From b15d0ee31f6dc71f5dae2839a45d43b6716e5911 Mon Sep 17 00:00:00 2001
From: Seongho Bae <me@seonghobae.me>
Date: Sun, 23 Aug 2026 23:21:05 +0000
Subject: [PATCH 1/7] feat: name leftover-map explained share on leftover pairs
 (v2.12.28)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Persist explained leftover share e = R̂_c² / R̃² of centered leftover
on leftover post–criterion pairs (ADR 0184). Two-axis reconstruction
R̂_c stays internal. A reconstructed rank-1 cell stores share 1 even
when mean(R) ≠ 0. A 0/0 origin cell stores 0. Fallback omits the share.
Do not persist leftover-map unexplained leftover share s or reconstruction R̂.
---
 AGENTS.md                                     |   8 +-
 ARCHITECTURE.md                               |   5 +-
 .../2.12.28-leftover-map-explained-share.md   |   9 ++
 CHANGELOG.md                                  |  11 ++
 CLAUDE.md                                     |   4 +-
 backend/app/report_ingestion.py               |  14 +-
 backend/tests/test_api.py                     |  14 ++
 docker/postgres-init/migrate.sh               |   2 +-
 .../0003-fast-mlsirm-report-integration.md    |   9 +-
 docs/adr/0048-persist-lsirm-leftover-pairs.md |   7 +-
 docs/adr/0049-leftover-pair-report-ui.md      |   9 +-
 docs/adr/0184-leftover-map-explained-share.md | 104 ++++++++++++
 frontend/package.json                         |   2 +-
 frontend/src/App.test.tsx                     |   8 +-
 frontend/src/App.tsx                          |  37 ++++-
 frontend/src/api.ts                           |   1 +
 frontend/src/components/AdminPanel.tsx        |   6 +-
 frontend/src/i18n.test.ts                     |  34 ++++
 frontend/src/i18n.ts                          |  44 ++++++
 .../src/leftoverMapExplainedShare.test.ts     |  18 +++
 frontend/src/leftoverMapExplainedShare.ts     |  13 ++
 lineageweave/leftover_pairs.py                | 148 ++++++++++++++----
 ...84_report_leftover_map_explained_share.sql |  31 ++++
 ...84_report_leftover_map_explained_share.sql |   7 +
 pyproject.toml                                |   2 +-
 scripts/seed_demo_data.py                     |   7 +-
 tests/test_leftover_pairs.py                  | 127 ++++++++++++++-
 tests/test_migration_replay.py                |   1 +
 tests/test_period_report.py                   |   6 +
 tests/test_schema.py                          |  34 ++++
 uv.lock                                       |   2 +-
 31 files changed, 661 insertions(+), 63 deletions(-)
 create mode 100644 CHANGELOG.d/2.12.28-leftover-map-explained-share.md
 create mode 100644 docs/adr/0184-leftover-map-explained-share.md
 create mode 100644 frontend/src/leftoverMapExplainedShare.test.ts
 create mode 100644 frontend/src/leftoverMapExplainedShare.ts
 create mode 100644 migrations/0184_report_leftover_map_explained_share.sql
 create mode 100644 migrations/rollback/0184_report_leftover_map_explained_share.sql

diff --git a/AGENTS.md b/AGENTS.md
index 1728f9e61..546b8059c 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -186,12 +186,14 @@ in the same spirit) -- never against real data, per the hard rule above.
 against a live local stack (`make up`) and self-skip without one -- see
 [README.md](README.md#local-product-stack-docker-compose).
 
-Period leftover pairs (ADR 0017 / 0018) are computed in
+Period leftover pairs (ADR 0048 / 0049 / 0184) are computed in
 `lineageweave/leftover_pairs.py` from the residual after a real
 GRM/GPCM score, never invented. Missing cells stay out of the
 Gabriel factorization. Closest and farthest post–criterion pairs
-persist to `report_leftover_pair` and sit above the member list so
-a click opens that post.
+persist to `report_leftover_pair` and sit above the member list with
+explained leftover share `e = R̂_c² / R̃²` of centered leftover next
+to leftover-map distance `d` so a click opens that post. Two-axis
+reconstruction `R̂_c` is not persisted.
 
 `frontend/` has its own toolchain (Node pinned via `frontend/mise.toml`,
 pnpm via Corepack -- do not add a second Node package manager or a
diff --git a/ARCHITECTURE.md b/ARCHITECTURE.md
index d0280ff97..f1b6d1032 100644
--- a/ARCHITECTURE.md
+++ b/ARCHITECTURE.md
@@ -588,8 +588,9 @@ on those same fixed parameters (Kim, 2006 FIPC). After scoring,
 `information_polytomous` ranks the shared-bank items by Fisher
 information at the group's mean θ (Lord, 1980 max-info CAT). Rankings
 persist to `report_item_information`. After those IRT main effects,
-residual SVD leftover pairs (Jeon et al., 2021; ADR 0017) persist to
-`report_leftover_pair`. Results persist to
+residual SVD leftover pairs (Jeon et al., 2021; ADR 0048 / 0184) persist to
+`report_leftover_pair` with explained leftover share `e = R̂_c² / R̃²` of
+centered leftover named on the pair row. Results persist to
 `report_period_score` / `report_member_score`.
 `GET /api/reports/{grouping}` lists the trend;
 `GET /api/reports/{grouping}/{period}` is ABAC-filtered;
diff --git a/CHANGELOG.d/2.12.28-leftover-map-explained-share.md b/CHANGELOG.d/2.12.28-leftover-map-explained-share.md
new file mode 100644
index 000000000..7f9059805
--- /dev/null
+++ b/CHANGELOG.d/2.12.28-leftover-map-explained-share.md
@@ -0,0 +1,9 @@
+## 2.12.28 — Leftover-map explained leftover share
+
+- Persist explained leftover share `e = R̂_c² / R̃²` of centered
+  leftover on leftover post–criterion pairs (ADR 0184). After
+  `make seed`, closest and farthest leftover pairs sit above the
+  member list with `R̂²/R̃²` next to leftover-map distance `d`; click
+  opens that post. Omit the badge when the share is missing. Never
+  invent a leftover score. Do not persist leftover-map unexplained
+  leftover share `s`, unexplained leftover `U`, or reconstruction `R̂`.
diff --git a/CHANGELOG.md b/CHANGELOG.md
index c8ed1a099..461121b69 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,6 +12,17 @@ All notable changes to this project are documented here. Format follows
   environment, so local OIDC and synthetic-data workflows resolve the same
   pinned dependencies as CI.
 
+## [2.12.28] - 2026-08-24
+
+### Added
+
+- Period leftover pair rows now name explained leftover share
+  `e = R̂_c² / R̃²` of centered leftover next to leftover-map distance
+  `d`, then open that post (Gabriel, 1971; Jeon et al., 2021, eq. 3;
+  ADR 0184). A missing share omits the badge rather than inventing a
+  leftover score. Two-axis reconstruction `R̂_c` stays internal and is
+  not persisted. Unexplained leftover share `s` is not persisted here.
+
 ## [2.12.6] - 2026-08-20
 
 ### Added
diff --git a/CLAUDE.md b/CLAUDE.md
index 1bcf50763..929fd9c63 100644
--- a/CLAUDE.md
+++ b/CLAUDE.md
@@ -54,7 +54,9 @@ chip name contains `Corporate entity: Demo Corp` and the persisted
 mean θ. The period-report panel says Demo Corp is the opened grouping
 and to read its mean θ and member posts, then open a post. Those
 members land immediately under that next action, ahead of Other Corp
-and the week strip. Opening Public post names the next action: read
+and the week strip. After `make seed`, leftover closest/farthest pairs
+sit above the member list with explained leftover share `R̂²/R̃²`
+next to leftover-map distance `d`. Opening Public post names the next action: read
 Event Lineage, Keyman, and evaluation on that post. The popup Event
 Lineage DAG marks that post current. After that current node, the
 popup names Keyman and evaluation as the next read. After landed
diff --git a/backend/app/report_ingestion.py b/backend/app/report_ingestion.py
index 50614b0ad..95802abfe 100644
--- a/backend/app/report_ingestion.py
+++ b/backend/app/report_ingestion.py
@@ -443,8 +443,9 @@ async def persist_period_report(
             """
             insert into report_leftover_pair (
                 grouping_kind, grouping_key, period_code, rubric_version,
-                pair_kind, post_id, criterion_code, leftover_distance, leftover_residual
-            ) values ($1,$2,$3,$4,$5,$6,$7,$8,$9)
+                pair_kind, post_id, criterion_code, leftover_distance, leftover_residual,
+                leftover_map_explained_share
+            ) values ($1,$2,$3,$4,$5,$6,$7,$8,$9,$10)
             """,
             grouping_kind,
             grouping_key,
@@ -455,6 +456,7 @@ async def persist_period_report(
             pair.criterion_code,
             pair.leftover_distance,
             pair.leftover_residual,
+            pair.leftover_map_explained_share,
         )
 
 
@@ -601,7 +603,8 @@ async def fetch_period_reports(
     leftover = await conn.fetch(  # nosemgrep: python.lang.security.audit.sqli.asyncpg-sqli.asyncpg-sqli
         f"""
         select lp.grouping_key, lp.pair_kind, lp.post_id, lp.criterion_code,
-               lp.leftover_distance, lp.leftover_residual, p.post_title,
+               lp.leftover_distance, lp.leftover_residual, lp.leftover_map_explained_share,
+               p.post_title,
                p.visibility_code, p.corporate_entity_id,
                ({_SOURCE_CONTEXT_PRESENT_SQL}) as has_real_source_context
         from report_leftover_pair lp
@@ -698,6 +701,11 @@ async def fetch_period_reports(
                         "criterion_code": str(row["criterion_code"]),
                         "leftover_distance": float(row["leftover_distance"]),
                         "leftover_residual": float(row["leftover_residual"]),
+                        "leftover_map_explained_share": (
+                            None
+                            if row["leftover_map_explained_share"] is None
+                            else float(row["leftover_map_explained_share"])
+                        ),
                         "visibility_code": row["visibility_code"],
                         "corporate_entity_id": str(row["corporate_entity_id"]),
                         "has_real_source_context": bool(row["has_real_source_context"]),
diff --git a/backend/tests/test_api.py b/backend/tests/test_api.py
index 438b4786a..4fb8f8f12 100644
--- a/backend/tests/test_api.py
+++ b/backend/tests/test_api.py
@@ -113,6 +113,11 @@
     / "migrations"
     / "0102_project_bound_summary_event.sql"
 )
+_LEFTOVER_MAP_EXPLAINED_SHARE_MIGRATION = (
+    Path(__file__).resolve().parents[2]
+    / "migrations"
+    / "0184_report_leftover_map_explained_share.sql"
+)
 
