(LEFTOVER_MAP_PLOT_AXIS_SHARE);
+    expect(leftoverMapPlotAxisBadge(1, undefined, 0.82)?.values.value).toBeUndefined();
+  });
+
+  it("stays distinct from leftover-axis, comparison leftover-axis, and comparison graphic copy", () => {
+    expect(LEFTOVER_MAP_PLOT_AXIS_SINGULAR).toBe("leftover-map axis {axis} σ {value}");
+    expect(LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE).toBe(
+      "leftover-map axis {axis} σ {value} ({share}%)",
+    );
+    expect(LEFTOVER_MAP_PLOT_AXIS_SINGULAR).not.toBe(LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR);
+    expect(LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE).not.toBe(
+      LEFTOVER_MAP_COMPARE_PLOT_AXIS_SINGULAR_SHARE,
+    );
+    expect(LEFTOVER_MAP_PLOT_AXIS_SINGULAR).not.toBe(LEFTOVER_MAP_COMPARE_AXIS_SINGULAR);
+    expect(LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE).not.toBe(LEFTOVER_MAP_AXIS_BADGE_SINGULAR);
+    expect(LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE).not.toBe(LEFTOVER_MAP_PLOT_AXIS_SHARE);
+  });
+});
diff --git a/frontend/src/leftoverMapPlotAxisSingular.ts b/frontend/src/leftoverMapPlotAxisSingular.ts
index 70130898e..8d0ab36d9 100644
--- a/frontend/src/leftoverMapPlotAxisSingular.ts
+++ b/frontend/src/leftoverMapPlotAxisSingular.ts
@@ -1,7 +1,10 @@
-/** Caption leftover-map plot axes with persisted Gabriel singular values. */
+/** Caption leftover-map plot axes with persisted Gabriel singular values (ADR 0324). */
 
 import type { LeftoverMapAxis } from "./api";
-import { formatLeftoverMapPlotAxisShare } from "./leftoverMapPlotAxisShare";
+import {
+  formatLeftoverMapPlotAxisShare,
+  LEFTOVER_MAP_PLOT_AXIS_SHARE,
+} from "./leftoverMapPlotAxisShare";
 
 export const LEFTOVER_MAP_PLOT_AXIS_SINGULAR = "leftover-map axis {axis} σ {value}";
 
@@ -63,6 +66,28 @@ export function formatLeftoverMapPlotAxisSingular(
   return leftoverSingular.toFixed(2);
 }
 
+export function leftoverMapPlotAxisBadge(
+  axisIndex: number,
+  leftoverSingular: number | null | undefined,
+  leftoverShare: number | null | undefined,
+): LeftoverMapCompareAxisBadge | null {
+  const singular = formatLeftoverMapPlotAxisSingular(leftoverSingular);
+  const percent = formatLeftoverMapPlotAxisShare(leftoverShare);
+  if (singular === null && percent === null) {
+    return null;
+  }
+  if (singular === null && percent !== null) {
+    return { key: LEFTOVER_MAP_PLOT_AXIS_SHARE, values: { axis: axisIndex, share: percent } };
+  }
+  if (singular !== null && percent === null) {
+    return { key: LEFTOVER_MAP_PLOT_AXIS_SINGULAR, values: { axis: axisIndex, value: singular } };
+  }
+  return {
+    key: LEFTOVER_MAP_PLOT_AXIS_SINGULAR_SHARE,
+    values: { axis: axisIndex, value: singular as string, share: percent as string },
+  };
+}
+
 export function leftoverMapCompareAxisBadge(
   axisIndex: number,
   leftoverSingular: number | null | undefined,
diff --git a/frontend/src/leftoverMapPlotLayout.test.ts b/frontend/src/leftoverMapPlotLayout.test.ts
index 88d118208..23a3ab3cc 100644
--- a/frontend/src/leftoverMapPlotLayout.test.ts
+++ b/frontend/src/leftoverMapPlotLayout.test.ts
@@ -1369,6 +1369,7 @@ describe("leftover map comparison graphic labels", () => {
     expect(LEFTOVER_MAP_COMPARE_PLOT_TICK).not.toBe(
       "leftover map comparison graphic leftover-map axis {axis} σ {value}",
     );
+    expect(LEFTOVER_MAP_COMPARE_PLOT_TICK).not.toBe("leftover-map axis {axis} σ {value}");
     expect(LEFTOVER_MAP_COMPARE_PLOT_TICK).not.toBe(
       "leftover map comparison leftover axis {axis} σ {value}",
     );
diff --git a/frontend/src/leftoverMapPlotLayout.ts b/frontend/src/leftoverMapPlotLayout.ts
index 217a56bae..df6cb0caa 100644
--- a/frontend/src/leftoverMapPlotLayout.ts
+++ b/frontend/src/leftoverMapPlotLayout.ts
@@ -1,5 +1,7 @@
 /** Gabriel leftover-map graphic display of persisted ``ξ_{1:2}`` / ``ζ_{1:2}``.
  *  Leftover-map axis share captions axes 1 and 2 when finite (ADR 0269).
+ *  Leftover-map singular values caption leftover-map graphic-display axes when
+ *  finite (ADR 0324).
  *  Axis ticks name persisted leftover-map coordinates (ADR 0270).
  *  Pair segments name persisted leftover-map distance ``d`` (ADR 0271),
  *  persisted leftover-map reconstruction ``R̂`` (ADR 0272), persisted
@@ -85,6 +87,8 @@
  *  singular values, not this graphic.
  *  ADR 0323 captions leftover-axis report badges on the grouping comparison strip
  *  with persisted leftover-map singular values, not this graphic.
+ *  ADR 0324 captions leftover-map graphic-display axes with persisted leftover-map
+ *  singular values `σ_k`.
  */
 
 import { formatLeftoverMapCoordinatePair } from "./leftoverMapCoordinates";
diff --git a/pyproject.toml b/pyproject.toml
index 95202a36c..d46ab31c7 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [project]
 name = "lineageweave"
-version = "2.80.0"
+version = "2.81.0"
 description = "Reconstructs git-branch-style lineage DAGs from scattered short records using multi-channel score fusion and LLM adjudication."
 readme = "README.md"
 license = { text = "MIT" }