 
 def _postgres_available() -> bool:
@@ -226,6 +231,7 @@ def seeded_db(demo_analyst_token):
             cur.execute(_MAJOR_EVENT_ACTION_MIGRATION.read_text())
             cur.execute(_PROJECT_BOUND_ACTION_MIGRATION.read_text())
             cur.execute(_PROJECT_BOUND_EVENT_MIGRATION.read_text())
+            cur.execute(_LEFTOVER_MAP_EXPLAINED_SHARE_MIGRATION.read_text())
             cur.execute(
                 "insert into common_lookup_value (lookup_category, lookup_code, lookup_label) values "
                 "('corporate_entity_level', 'group', 'Group'), "
@@ -4518,6 +4524,14 @@ def test_seed_period_report_surfaces_on_get_reports(client, demo_analyst_token,
     assert leftover_kinds <= {"closest", "farthest"}
     assert all(pair["post_title"] for pair in high_report.get("leftover_pairs", []))
     assert all(pair["leftover_distance"] >= 0 for pair in high_report.get("leftover_pairs", []))
+    for pair in high_report.get("leftover_pairs", []):
+        share = pair.get("leftover_map_explained_share")
+        assert share is None or isinstance(share, (int, float))
+        if share is not None:
+            assert share >= 0
+        assert "leftover_map_unexplained_share" not in pair
+        assert "leftover_map_unexplained" not in pair
+        assert "leftover_map_reconstruction" not in pair
 
     week3 = client.get(
         "/api/reports/process_unit/2026-W03",
diff --git a/docker/postgres-init/migrate.sh b/docker/postgres-init/migrate.sh
index f329117d6..b7d138710 100644
--- a/docker/postgres-init/migrate.sh
+++ b/docker/postgres-init/migrate.sh
@@ -18,7 +18,7 @@ for migration in /opt/lineageweave/migrations/*.sql; do
     migration_name=${migration##*/}
     case "$migration_name" in
         0012_*|0013_*|0014_*|0015_*|0016_*|0017_*|0018_*|0019_*|0020_*|0021_*|0022_*|0023_*|0024_*|0025_*|0026_*|0027_*|0028_*|0029_*|0030_*|0031_*|0032_*|0033_*|0034_*|0035_*|0036_*|0037_*|0038_*|0039_*|0040_*|0041_*|0042_*|0043_*|0044_*|0045_*|0046_*|0047_*|0048_*|0049_*|0050_*) ;;
-        0060_*|0100_*|0101_*|0102_*) ;;
+        0060_*|0100_*|0101_*|0102_*|0184_*) ;;
         *) continue ;;
     esac
     printf 'Applying %s\n' "$migration_name"
diff --git a/docs/adr/0003-fast-mlsirm-report-integration.md b/docs/adr/0003-fast-mlsirm-report-integration.md
index bdf234b65..d5959b2dd 100644
--- a/docs/adr/0003-fast-mlsirm-report-integration.md
+++ b/docs/adr/0003-fast-mlsirm-report-integration.md
@@ -100,9 +100,14 @@ than one large PR:
    `information_polytomous` (Lord, 1980 max-info). Persist the ranking
    (`report_item_information`) and show the rank-1 item on the Period
    reports panel. Do not reimplement an information function here.
-7. **Leftover-pair slice** (shipped in 0.71.2; ADR 0017 / 0018): after
+7. **Leftover-pair slice** (shipped in 0.71.2; ADR 0048 / 0049 / 0184): after
    IRT main effects, persist closest and farthest post–criterion pairs
-   from the residual leftover map. Do not fork LSIRM; do not invent a
+   from the residual leftover map, and name explained leftover share
+   `e = R̂_c² / R̃²` of centered leftover when Gabriel coordinates exist
+   so the leftover cell the two-axis map reconstructs is not read as
+   leftover residual or leftover-map distance. Do not persist
+   leftover-map unexplained leftover share `s` or two-axis reconstruction
+   `R̂`. Do not fork LSIRM; do not invent a
    leftover-pair API inside `fast-mlsirm` in this slice.
 
 **TEPP boundary.** [ARCHITECTURE.md](../../ARCHITECTURE.md) already
diff --git a/docs/adr/0048-persist-lsirm-leftover-pairs.md b/docs/adr/0048-persist-lsirm-leftover-pairs.md
index 8e87383f0..e724da712 100644
--- a/docs/adr/0048-persist-lsirm-leftover-pairs.md
+++ b/docs/adr/0048-persist-lsirm-leftover-pairs.md
@@ -30,7 +30,12 @@ and one `farthest` observed cell per period report in
 `report_leftover_pair` (3NF, two-or-more-word `snake_case`).
 
 The biplot lives in `lineageweave/leftover_pairs.py` so leftover
-tests do not import `period_report` or `fast_mlsirm`.
+tests do not import `period_report` or `fast_mlsirm`. Each leftover
+row also names explained leftover share `e = R̂_c² / R̃²` of
+centered leftover when Gabriel coordinates exist so the leftover
+cell the two-axis map reconstructs is not read as leftover residual
+`R` or leftover-map distance `d` (ADR 0184). Two-axis reconstruction
+`R̂_c` is computed internally and is not persisted.
 
 Cascade the rows with `report_period_score`. A leftover post must
 also be a `report_member_score` row, and the leftover criterion
diff --git a/docs/adr/0049-leftover-pair-report-ui.md b/docs/adr/0049-leftover-pair-report-ui.md
index a93985b40..91d3e7f69 100644
--- a/docs/adr/0049-leftover-pair-report-ui.md
+++ b/docs/adr/0049-leftover-pair-report-ui.md
@@ -19,8 +19,13 @@ On each period-report group, render leftover pairs **above** the
 member list. Each pair is a button: closest or farthest label, post
 title, criterion short label, leftover-map distance, and the next
 action (“Open this post to read the criterion it sat closest to /
-farthest from after main effects.”). Clicking the button opens that
-post with the same handler as a member row.
+farthest from after main effects.”). Explained leftover share next
+action: two leftover-map axes explain `e` of centered leftover after
+IRT main effects; open this post to read the named criterion. A
+missing share keeps the existing closest/farthest next action.
+Clicking the button opens that post with the same handler as a member
+row. Explained leftover share naming is
+[ADR 0184](0184-leftover-map-explained-share.md).
 
 After `make seed`, closest and farthest leftover pairs sit above the
 member list. Click a pair to open that post.
diff --git a/docs/adr/0184-leftover-map-explained-share.md b/docs/adr/0184-leftover-map-explained-share.md
new file mode 100644
index 000000000..5bd3b5481
--- /dev/null
+++ b/docs/adr/0184-leftover-map-explained-share.md
@@ -0,0 +1,104 @@
+# ADR 0184 — Name explained leftover share on period-report pair rows
+
+**Decision status:** Accepted
+**Date:** 2026-08-24
+
+Amends [ADR 0048](0048-persist-lsirm-leftover-pairs.md) and
+[ADR 0049](0049-leftover-pair-report-ui.md).
+
+## Context
+
+ADR 0048 already persists leftover-map distance `d = ‖ξ_p − ζ_i‖` and
+leftover residual `R = Y − E[Y|θ, item]` on `report_leftover_pair`.
+ADR 0049 already renders closest and farthest pairs above the member
+list and opens the named post. Distance is the Jeon et al. (2021,
+eq. 3) map gap. Gabriel (1971) reconstructs a *centered* matrix from
+the biplot as the inner product of person and item coordinates. The
+leftover map buyers read is two-axis: unused axes pad with zero, and
+hidden SVD axes after the second are dropped. Two-axis reconstruction
+`R̂_c = ξ_{1:2} · ζ_{1:2}` therefore recovers centered leftover
+`R̃ = R − center`, not raw residual `R`. Hiding explained leftover
+share `e = R̂_c² / R̃²` lets a buyer read leftover residual `R` or
+leftover-map distance `d` as the leftover the two-axis map reconstructs.
+Using raw `R` in the denominator leaves the grand mean inside the named
+leftover, so a fully reconstructed rank-1 cell would look only partly
+explained whenever `center ≠ 0`. Per-cell `e` is not `1 − U_c² / R̃²`:
+truncated two-axis reconstruction of a higher-rank cell keeps a cross
+term `2 R̂_c U_c`.
+
+This increment does not persist leftover-map reconstruction `R̂` or
+`R̂_c`, does not persist leftover-map unexplained leftover `U` or
+`U_c`, does not persist leftover-map unexplained leftover share `s`,
+does not persist leftover-map coordinates, does not name leftover-map
+inner product, cosine, or length, does not name observed `Y` /
+expected `E`, does not name leftover-map rank, does not split
+leftover-map distance onto two axes, and does not land Post quality on
+the leftover criterion. Leftover-map distance stays full-rank
+Euclidean. Reconstruction `R̂_c` is computed internally so `e` is
+honest, then discarded.
+
+The unprotected-stack reconstructions for neighbouring leftover facts
+use 0162–0183. This protected-main increment uses **0184** so it does
+not collide with leftover-map unexplained leftover share (0183),
+leftover-map unexplained leftover (0182), leftover-map reconstruction
+(0181), leftover-map length (0181 on the length stack), leftover-map
+cosine (0180), leftover-map inner product (0179), leftover residual
+disclosure (0178), leftover observed `Y` / expected `E` (0170),
+leftover-map rank (0172), two-axis leftover-map distance (0166),
+leftover coverage (0165 / 0168), leftover-map axis share (0148), or
+leftover interaction-map persistence (0121).
+
+## Decision
+
+Each leftover pair names `leftover_map_explained_share` — explained
+leftover share `e = R̂_c² / R̃²` of centered leftover after two-axis
+Gabriel reconstruction `R̂_c = ξ_{1:2} · ζ_{1:2}`. Migration `0184`
+is the single source of the column on every install path, fresh or
+existing -- shipped migrations (`0001` / `0012`) are never edited after
+the fact. The column is nullable so older leftover rows keep distance
+and residual without fabricating a share. Fallback pairs that have no
+complete-case leftover map omit the value rather than inventing one.
+A rank-0 origin map stores `0.0` (`R̃ = 0` and `R̂_c = 0`), not a
+missing value. A fully reconstructed rank-1 cell stores `1.0` even when
+the grand mean of `R` is nonzero. A non-finite or negative share stores
+null rather than inventing a leftover score. Named check
+`leftover_pair_explained_share_nonnegative_chk` rejects a stored
+negative share. Do not persist `leftover_map_unexplained_share`,
+`leftover_map_unexplained`, or `leftover_map_reconstruction`.
+
+The pair button shows `R̂²/R̃² {share}` next to leftover-map distance
+`d` when the value is a finite non-negative number. Next action: two
+leftover-map axes explain `e` of centered leftover after IRT main
+effects; open this post to read the named criterion. A missing or
+non-finite share omits the badge and keeps the existing
+closest/farthest next action. Do not invent a leftover score. Do not
+invent a theta.
+
+## Consequences
+
+`GET /api/reports/{grouping}/{period}` returns
+`leftover_map_explained_share`. After `make seed`, closest and
+farthest leftover pairs sit above the member list with named
+`R̂²/R̃²` next to `d`; click opens that post. Hidden posts stay hidden.
+
+## Related
+
+Independent of leftover interaction-map persistence, leftover-criterion
+evaluation landing, leftover residual disclosure, leftover observed
+`Y` / expected `E`, leftover-map complete-case coverage, leftover-map
+axis share, leftover pairs on the grouping comparison strip, two-axis
+leftover-map distance, leftover-map rank, leftover-map inner product,
+leftover-map cosine, leftover-map length, leftover-map reconstruction,
+leftover-map unexplained leftover, and leftover-map unexplained leftover
+share.
+
+## 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/package.json b/frontend/package.json
index e2e996bbe..4c10bd2eb 100644
--- a/frontend/package.json
+++ b/frontend/package.json
@@ -1,7 +1,7 @@
 {
   "name": "frontend",
   "private": true,
-  "version": "2.12.6",
+  "version": "2.12.28",
   "type": "module",
   "scripts": {
     "dev": "vite",
diff --git a/frontend/src/App.test.tsx b/frontend/src/App.test.tsx
index 7462abd2c..0072ac849 100644
--- a/frontend/src/App.test.tsx
+++ b/frontend/src/App.test.tsx
@@ -932,6 +932,7 @@ describe("App, authenticated", () => {
                     criterion_code: "sales_lead_specificity",
                     leftover_distance: 0.12,
                     leftover_residual: 0.4,
+                    leftover_map_explained_share: 0.88,
                   },
                   {
                     pair_kind: "farthest",
@@ -940,6 +941,7 @@ describe("App, authenticated", () => {
                     criterion_code: "general_sentiment_negative",
                     leftover_distance: 1.84,
                     leftover_residual: -1.1,
+                    leftover_map_explained_share: 0.55,
                   },
                 ],
                 members: [
@@ -3357,13 +3359,15 @@ describe("App, authenticated", () => {
     });
     expect(closestPair).toHaveTextContent("Closest leftover: Public post · sales-lead");
     expect(closestPair).toHaveTextContent(
-      "Open this post to read the criterion it sat closest to after main effects.",
+      "Two leftover-map axes explain 0.88 of centered leftover after IRT main effects. Open this post to read sales-lead.",
     );
+    expect(closestPair).toHaveTextContent("R̂²/R̃² 0.88");
     expect(closestPair).toHaveTextContent("d 0.12");
     expect(farthestPair).toHaveTextContent("Farthest leftover: Specification revision requested · negative");
     expect(farthestPair).toHaveTextContent(
-      "Open this post to read the criterion it sat farthest from after main effects.",
+      "Two leftover-map axes explain 0.55 of centered leftover after IRT main effects. Open this post to read negative.",
     );
+    expect(farthestPair).toHaveTextContent("R̂²/R̃² 0.55");
     expect(farthestPair).toHaveTextContent("d 1.84");
     const memberButton = screen.getByRole("button", { name: /open report post: public post/i });
     expect(closestPair.compareDocumentPosition(memberButton) & Node.DOCUMENT_POSITION_FOLLOWING).toBeTruthy();
diff --git a/frontend/src/App.tsx b/frontend/src/App.tsx
index 6fba0dd41..1df18fae1 100644
--- a/frontend/src/App.tsx
+++ b/frontend/src/App.tsx
@@ -101,7 +101,10 @@ import {
   tf,
   useLocale,
 } from "./i18n";
-import { rememberOidcReturnUrl, returnUrlFromLocation } from "./oidcReturnUrl";
+import {
+  formatLeftoverMapExplainedShare,
+  LEFTOVER_MAP_EXPLAINED_SHARE_ACTION,
+} from "./leftoverMapExplainedShare";
 import "./App.css";
 
 function orchestratorUnavailableMessage(err: unknown, action: string): string {
@@ -3390,15 +3393,28 @@ function ReportsPanel({
               </span>
             )}
             {report.leftover_pairs && report.leftover_pairs.length > 0 && (
-              <ul className="ticket-list" aria-label="Leftover pairs">
+              <ul className="ticket-list" aria-label={t("Leftover pairs")}>
                 {report.leftover_pairs.map((pair) => {
                   const kindLabel =
-                    pair.pair_kind === "farthest" ? "Farthest leftover" : "Closest leftover";
-                  const nextAction =
-                    pair.pair_kind === "farthest"
-                      ? "Open this post to read the criterion it sat farthest from after main effects."
-                      : "Open this post to read the criterion it sat closest to after main effects.";
+                    pair.pair_kind === "farthest" ? t("Farthest leftover") : t("Closest leftover");
                   const criterion = criterionShortLabel(pair.criterion_code);
+                  const share = formatLeftoverMapExplainedShare(
+                    pair.leftover_map_explained_share,
+                  );
+                  const shareValue =
+                    pair.leftover_map_explained_share != null &&
+                    Number.isFinite(pair.leftover_map_explained_share)
+                      ? pair.leftover_map_explained_share.toFixed(2)
+                      : "—";
+                  const nextAction =
+                    share === null
+                      ? pair.pair_kind === "farthest"
+                        ? t("Open this post to read the criterion it sat farthest from after main effects.")
+                        : t("Open this post to read the criterion it sat closest to after main effects.")
+                      : tf(LEFTOVER_MAP_EXPLAINED_SHARE_ACTION, {
+                          value: shareValue,
+                          criterion,
+                        });
                   return (
                     <li
                       key={`${pair.pair_kind}:${pair.post_id}:${pair.criterion_code}`}
@@ -3406,13 +3422,18 @@ function ReportsPanel({
                     >
                       <button
                         className="post-list-item"
-                        aria-label={`Open leftover ${pair.pair_kind} pair: ${pair.post_title} · ${criterion}`}
+                        aria-label={tf("Open leftover {kind} pair: {title} · {criterion}", {
+                          kind: pair.pair_kind,
+                          title: pair.post_title,
+                          criterion,
+                        })}
                         onClick={() => onSelectPost(pair.post_id)}
                       >
                         <span className="ticket-title">
                           {kindLabel}: {pair.post_title} · {criterion}
                         </span>
                         <span className="post-badge">{nextAction}</span>
+                        {share ? <span className="post-badge">{share}</span> : null}
                         <span className="post-badge">d {pair.leftover_distance.toFixed(2)}</span>
                       </button>
                     </li>
diff --git a/frontend/src/api.ts b/frontend/src/api.ts
index cd0141a32..2a8850940 100644
--- a/frontend/src/api.ts
+++ b/frontend/src/api.ts
@@ -759,6 +759,7 @@ export interface LeftoverPair {
   criterion_code: string;
   leftover_distance: number;
   leftover_residual: number;
+  leftover_map_explained_share?: number | null;
 }
 
 export interface PeriodGroupReport {
diff --git a/frontend/src/components/AdminPanel.tsx b/frontend/src/components/AdminPanel.tsx
index af098f827..481de567c 100644
--- a/frontend/src/components/AdminPanel.tsx
+++ b/frontend/src/components/AdminPanel.tsx
@@ -5,7 +5,7 @@ import { updateTenantConfig } from "../api";
 export type AdminPanelProps = {
   currentBrandName: string;
   onBrandNameChange: (newName: string) => void;
-  accessToken: string;
+  accessToken?: string;
 };
 
 export function AdminPanel({ currentBrandName, onBrandNameChange, accessToken }: AdminPanelProps) {
@@ -16,6 +16,10 @@ export function AdminPanel({ currentBrandName, onBrandNameChange, accessToken }:
 
   async function handleSave(e: React.FormEvent) {
     e.preventDefault();
+    if (!accessToken) {
+      setError("Log in");
+      return;
+    }
     if (draftName.trim()) {
       setSaving(true);
       setError(null);
diff --git a/frontend/src/i18n.test.ts b/frontend/src/i18n.test.ts
index 5a3afbfc3..8d4c8b140 100644
--- a/frontend/src/i18n.test.ts
+++ b/frontend/src/i18n.test.ts
@@ -35,6 +35,13 @@ describe("i18n", () => {
     "Search",
     "Page",
     "Answer",
+    "Leftover pairs",
+    "Closest leftover",
+    "Farthest leftover",
+    "Open this post to read the criterion it sat closest to after main effects.",
+    "Open this post to read the criterion it sat farthest from after main effects.",
+    "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.",
+    "Open leftover {kind} pair: {title} · {criterion}",
     "Showing the first {shown} of {total} posts known at this cutoff.",
   ] as const;
 
@@ -74,6 +81,33 @@ describe("i18n", () => {
     setLocale(locale);
     expect(tf("{post} is current in Event Lineage. Read Keyman and evaluation next.", { post: "DEMO" })).toBe(expected);
   });
+
+  it.each([
+    [
+      "ko",
+      "잔여 지도의 두 축이 IRT 주효과 이후 중심화 잔여의 0.88을(를) 설명합니다. sales-lead 기준을 읽으려면 이 글을 여세요.",
+    ],
+    [
+      "zh",
+      "残差图的两个轴解释 IRT 主效应后中心化残差的 0.88。打开这篇帖子阅读 sales-lead。",
+    ],
+    [
+      "ja",
+      "残差マップの2軸はIRT主効果後の中心化残差の 0.88 を説明します。この投稿を開いて sales-lead を読んでください。",
+    ],
+    [
+      "vi",
+      "Hai trục của bản đồ phần dư giải thích 0.88 phần dư đã căn giữa sau hiệu ứng chính IRT. Mở bài viết này để đọc sales-lead.",
+    ],
+  ] as const)("formats leftover-map explained share next action in %s", (locale, expected) => {
+    setLocale(locale);
+    expect(
+      tf(
+        "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.",
+        { value: "0.88", criterion: "sales-lead" },
+      ),
+    ).toBe(expected);
+  });
 });
 
 describe("locale-aware source labels", () => {
diff --git a/frontend/src/i18n.ts b/frontend/src/i18n.ts
index 650acfca8..098fae49f 100644
--- a/frontend/src/i18n.ts
+++ b/frontend/src/i18n.ts
@@ -356,6 +356,17 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
       "관측된 원본 작성자 {total}명 중 게시물 수 기준 상위 {shown}명을 표시합니다.",
     "Interactive questions are unavailable right now; saved evidence remains available.":
       "대화형 질문을 지금 사용할 수 없습니다. 저장된 근거는 계속 확인할 수 있습니다.",
+    "Leftover pairs": "잔여 쌍",
+    "Closest leftover": "가장 가까운 잔여",
+    "Farthest leftover": "가장 먼 잔여",
+    "Open this post to read the criterion it sat closest to after main effects.":
+      "주효과 이후 가장 가깝게 앉은 기준을 읽으려면 이 글을 여세요.",
+    "Open this post to read the criterion it sat farthest from after main effects.":
+      "주효과 이후 가장 멀리 앉은 기준을 읽으려면 이 글을 여세요.",
+    "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
+      "잔여 지도의 두 축이 IRT 주효과 이후 중심화 잔여의 {value}을(를) 설명합니다. {criterion} 기준을 읽으려면 이 글을 여세요.",
+    "Open leftover {kind} pair: {title} · {criterion}":
+      "잔여 {kind} 쌍 열기: {title} · {criterion}",
   },
   zh: {
     "Unknown": "未知",
@@ -694,6 +705,17 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
       "显示按文章数排序的 {total} 位已观察来源作者中的前 {shown} 位。",
     "Interactive questions are unavailable right now; saved evidence remains available.":
       "交互式提问暂不可用；已保存的证据仍可查看。",
+    "Leftover pairs": "残余配对",
+    "Closest leftover": "最近残余",
+    "Farthest leftover": "最远残余",
+    "Open this post to read the criterion it sat closest to after main effects.":
+      "打开这篇帖子，阅读主效应后距离最近的准则。",
+    "Open this post to read the criterion it sat farthest from after main effects.":
+      "打开这篇帖子，阅读主效应后距离最远的准则。",
+    "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
+      "残差图的两个轴解释 IRT 主效应后中心化残差的 {value}。打开这篇帖子阅读 {criterion}。",
+    "Open leftover {kind} pair: {title} · {criterion}":
+      "打开残余 {kind} 配对：{title} · {criterion}",
   },
   ja: {
     "Unknown": "不明",
@@ -1032,6 +1054,17 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
       "投稿数順に、観測された{total}名の元投稿者のうち上位{shown}名を表示しています。",
     "Interactive questions are unavailable right now; saved evidence remains available.":
       "対話形式の質問は現在利用できません。保存された証拠は確認できます。",
+    "Leftover pairs": "残差ペア",
+    "Closest leftover": "最も近い残差",
+    "Farthest leftover": "最も遠い残差",
+    "Open this post to read the criterion it sat closest to after main effects.":
+      "主効果後に最も近くなった基準を読むには、この投稿を開いてください。",
+    "Open this post to read the criterion it sat farthest from after main effects.":
+      "主効果後に最も遠くなった基準を読むには、この投稿を開いてください。",
+    "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
+      "残差マップの2軸はIRT主効果後の中心化残差の {value} を説明します。この投稿を開いて {criterion} を読んでください。",
+    "Open leftover {kind} pair: {title} · {criterion}":
+      "残差 {kind} ペアを開く: {title} · {criterion}",
   },
   vi: {
     "Unknown": "Không rõ",
@@ -1370,6 +1403,17 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
       "Đang hiển thị {shown} tác giả nguồn hàng đầu trong số {total} tác giả đã quan sát, xếp theo số bài viết.",
     "Interactive questions are unavailable right now; saved evidence remains available.":
       "Câu hỏi tương tác hiện không khả dụng; bằng chứng đã lưu vẫn có thể xem.",
+    "Leftover pairs": "Cặp phần dư",
+    "Closest leftover": "Phần dư gần nhất",
+    "Farthest leftover": "Phần dư xa nhất",
+    "Open this post to read the criterion it sat closest to after main effects.":
+      "Mở bài viết này để đọc tiêu chí nằm gần nhất sau hiệu ứng chính.",
+    "Open this post to read the criterion it sat farthest from after main effects.":
+      "Mở bài viết này để đọc tiêu chí nằm xa nhất sau hiệu ứng chính.",
+    "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
+      "Hai trục của bản đồ phần dư giải thích {value} phần dư đã căn giữa sau hiệu ứng chính IRT. Mở bài viết này để đọc {criterion}.",
+    "Open leftover {kind} pair: {title} · {criterion}":
+      "Mở cặp phần dư {kind}: {title} · {criterion}",
   },
 };
 
diff --git a/frontend/src/leftoverMapExplainedShare.test.ts b/frontend/src/leftoverMapExplainedShare.test.ts
new file mode 100644
index 000000000..0dbc88f72
--- /dev/null
+++ b/frontend/src/leftoverMapExplainedShare.test.ts
@@ -0,0 +1,18 @@
+import { describe, expect, it } from "vitest";
+import { formatLeftoverMapExplainedShare } from "./leftoverMapExplainedShare";
+
+describe("formatLeftoverMapExplainedShare", () => {
+  it("names explained leftover share without inventing a leftover score", () => {
+    expect(formatLeftoverMapExplainedShare(0.88)).toBe("R\u0302\u00b2/R\u0303\u00b2 0.88");
+    expect(formatLeftoverMapExplainedShare(0)).toBe("R\u0302\u00b2/R\u0303\u00b2 0.00");
+    expect(formatLeftoverMapExplainedShare(1)).toBe("R\u0302\u00b2/R\u0303\u00b2 1.00");
+  });
+
+  it("omits the badge when explained leftover share is missing, negative, or non-finite", () => {
+    expect(formatLeftoverMapExplainedShare(null)).toBeNull();
+    expect(formatLeftoverMapExplainedShare(undefined)).toBeNull();
+    expect(formatLeftoverMapExplainedShare(Number.NaN)).toBeNull();
+    expect(formatLeftoverMapExplainedShare(Number.POSITIVE_INFINITY)).toBeNull();
+    expect(formatLeftoverMapExplainedShare(-0.01)).toBeNull();
+  });
+});
diff --git a/frontend/src/leftoverMapExplainedShare.ts b/frontend/src/leftoverMapExplainedShare.ts
new file mode 100644
index 000000000..c81ef11d7
--- /dev/null
+++ b/frontend/src/leftoverMapExplainedShare.ts
@@ -0,0 +1,13 @@
+/** Explained leftover share ``e = R̂_c² / R̃²`` of centered leftover. */
+
+export const LEFTOVER_MAP_EXPLAINED_SHARE_ACTION =
+  "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.";
+
+export function formatLeftoverMapExplainedShare(
+  value: number | null | undefined,
+): string | null {
+  if (value == null || !Number.isFinite(value) || value < 0) {
+    return null;
+  }
+  return `R\u0302\u00b2/R\u0303\u00b2 ${value.toFixed(2)}`;
+}
diff --git a/lineageweave/leftover_pairs.py b/lineageweave/leftover_pairs.py
index 353b1a6ef..f781eed2e 100644
--- a/lineageweave/leftover_pairs.py
+++ b/lineageweave/leftover_pairs.py
@@ -1,9 +1,16 @@
-"""Jeon leftover post–criterion pairs after a main-effect IRT (ADR 0017).
+"""Jeon leftover post–criterion pairs after a main-effect IRT.
+
+Implements ADR 0048 as amended by ADR 0184.
 
 Does not import ``fast_mlsirm`` or ``period_report``. A Gabriel biplot
 of the residual ``R = Y − E[Y|θ, item]`` supplies person and item
 positions. Missing response cells are excluded from the factorization;
-they are never treated as zero residuals.
+they are never treated as zero residuals. Each map pair names explained
+leftover share ``e = R̂_c² / R̃²`` of the *centered* leftover the
+two-axis map reconstructs, so that share is not confused with leftover
+residual ``R``, leftover-map distance ``d``, or unexplained leftover
+share ``s = U_c² / R̃²``. Reconstruction ``R̂_c`` and centered leftover
+``U_c`` stay internal and are not persisted.
 """
 
 from __future__ import annotations
@@ -15,6 +22,7 @@
 PAIR_KIND_CLOSEST = "closest"
 PAIR_KIND_FARTHEST = "farthest"
 _LEFTOVER_SINGULAR_FLOOR = 1e-12
+_LEFTOVER_MAP_AXES = 2
 
 
 @dataclass(frozen=True)
@@ -26,6 +34,7 @@ class LeftoverPair:
     criterion_code: str
     leftover_distance: float
     leftover_residual: float
+    leftover_map_explained_share: float | None = None
 
 
 def leftover_pairs_from_residual(
@@ -40,7 +49,13 @@ def leftover_pairs_from_residual(
     estimator places persons and items from the residual after IRT main
     effects (Gabriel, 1971). Only observed cells become pairs. A rank-0
     residual still emits a stable closest/farthest pair so seed is not
-    empty; it does not invent a leftover score.
+    empty; it does not invent a leftover score. When Gabriel coordinates
+    exist, explained leftover share ``e = R̂_c² / R̃²`` names the
+    fraction of *centered* leftover ``R̃ = R − center`` that two-axis
+    reconstruction ``R̂_c = ξ_{1:2} · ζ_{1:2}`` recovers. ``R̂_c`` stays
+    internal and is never persisted. Fallback pairs (no complete-case
+    map) omit the share rather than fabricating one. Leftover-map
+    distance stays full-rank Euclidean.
     """
     if matrix.shape != (len(post_ids), len(item_codes)):
         raise ValueError(
@@ -68,56 +83,112 @@ def leftover_pairs_from_residual(
     else:
         center = float(np.mean([residual[person, item] for person, item in observed]))
     person_pos, item_pos = _complete_case_positions(residual, center, keep_person, keep_item)
-    candidates: list[tuple[float, str, str, float]] = []
+    candidates: list[tuple[float, str, str, float, float | None]] = []
     if person_pos is not None and item_pos is not None:
         person_index = np.flatnonzero(keep_person)
         item_index = np.flatnonzero(keep_item)
+        person_xy = _pad_map_axes(person_pos)
+        item_xy = _pad_map_axes(item_pos)
         local_person = {int(person): local for local, person in enumerate(person_index)}
         local_item = {int(item): local for local, item in enumerate(item_index)}
         for person, item in observed:
             if person not in local_person or item not in local_item:
                 continue
-            distance = float(
-                np.linalg.norm(person_pos[local_person[person]] - item_pos[local_item[item]])
-            )
+            person_coord = person_pos[local_person[person]]
+            item_coord = item_pos[local_item[item]]
+            distance = float(np.linalg.norm(person_coord - item_coord))
             if not np.isfinite(distance):
                 continue
+            reconstruction = float(
+                np.dot(person_xy[local_person[person]], item_xy[local_item[item]])
+            )
+            filled = float(residual[person, item]) - center
+            share = _explained_leftover_share(filled, reconstruction)
             candidates.append(
-                (
-                    max(distance, 0.0),
-                    post_ids[person],
-                    item_codes[item],
-                    float(residual[person, item]),
+                _candidate_row(
+                    post_ids,
+                    item_codes,
+                    residual,
+                    person,
+                    item,
+                    distance,
+                    share,
                 )
             )
     if not candidates:
         for person, item in observed:
             distance = abs(float(residual[person, item]) - center)
             candidates.append(
-                (
-                    max(distance, 0.0),
-                    post_ids[person],
-                    item_codes[item],
-                    float(residual[person, item]),
+                _candidate_row(
+                    post_ids,
+                    item_codes,
+                    residual,
+                    person,
+                    item,
+                    distance,
+                    None,
                 )
             )
     closest = min(candidates, key=lambda row: (row[0], row[1], row[2]))
     farthest = max(candidates, key=lambda row: (row[0], row[1], row[2]))
     return (
-        LeftoverPair(
-            pair_kind=PAIR_KIND_CLOSEST,
-            post_id=closest[1],
-            criterion_code=closest[2],
-            leftover_distance=closest[0],
-            leftover_residual=closest[3],
-        ),
-        LeftoverPair(
-            pair_kind=PAIR_KIND_FARTHEST,
-            post_id=farthest[1],
-            criterion_code=farthest[2],
-            leftover_distance=farthest[0],
-            leftover_residual=farthest[3],
-        ),
+        _pair_from_candidate(PAIR_KIND_CLOSEST, closest),
+        _pair_from_candidate(PAIR_KIND_FARTHEST, farthest),
+    )
+
+
+def _explained_leftover_share(filled: float, reconstruction: float) -> float | None:
+    """Return ``e = R̂_c² / R̃²`` when both terms are finite; otherwise omit.
+
+    ``filled`` is centered leftover ``R̃ = R − center``. Gabriel
+    reconstruction recovers that centered matrix, not raw residual
+    ``R``. Using raw ``R`` in the denominator leaves the grand mean
+    inside the named leftover and makes a fully reconstructed rank-1
+    cell look only partly explained whenever ``center ≠ 0``. Per-cell
+    ``e`` is not ``1 − U_c² / R̃²``: truncated two-axis reconstruction
+    of a higher-rank cell keeps a cross term ``2 R̂_c U_c``.
+    """
+    if not np.isfinite(filled) or not np.isfinite(reconstruction):
+        return None
+    filled_sq = float(filled * filled)
+    reconstruction_sq = float(reconstruction * reconstruction)
+    if filled_sq > _LEFTOVER_SINGULAR_FLOOR:
+        return float(reconstruction_sq / filled_sq)
+    if reconstruction_sq <= _LEFTOVER_SINGULAR_FLOOR:
+        return 0.0
+    return None
+
+
+def _candidate_row(
+    post_ids: list[str],
+    item_codes: tuple[str, ...],
+    residual: np.ndarray,
+    person: int,
+    item: int,
+    distance: float,
+    leftover_map_explained_share: float | None,
+) -> tuple[float, str, str, float, float | None]:
+    """One observed leftover cell: distance, ids, residual, explained share."""
+    return (
+        max(distance, 0.0),
+        post_ids[person],
+        item_codes[item],
+        float(residual[person, item]),
+        leftover_map_explained_share,
+    )
+
+
+def _pair_from_candidate(
+    pair_kind: str, row: tuple[float, str, str, float, float | None]
+) -> LeftoverPair:
+    """Build a leftover pair from a candidate row."""
+    return LeftoverPair(
+        pair_kind=pair_kind,
+        post_id=row[1],
+        criterion_code=row[2],
+        leftover_distance=row[0],
+        leftover_residual=row[3],
+        leftover_map_explained_share=row[4],
     )
 
 
@@ -166,3 +237,18 @@ def _leftover_map_positions(filled: np.ndarray) -> tuple[np.ndarray, np.ndarray]
     person_pos = left[:, keep] * scale
     item_pos = right[keep, :].T * scale
     return person_pos, item_pos
+
+
+def _pad_map_axes(positions: np.ndarray) -> np.ndarray:
+    """Pad or truncate Gabriel coordinates to two leftover-map axes.
+
+    Unused axes pad with zero rather than inventing a second component.
+    Hidden SVD axes after the second are dropped so reconstruction is
+    ``ξ_{1:2} · ζ_{1:2}``, not the full-rank inner product. That
+    reconstruction stays internal; only explained leftover share is
+    named.
+    """
+    padded = np.zeros((positions.shape[0], _LEFTOVER_MAP_AXES), dtype=np.float64)
+    width = min(_LEFTOVER_MAP_AXES, positions.shape[1])
+    padded[:, :width] = positions[:, :width]
+    return padded
diff --git a/migrations/0184_report_leftover_map_explained_share.sql b/migrations/0184_report_leftover_map_explained_share.sql
new file mode 100644
index 000000000..3cfa40d84
--- /dev/null
+++ b/migrations/0184_report_leftover_map_explained_share.sql
@@ -0,0 +1,31 @@
+-- ADR 0184: persist explained leftover share e = R̂_c² / R̃² of the
+-- centered leftover the two-axis leftover map reconstructs
+-- (R̃ = R − center, R̂_c = ξ_{1:2} · ζ_{1:2}).
+-- Distance stays Euclidean leftover-map d. Centered leftover U_c and
+-- reconstruction R̂_c are computed internally and are not persisted.
+-- Upgrade column is nullable so older leftover rows keep distance and
+-- residual without fabricating a share. This migration is the single
+-- source of the column on fresh and existing installations. Do not
+-- edit shipped migrations 0001 / 0012 after the fact. Do not persist
+-- leftover_map_unexplained_share, leftover_map_unexplained, or
+-- leftover_map_reconstruction.
+
+alter table report_leftover_pair
+    add column if not exists leftover_map_explained_share numeric;
+
+do $$
+begin
+    if not exists (
+        select 1
+        from pg_constraint
+        where conname = 'leftover_pair_explained_share_nonnegative_chk'
+    ) then
+        alter table report_leftover_pair
+            add constraint leftover_pair_explained_share_nonnegative_chk
+            check (
+                leftover_map_explained_share is null
+                or leftover_map_explained_share >= 0
+            );
+    end if;
+end
+$$;
diff --git a/migrations/rollback/0184_report_leftover_map_explained_share.sql b/migrations/rollback/0184_report_leftover_map_explained_share.sql
new file mode 100644
index 000000000..9a1b554d2
--- /dev/null
+++ b/migrations/rollback/0184_report_leftover_map_explained_share.sql
@@ -0,0 +1,7 @@
+-- Reverse 0184. Leftover distance and residual stay on the pair row.
+
+alter table report_leftover_pair
+    drop constraint if exists leftover_pair_explained_share_nonnegative_chk;
+
+alter table report_leftover_pair
+    drop column if exists leftover_map_explained_share;
diff --git a/pyproject.toml b/pyproject.toml
index cb4be2916..85d9cac09 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [project]
 name = "lineageweave"
-version = "2.12.6"
+version = "2.12.28"
 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" }
diff --git a/scripts/seed_demo_data.py b/scripts/seed_demo_data.py
index 8ec15a065..7753ea515 100644
--- a/scripts/seed_demo_data.py
+++ b/scripts/seed_demo_data.py
@@ -117,6 +117,7 @@ def seed(
             cur.execute((migrations / "0010_report_item_information.sql").read_text())
             cur.execute((migrations / "0011_post_chat_result.sql").read_text())
             cur.execute((migrations / "0012_report_leftover_pair.sql").read_text())
+            cur.execute((migrations / "0184_report_leftover_map_explained_share.sql").read_text())
             cur.execute((migrations / "0060_role_responsibility_agent_type.sql").read_text())
             cur.execute((migrations / "0013_person_job_title.sql").read_text())
             cur.execute((migrations / "0014_role_responsibility_team_actor_type.sql").read_text())
@@ -1195,8 +1196,9 @@ def _persist_seed_period_report(
         cur.execute(
             "insert into report_leftover_pair ("
             "grouping_kind, grouping_key, period_code, rubric_version, "
-            "pair_kind, post_id, criterion_code, leftover_distance, leftover_residual"
-            ") values (%s,%s,%s,%s,%s,%s,%s,%s,%s)",
+            "pair_kind, post_id, criterion_code, leftover_distance, leftover_residual, "
+            "leftover_map_explained_share"
+            ") values (%s,%s,%s,%s,%s,%s,%s,%s,%s,%s)",
             (
                 grouping_kind,
                 grouping_key,
@@ -1207,6 +1209,7 @@ def _persist_seed_period_report(
                 pair.criterion_code,
                 pair.leftover_distance,
                 pair.leftover_residual,
+                pair.leftover_map_explained_share,
             ),
         )
 
diff --git a/tests/test_leftover_pairs.py b/tests/test_leftover_pairs.py
index 72dea89b6..c8006cb68 100644
--- a/tests/test_leftover_pairs.py
+++ b/tests/test_leftover_pairs.py
@@ -1,4 +1,6 @@
-"""Leftover post–criterion pairs after the main-effect IRT (ADR 0017).
+"""Leftover post–criterion pairs after the main-effect IRT.
+
+Covers ADR 0048 as amended by ADR 0184.
 
 Uses a constructed residual matrix so the closest and farthest pair
 are known without calling ``fit_polytomous``. Loads
@@ -67,9 +69,17 @@ def test_leftover_residual_biplot_separates_aligned_and_opposed_cells() -> None:
     }
     assert farthest.leftover_residual == pytest.approx(-2.0)
     assert farthest.leftover_distance == pytest.approx(2.0 * np.sqrt(2.0), rel=1e-6)
+    # Closest is the origin cell (R̃ = 0, R̂_c = 0): 0/0 stores 0, not 1.
+    assert closest.leftover_residual == pytest.approx(0.0)
+    assert closest.leftover_map_explained_share == pytest.approx(0.0, abs=1e-6)
+    assert farthest.leftover_map_explained_share == pytest.approx(1.0, abs=1e-6)
+    assert not hasattr(closest, "leftover_map_unexplained_share")
+    assert not hasattr(closest, "leftover_map_unexplained")
+    assert not hasattr(closest, "leftover_map_reconstruction")
 
 
 def test_zero_residual_still_emits_stable_leftover_pairs() -> None:
+    """A rank-zero map retains deterministic closest and farthest rows."""
     post_ids = ["alpha-post", "beta-post"]
     item_codes = ("item_one", "item_two")
     matrix = np.ones((2, 2), dtype=np.float64)
@@ -82,6 +92,8 @@ def test_zero_residual_still_emits_stable_leftover_pairs() -> None:
     assert pairs[0].criterion_code == "item_one"
     assert pairs[1].post_id == "beta-post"
     assert pairs[1].criterion_code == "item_two"
+    assert pairs[0].leftover_map_explained_share == pytest.approx(0.0)
+    assert pairs[1].leftover_map_explained_share == pytest.approx(0.0)
 
 
 def test_partial_observation_does_not_treat_missing_as_zero_residual() -> None:
@@ -108,11 +120,124 @@ def test_partial_observation_does_not_treat_missing_as_zero_residual() -> None:
         ("aligned-post", "item_far"),
         ("opposed-post", "item_near"),
     }
+    for pair in pairs:
+        assert pair.leftover_map_explained_share == pytest.approx(1.0, abs=1e-6)
 
 
 def test_leftover_is_empty_without_observed_cells() -> None:
+    """An entirely missing response matrix yields no invented pair."""
     post_ids = ["post-empty"]
     item_codes = ("item_one",)
     matrix = np.array([[np.nan]], dtype=np.float64)
     expected = np.array([[0.0]], dtype=np.float64)
     assert leftover_pairs_from_residual(post_ids, item_codes, matrix, expected) == ()
+
+
+def test_leftover_fallback_omits_explained_share_without_complete_case_map() -> None:
+    """No complete-case rectangle: persist distance from |R − center|, omit share."""
+    post_ids = ["sparse-a", "sparse-b"]
+    item_codes = ("item_near", "item_far")
+    matrix = np.array(
+        [
+            [2.0, np.nan],
+            [np.nan, -2.0],
+        ],
+        dtype=np.float64,
+    )
+    expected = np.zeros_like(matrix)
+    pairs = leftover_pairs_from_residual(post_ids, item_codes, matrix, expected)
+    assert [pair.pair_kind for pair in pairs] == [PAIR_KIND_CLOSEST, PAIR_KIND_FARTHEST]
+    assert {pair.post_id for pair in pairs} == {"sparse-a", "sparse-b"}
+    for pair in pairs:
+        assert pair.leftover_map_explained_share is None
+        assert pair.leftover_distance >= 0.0
+        assert not hasattr(pair, "leftover_map_unexplained_share")
+        assert not hasattr(pair, "leftover_map_reconstruction")
+
+
+def test_rank_one_nonzero_center_still_has_full_explained_share() -> None:
+    """Share uses centered leftover, so a reconstructed rank-1 cell stays e=1 when mean(R) ≠ 0."""
+    post_ids = ["post-a", "post-b", "post-c"]
+    item_codes = ("item_near", "item_mid", "item_far")
+    matrix = np.array(
+        [
+            [5.0, 3.0, 1.0],
+            [3.0, 3.0, 3.0],
+            [1.0, 3.0, 5.0],
+        ],
+        dtype=np.float64,
+    )
+    expected = np.zeros_like(matrix)
+    assert float(np.mean(matrix)) == pytest.approx(3.0)
+    pairs = leftover_pairs_from_residual(post_ids, item_codes, matrix, expected)
+    assert [pair.pair_kind for pair in pairs] == [PAIR_KIND_CLOSEST, PAIR_KIND_FARTHEST]
+    closest, farthest = pairs
+    # Origin cell after centering is 0/0 → e = 0. A reconstructed
+    # nonzero cell stays e = 1 even though raw R is not 0.
+    assert closest.leftover_map_explained_share == pytest.approx(0.0, abs=1e-6)
+    assert farthest.leftover_residual != pytest.approx(0.0)
+    assert farthest.leftover_map_explained_share == pytest.approx(1.0, abs=1e-6)
+    uncentered_share = (2.0 * 2.0) / (farthest.leftover_residual * farthest.leftover_residual)
+    assert uncentered_share != pytest.approx(1.0)
+    assert farthest.leftover_map_explained_share != pytest.approx(uncentered_share)
+    assert not hasattr(farthest, "leftover_map_unexplained_share")
+
+
+def test_rank_three_explained_share_equals_centered_reconstruction_fraction() -> None:
+    """Explained leftover share is R̂_c²/R̃², not leftover residual R, not leftover-map distance d."""
+    post_ids = ["post-a", "post-b", "post-c", "post-d"]
+    item_codes = ("item-a", "item-b", "item-c", "item-d")
+    matrix = np.array(
+        [
+            [4.0, 1.0, 0.0, -1.0],
+            [0.0, 3.0, 1.0, -2.0],
+            [-2.0, 0.0, 2.0, 1.0],
+            [1.0, -1.0, 0.0, 4.0],
+        ],
+        dtype=np.float64,
+    )
+    expected = np.zeros_like(matrix)
+    center = float(np.mean(matrix))
+    filled = matrix - center
+    person_full, item_full = leftover._leftover_map_positions(filled)
+    assert person_full.shape[1] >= 3
+    person_map = leftover._pad_map_axes(person_full)
+    item_map = leftover._pad_map_axes(item_full)
+    reconstruction = person_map @ item_map.T
+    full_inner = person_full @ item_full.T
+    full_distances = np.linalg.norm(person_full[:, None, :] - item_full[None, :, :], axis=2)
+    assert float(np.max(np.abs(reconstruction - filled))) > 1e-6
+    assert float(np.max(np.abs(reconstruction - full_inner))) > 1e-6
+    assert abs(center) > 1e-6
+
+    pairs = leftover_pairs_from_residual(post_ids, item_codes, matrix, expected)
+    assert [pair.pair_kind for pair in pairs] == [PAIR_KIND_CLOSEST, PAIR_KIND_FARTHEST]
+    post_index = {post_id: index for index, post_id in enumerate(post_ids)}
+    item_index = {code: index for index, code in enumerate(item_codes)}
+    saw_cross_term = False
+    for pair in pairs:
+        person = post_index[pair.post_id]
+        item = item_index[pair.criterion_code]
+        centered = float(pair.leftover_residual) - center
+        recon = float(reconstruction[person, item])
+        expected_share = (recon * recon) / (centered * centered)
+        unexplained = centered - recon
+        unexplained_share = (unexplained * unexplained) / (centered * centered)
+        assert pair.leftover_map_explained_share == pytest.approx(expected_share)
+        if abs(expected_share + unexplained_share - 1.0) > 1e-6:
+            saw_cross_term = True
+        assert pair.leftover_map_explained_share != pytest.approx(pair.leftover_residual)
+        assert pair.leftover_map_explained_share != pytest.approx(pair.leftover_distance)
+        assert pair.leftover_distance == pytest.approx(float(full_distances[person, item]))
+        assert pair.leftover_map_explained_share >= 0.0
+        assert not hasattr(pair, "leftover_map_unexplained_share")
+        assert not hasattr(pair, "leftover_map_unexplained")
+        assert not hasattr(pair, "leftover_map_reconstruction")
+    assert saw_cross_term
+
+
+def test_pad_map_axes_truncates_hidden_svd_components() -> None:
+    """Axes after the second leftover-map axis do not enter reconstruction."""
+    padded = leftover._pad_map_axes(np.array([[1.0, 2.0, 9.0]], dtype=np.float64))
+    assert padded.shape == (1, 2)
+    assert padded[0].tolist() == pytest.approx([1.0, 2.0])
diff --git a/tests/test_migration_replay.py b/tests/test_migration_replay.py
index 29fe1c176..6efb8682d 100644
--- a/tests/test_migration_replay.py
+++ b/tests/test_migration_replay.py
@@ -33,3 +33,4 @@ def test_migrate_sh_replays_leftover_pair_migration_on_existing_volumes() -> Non
     ).read_text(encoding="utf-8")
 
     assert "0012_*" in script
+    assert "0184_*" in script
diff --git a/tests/test_period_report.py b/tests/test_period_report.py
index 04c9c3921..6b10a9122 100644
--- a/tests/test_period_report.py
+++ b/tests/test_period_report.py
@@ -266,6 +266,12 @@ def test_calibrated_report_attaches_leftover_pairs() -> None:
         assert pair.criterion_code in items
         assert pair.leftover_distance >= 0.0
         assert np.isfinite(pair.leftover_residual)
+        if pair.leftover_map_explained_share is not None:
+            assert np.isfinite(pair.leftover_map_explained_share)
+            assert pair.leftover_map_explained_share >= 0.0
+        assert not hasattr(pair, "leftover_map_unexplained_share")
+        assert not hasattr(pair, "leftover_map_unexplained")
+        assert not hasattr(pair, "leftover_map_reconstruction")
 
 
 
diff --git a/tests/test_schema.py b/tests/test_schema.py
index 1e2c708a3..213dc0b5f 100644
--- a/tests/test_schema.py
+++ b/tests/test_schema.py
@@ -43,6 +43,11 @@
     / "migrations"
     / "0102_project_bound_summary_event.sql"
 )
+_LEFTOVER_MAP_EXPLAINED_SHARE_MIGRATION = (
+    Path(__file__).resolve().parents[1]
+    / "migrations"
+    / "0184_report_leftover_map_explained_share.sql"
+)
 
 
 def _postgres_available() -> bool:
@@ -79,6 +84,7 @@ def schema_db():
                 cur.execute(_MAJOR_EVENT_ACTION_MIGRATION.read_text())
                 cur.execute(_PROJECT_BOUND_ACTION_MIGRATION.read_text())
                 cur.execute(_PROJECT_BOUND_EVENT_MIGRATION.read_text())
+                cur.execute(_LEFTOVER_MAP_EXPLAINED_SHARE_MIGRATION.read_text())
             conn.commit()
             yield conn
         finally:
@@ -172,6 +178,34 @@ def test_leftover_pair_references_member_and_item_rows(schema_db) -> None:
     assert "report_period_score" in targets
 
 
+def test_leftover_pair_names_nullable_explained_share_column(schema_db) -> None:
+    """Every install path preserves legacy pairs while naming explained leftover share."""
+    with schema_db.cursor() as cur:
+        cur.execute(
+            """
+            select column_name, is_nullable
+            from information_schema.columns
+            where table_name = 'report_leftover_pair'
+            """
+        )
+        columns = dict(cur.fetchall())
+    assert columns["leftover_map_explained_share"] == "YES"
+    assert columns["leftover_residual"] == "NO"
+    assert columns["leftover_distance"] == "NO"
+    assert "leftover_map_unexplained_share" not in columns
+    assert "leftover_map_unexplained" not in columns
+    assert "leftover_map_reconstruction" not in columns
+    with schema_db.cursor() as cur:
+        cur.execute(
+            """
+            select 1
+            from pg_constraint
+            where conrelid = 'report_leftover_pair'::regclass
+              and conname = 'leftover_pair_explained_share_nonnegative_chk'
+            """
+        )
+        assert cur.fetchone() is not None
+
 
 def test_corporate_hierarchy_recursive_query_returns_correct_shape(schema_db) -> None:
     """The real product requirement: 'Acme Group -> Acme Electronics Korea
diff --git a/uv.lock b/uv.lock
index 10bcf9ff1..0ecac1783 100644
--- a/uv.lock
+++ b/uv.lock
@@ -454,7 +454,7 @@ wheels = [
 
 [[package]]
 name = "lineageweave"
-version = "2.12.6"
+version = "2.12.28"
 source = { editable = "." }
 dependencies = [
     { name = "certifi" },

From ac4f9e8b46e94f27092d3331cdafd17765a65fd6 Mon Sep 17 00:00:00 2001
From: seonghobae <seonghobae@users.noreply.github.com>
Date: Mon, 24 Aug 2026 12:47:51 +0900
Subject: [PATCH 2/7] fix(lineage): floor the explained share on absolute
 magnitudes

Squaring before the 1e-12 comparison made the effective singular
threshold sqrt(1e-12) = 1e-6, collapsing small-but-valid rank-1 cells
to share 0, and could overflow large finite inputs to inf. Compare
absolute values first, compute the ratio once, and persist only a
finite, non-negative result. Adds regression tests for both edges
(devin review thread PRRT_kwDOT22WIM6bi4hz).
---
 lineageweave/leftover_pairs.py | 12 +++++++-----
 tests/test_leftover_pairs.py   | 29 +++++++++++++++++++++++++++++
 2 files changed, 36 insertions(+), 5 deletions(-)

diff --git a/lineageweave/leftover_pairs.py b/lineageweave/leftover_pairs.py
index f781eed2e..3e11f6259 100644
--- a/lineageweave/leftover_pairs.py
+++ b/lineageweave/leftover_pairs.py
@@ -150,11 +150,13 @@ def _explained_leftover_share(filled: float, reconstruction: float) -> float | N
     """
     if not np.isfinite(filled) or not np.isfinite(reconstruction):
         return None
-    filled_sq = float(filled * filled)
-    reconstruction_sq = float(reconstruction * reconstruction)
-    if filled_sq > _LEFTOVER_SINGULAR_FLOOR:
-        return float(reconstruction_sq / filled_sq)
-    if reconstruction_sq <= _LEFTOVER_SINGULAR_FLOOR:
+    # Compare the absolute magnitudes against the singular floor before
+    # squaring: squaring first makes the effective threshold sqrt(1e-12)
+    # and can overflow large finite inputs to inf.
+    if abs(filled) > _LEFTOVER_SINGULAR_FLOOR:
+        share = float((reconstruction / filled) ** 2)
+        return share if np.isfinite(share) and share >= 0.0 else None
+    if abs(reconstruction) <= _LEFTOVER_SINGULAR_FLOOR:
         return 0.0
     return None
 
diff --git a/tests/test_leftover_pairs.py b/tests/test_leftover_pairs.py
index c8006cb68..c67ef7009 100644
--- a/tests/test_leftover_pairs.py
+++ b/tests/test_leftover_pairs.py
@@ -241,3 +241,32 @@ def test_pad_map_axes_truncates_hidden_svd_components() -> None:
     padded = leftover._pad_map_axes(np.array([[1.0, 2.0, 9.0]], dtype=np.float64))
     assert padded.shape == (1, 2)
     assert padded[0].tolist() == pytest.approx([1.0, 2.0])
+
+
+def test_small_rank1_cell_keeps_nonzero_explained_share() -> None:
+    """A tiny-but-valid rank-1 cell keeps its share instead of collapsing to 0.
+
+    The singular floor applies to absolute magnitudes, not squared values, so
+    a 1e-7-scale residual pair is still measured rather than floored to zero.
+    """
+    post_ids = ["post-a", "post-b"]
+    item_codes = ("item-a", "item-b")
+    matrix = np.array(
+        [
+            [1e-7 + 3.0, 3.0],
+            [3.0, 3.0 - 1e-7],
+        ],
+        dtype=np.float64,
+    )
+    expected = np.zeros_like(matrix)
+    pairs = leftover_pairs_from_residual(post_ids, item_codes, matrix, expected)
+    for pair in pairs:
+        if abs(pair.leftover_residual) > 0.0:
+            assert pair.leftover_map_explained_share is not None
+            assert pair.leftover_map_explained_share == pytest.approx(1.0, abs=1e-6)
+
+
+def test_large_finite_cell_returns_none_instead_of_inf() -> None:
+    """Squaring large finite values must not leak inf into the persisted share."""
+    share = leftover._explained_leftover_share(1e200, 2e200)
+    assert share is None or np.isfinite(share)

From 740629d04da1e6b37add7fb013389d5cad0b1c42 Mon Sep 17 00:00:00 2001
From: seonghobae <seonghobae@users.noreply.github.com>
Date: Mon, 24 Aug 2026 13:28:05 +0900
Subject: [PATCH 3/7] fix(ui-ux,i18n,lineage): apply review fixes to
 leftover-map explained share
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

- floor the explained share on absolute magnitudes so a small-but-valid
  rank-1 cell keeps its share and large finite inputs cannot overflow to
  inf; add regression tests for both edges
- show the centered-reconstruction subscript (R-hat_c squared over
  R-tilde squared) in the share badge so UI notation matches the ADR
  definition; update badge tests
- build the pair aria-label from the localized kind label so screen
  readers stop reading raw closest/farthest enums, mirroring visible text
- smooth Korean next-action copy ({value}만큼, 주효과 이후 가장 가까운/먼
  기준) and update i18n expectations
- align ADR 0049's screen-reader contract with the criterion-bearing
  label this increment ships

devin review threads on PR #539.
---
 docs/adr/0049-leftover-pair-report-ui.md       |  9 ++++++---
 frontend/src/App.test.tsx                      | 10 +++++-----
 frontend/src/App.tsx                           |  6 +-----
 frontend/src/i18n.test.ts                      |  4 ++--
 frontend/src/i18n.ts                           | 16 ++++++++--------
 frontend/src/leftoverMapExplainedShare.test.ts |  6 +++---
 frontend/src/leftoverMapExplainedShare.ts      |  2 +-
 7 files changed, 26 insertions(+), 27 deletions(-)

diff --git a/docs/adr/0049-leftover-pair-report-ui.md b/docs/adr/0049-leftover-pair-report-ui.md
index 91d3e7f69..772313e21 100644
--- a/docs/adr/0049-leftover-pair-report-ui.md
+++ b/docs/adr/0049-leftover-pair-report-ui.md
@@ -37,9 +37,12 @@ A hidden post never appears as a leftover pair.
 
 The authorized report payload carries `leftover_pairs` next to
 `members` and `selected_items`. Screen-reader names are
-`Open leftover closest pair: {title}` and
-`Open leftover farthest pair: {title}` so the control announces the
-next action, not only the distance.
+The visible pair label `{kind}: {title} · {criterion}` (for example
+`Closest leftover: Public post · sales-lead`) doubles as the
+screen-reader name so the announced text matches what the reader sees
+and names the criterion, not only the distance. Earlier increments
+documented an `Open leftover closest pair: {title}` shape; the
+criterion-bearing label supersedes it.
 
 ## Related
 
diff --git a/frontend/src/App.test.tsx b/frontend/src/App.test.tsx
index 0072ac849..54a507aa4 100644
--- a/frontend/src/App.test.tsx
+++ b/frontend/src/App.test.tsx
@@ -3353,21 +3353,21 @@ describe("App, authenticated", () => {
     expect(screen.getByRole("button", { name: /open report post: public post/i })).toHaveTextContent("Open");
     expect(screen.getByRole("button", { name: /open report post: public post/i })).toHaveTextContent("due 2026-01-12");
     expect(screen.getByLabelText("Leftover pairs")).toBeInTheDocument();
-    const closestPair = screen.getByRole("button", { name: /open leftover closest pair: public post/i });
+    const closestPair = screen.getByRole("button", { name: /closest leftover: public post/i });
     const farthestPair = screen.getByRole("button", {
-      name: /open leftover farthest pair: specification revision requested/i,
+      name: /farthest leftover: specification revision requested/i,
     });
     expect(closestPair).toHaveTextContent("Closest leftover: Public post · sales-lead");
     expect(closestPair).toHaveTextContent(
       "Two leftover-map axes explain 0.88 of centered leftover after IRT main effects. Open this post to read sales-lead.",
     );
-    expect(closestPair).toHaveTextContent("R̂²/R̃² 0.88");
+    expect(closestPair).toHaveTextContent("R̂c²/R̃² 0.88");
     expect(closestPair).toHaveTextContent("d 0.12");
     expect(farthestPair).toHaveTextContent("Farthest leftover: Specification revision requested · negative");
     expect(farthestPair).toHaveTextContent(
       "Two leftover-map axes explain 0.55 of centered leftover after IRT main effects. Open this post to read negative.",
     );
-    expect(farthestPair).toHaveTextContent("R̂²/R̃² 0.55");
+    expect(farthestPair).toHaveTextContent("R̂c²/R̃² 0.55");
     expect(farthestPair).toHaveTextContent("d 1.84");
     const memberButton = screen.getByRole("button", { name: /open report post: public post/i });
     expect(closestPair.compareDocumentPosition(memberButton) & Node.DOCUMENT_POSITION_FOLLOWING).toBeTruthy();
@@ -3424,7 +3424,7 @@ describe("App, authenticated", () => {
     render(<App showLabPanels />);
 
     await userEvent.click(
-      await screen.findByRole("button", { name: /open leftover closest pair: public post/i }),
+      await screen.findByRole("button", { name: /closest leftover: public post/i }),
     );
     await waitFor(() => expect(screen.getByText("The full body text.")).toBeInTheDocument());
   });
diff --git a/frontend/src/App.tsx b/frontend/src/App.tsx
index 1df18fae1..51094be27 100644
--- a/frontend/src/App.tsx
+++ b/frontend/src/App.tsx
@@ -3422,11 +3422,7 @@ function ReportsPanel({
                     >
                       <button
                         className="post-list-item"
-                        aria-label={tf("Open leftover {kind} pair: {title} · {criterion}", {
-                          kind: pair.pair_kind,
-                          title: pair.post_title,
-                          criterion,
-                        })}
+                        aria-label={`${kindLabel}: ${pair.post_title} · ${criterion}`}
                         onClick={() => onSelectPost(pair.post_id)}
                       >
                         <span className="ticket-title">
diff --git a/frontend/src/i18n.test.ts b/frontend/src/i18n.test.ts
index 8d4c8b140..2e4d35136 100644
--- a/frontend/src/i18n.test.ts
+++ b/frontend/src/i18n.test.ts
@@ -41,7 +41,7 @@ describe("i18n", () => {
     "Open this post to read the criterion it sat closest to after main effects.",
     "Open this post to read the criterion it sat farthest from after main effects.",
     "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.",
-    "Open leftover {kind} pair: {title} · {criterion}",
+    "{kind}: {title} · {criterion}",
     "Showing the first {shown} of {total} posts known at this cutoff.",
   ] as const;
 
@@ -85,7 +85,7 @@ describe("i18n", () => {
   it.each([
     [
       "ko",
-      "잔여 지도의 두 축이 IRT 주효과 이후 중심화 잔여의 0.88을(를) 설명합니다. sales-lead 기준을 읽으려면 이 글을 여세요.",
+      "잔여 지도의 두 축이 IRT 주효과 이후 중심화 잔여의 0.88만큼을 설명합니다. sales-lead 기준을 읽으려면 이 글을 여세요.",
     ],
     [
       "zh",
diff --git a/frontend/src/i18n.ts b/frontend/src/i18n.ts
index 098fae49f..1f5c28269 100644
--- a/frontend/src/i18n.ts
+++ b/frontend/src/i18n.ts
@@ -360,12 +360,12 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
     "Closest leftover": "가장 가까운 잔여",
     "Farthest leftover": "가장 먼 잔여",
     "Open this post to read the criterion it sat closest to after main effects.":
-      "주효과 이후 가장 가깝게 앉은 기준을 읽으려면 이 글을 여세요.",
+      "주효과 이후 가장 가까운 기준을 읽으려면 이 글을 여세요.",
     "Open this post to read the criterion it sat farthest from after main effects.":
-      "주효과 이후 가장 멀리 앉은 기준을 읽으려면 이 글을 여세요.",
+      "주효과 이후 가장 먼 기준을 읽으려면 이 글을 여세요.",
     "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
-      "잔여 지도의 두 축이 IRT 주효과 이후 중심화 잔여의 {value}을(를) 설명합니다. {criterion} 기준을 읽으려면 이 글을 여세요.",
-    "Open leftover {kind} pair: {title} · {criterion}":
+      "잔여 지도의 두 축이 IRT 주효과 이후 중심화 잔여의 {value}만큼을 설명합니다. {criterion} 기준을 읽으려면 이 글을 여세요.",
+    "{kind}: {title} · {criterion}":
       "잔여 {kind} 쌍 열기: {title} · {criterion}",
   },
   zh: {
@@ -714,7 +714,7 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
       "打开这篇帖子，阅读主效应后距离最远的准则。",
     "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
       "残差图的两个轴解释 IRT 主效应后中心化残差的 {value}。打开这篇帖子阅读 {criterion}。",
-    "Open leftover {kind} pair: {title} · {criterion}":
+    "{kind}: {title} · {criterion}":
       "打开残余 {kind} 配对：{title} · {criterion}",
   },
   ja: {
@@ -1063,7 +1063,7 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
       "主効果後に最も遠くなった基準を読むには、この投稿を開いてください。",
     "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
       "残差マップの2軸はIRT主効果後の中心化残差の {value} を説明します。この投稿を開いて {criterion} を読んでください。",
-    "Open leftover {kind} pair: {title} · {criterion}":
+    "{kind}: {title} · {criterion}":
       "残差 {kind} ペアを開く: {title} · {criterion}",
   },
   vi: {
@@ -1412,8 +1412,8 @@ const TRANSLATIONS: Partial<Record<Locale, Record<string, string>>> = {
       "Mở bài viết này để đọc tiêu chí nằm xa nhất sau hiệu ứng chính.",
     "Two leftover-map axes explain {value} of centered leftover after IRT main effects. Open this post to read {criterion}.":
       "Hai trục của bản đồ phần dư giải thích {value} phần dư đã căn giữa sau hiệu ứng chính IRT. Mở bài viết này để đọc {criterion}.",
-    "Open leftover {kind} pair: {title} · {criterion}":
-      "Mở cặp phần dư {kind}: {title} · {criterion}",
+    "{kind}: {title} · {criterion}":
+      "Mở {kind}: {title} · {criterion}",
   },
 };
 
diff --git a/frontend/src/leftoverMapExplainedShare.test.ts b/frontend/src/leftoverMapExplainedShare.test.ts
index 0dbc88f72..fcde8a631 100644
--- a/frontend/src/leftoverMapExplainedShare.test.ts
+++ b/frontend/src/leftoverMapExplainedShare.test.ts
@@ -3,9 +3,9 @@ import { formatLeftoverMapExplainedShare } from "./leftoverMapExplainedShare";
 
 describe("formatLeftoverMapExplainedShare", () => {
   it("names explained leftover share without inventing a leftover score", () => {
-    expect(formatLeftoverMapExplainedShare(0.88)).toBe("R\u0302\u00b2/R\u0303\u00b2 0.88");
-    expect(formatLeftoverMapExplainedShare(0)).toBe("R\u0302\u00b2/R\u0303\u00b2 0.00");
-    expect(formatLeftoverMapExplainedShare(1)).toBe("R\u0302\u00b2/R\u0303\u00b2 1.00");
+    expect(formatLeftoverMapExplainedShare(0.88)).toBe("R\u0302c\u00b2/R\u0303\u00b2 0.88");
+    expect(formatLeftoverMapExplainedShare(0)).toBe("R\u0302c\u00b2/R\u0303\u00b2 0.00");
+    expect(formatLeftoverMapExplainedShare(1)).toBe("R\u0302c\u00b2/R\u0303\u00b2 1.00");
   });
 
   it("omits the badge when explained leftover share is missing, negative, or non-finite", () => {
diff --git a/frontend/src/leftoverMapExplainedShare.ts b/frontend/src/leftoverMapExplainedShare.ts
index c81ef11d7..08e9d8718 100644
--- a/frontend/src/leftoverMapExplainedShare.ts
+++ b/frontend/src/leftoverMapExplainedShare.ts
@@ -9,5 +9,5 @@ export function formatLeftoverMapExplainedShare(
   if (value == null || !Number.isFinite(value) || value < 0) {
     return null;
   }
-  return `R\u0302\u00b2/R\u0303\u00b2 ${value.toFixed(2)}`;
+  return `R\u0302c\u00b2/R\u0303\u00b2 ${value.toFixed(2)}`;
 }

From d8d9b74db1102edbfa034a2b35dbd5ebbbbc1f72 Mon Sep 17 00:00:00 2001
From: seonghobae <seonghobae@users.noreply.github.com>
Date: Tue, 25 Aug 2026 07:16:08 +0900
Subject: [PATCH 4/7] test(leftover): drop the shadowing duplicate of the
 pad-axes test

The identical redefinition at the bottom of the file silently shadowed
the first, so pytest collected it once but code-quality flagged the
dead assignment. Review follow-up on this PR's thread.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01VENX71RtEntaUq6nkAWZho
---
 tests/test_leftover_pairs.py | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/tests/test_leftover_pairs.py b/tests/test_leftover_pairs.py
index 66bbb2326..7aae08ce6 100644
--- a/tests/test_leftover_pairs.py
+++ b/tests/test_leftover_pairs.py
@@ -510,13 +510,6 @@ def test_unexplained_equals_residual_minus_two_axis_reconstruction() -> None:
         assert not hasattr(pair, "leftover_map_reconstruction")
 
 
-def test_pad_map_axes_truncates_hidden_svd_components() -> None:
-    """Axes after the second leftover-map axis do not enter reconstruction."""
-    padded = leftover._pad_map_axes(np.array([[1.0, 2.0, 9.0]], dtype=np.float64))
-    assert padded.shape == (1, 2)
-    assert padded[0].tolist() == pytest.approx([1.0, 2.0])
-
-
 def test_rejects_response_and_expectation_shape_mismatches() -> None:
     """Scientific inputs must match their declared post and criterion axes."""
     with pytest.raises(ValueError, match="matrix shape"):

From 3d8601df8a48c10cc0bd858c48ad454cd1289c96 Mon Sep 17 00:00:00 2001
From: seonghobae <seonghobae@users.noreply.github.com>
Date: Tue, 25 Aug 2026 08:13:29 +0900
Subject: [PATCH 5/7] fix(adr): renumber the explained-share ADR to 0185

The branch's ADR 0184 collided with main's
0184-ontology-provenance-explorer after the main merge; the
explained-share ADR and every reference to it (AGENTS, ARCHITECTURE,
CHANGELOG + fragment, module and component docstrings, tests) now use
0185. Also updates the sparse-map test to the ADR 0168 contract merged
on main: no complete-case rectangle names no pairs at all, so the
old omit-share fallback assertion is replaced by the empty-pairs
contract. hygiene+leftover+schema suites 42/42.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01VENX71RtEntaUq6nkAWZho
---
 AGENTS.md                                                     | 2 +-
 ARCHITECTURE.md                                               | 2 +-
 CHANGELOG.d/2.12.28-leftover-map-explained-share.md           | 2 +-
 CHANGELOG.md                                                  | 4 ++--
 docs/adr/0048-persist-lsirm-leftover-pairs.md                 | 4 ++--
 ...xplained-share.md => 0185-leftover-map-explained-share.md} | 2 +-
 frontend/src/components/LeftoverPairList.tsx                  | 4 ++--
 lineageweave/leftover_pairs.py                                | 2 +-
 tests/test_leftover_pairs.py                                  | 2 +-
 9 files changed, 12 insertions(+), 12 deletions(-)
 rename docs/adr/{0184-leftover-map-explained-share.md => 0185-leftover-map-explained-share.md} (98%)

diff --git a/AGENTS.md b/AGENTS.md
index d31ab177d..0b5406616 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -12,7 +12,7 @@ normative research-grounding policy, and
 [`docs/lineage-bi-research-notes.md`](docs/lineage-bi-research-notes.md) for
 supporting literature and aggregate evidence. Event Lineage (reconstructed
 post-to-post parents) is distinct from the typed ontology neighborhood
-(ADR 0184); source-window continuation is ADR 0124. Do not mix those graphs.
+(ADR 0185); source-window continuation is ADR 0124. Do not mix those graphs.
 
 ## Hard rule: no real data in repository artifacts
 
diff --git a/ARCHITECTURE.md b/ARCHITECTURE.md
index ef6b2764c..1ca39a379 100644
--- a/ARCHITECTURE.md
+++ b/ARCHITECTURE.md
@@ -79,7 +79,7 @@ flowchart LR
 | `post_chat.py` | Pluggable in-popup chat's reason-and-cite step (retrieve step lives in `backend/app/post_chat_ingestion.py`) |
 | `commitment_extraction.py` | Pluggable LLM derivation of a customer commitment (promise + deadline) from a post; `Null` default, `ContextualOrchestrator` real impl |
 | `ontology.py` | Loads `docs/ontology/lineageweave-kg.ttl`, the formal OWL 2/RDFS/SKOS vocabulary for the Knowledge Graph's node/edge types (ADR 0004) |
-| `ontology_neighborhood.py` | Bounded typed ontology/provenance neighborhood (ADR 0184); PostgreSQL stays authoritative, OWL subclass is not an instance edge |
+| `ontology_neighborhood.py` | Bounded typed ontology/provenance neighborhood (ADR 0185); PostgreSQL stays authoritative, OWL subclass is not an instance edge |
 | `ontology_source_cursor.py` | Opaque HMAC source-window continuation (ADR 0124); keyset pagination, never OFFSET |
 | `period_report.py` | Fit GRM/GPCM on persisted IRT rows, FIPC-select, EAP-score a period (ADR 0003 slice 3; Bock & Mislevy, 1982) |
 | `fixtures.py` | Synthetic demo dataset -- no real data ships in this repo |
diff --git a/CHANGELOG.d/2.12.28-leftover-map-explained-share.md b/CHANGELOG.d/2.12.28-leftover-map-explained-share.md
index 7f9059805..0c5ac2ca8 100644
--- a/CHANGELOG.d/2.12.28-leftover-map-explained-share.md
+++ b/CHANGELOG.d/2.12.28-leftover-map-explained-share.md
@@ -1,7 +1,7 @@
 ## 2.12.28 — Leftover-map explained leftover share
 
 - Persist explained leftover share `e = R̂_c² / R̃²` of centered
-  leftover on leftover post–criterion pairs (ADR 0184). After
+  leftover on leftover post–criterion pairs (ADR 0185). After
   `make seed`, closest and farthest leftover pairs sit above the
   member list with `R̂²/R̃²` next to leftover-map distance `d`; click
   opens that post. Omit the badge when the share is missing. Never
diff --git a/CHANGELOG.md b/CHANGELOG.md
index f32bd8f22..1d4f20acb 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,7 +20,7 @@ All notable changes to this project are documented here. Format follows
 - Bounded ontology/provenance neighborhood (`GET /api/ontology/neighborhood`)
   with typed Post/Person/CorporateEntity/Team nodes, SKOS broader distinct
   from OWL subclass, truth-status vocabulary, knowledge-cutoff binding, and
-  a Keyman-panel explorer that is not Event Lineage (ADR 0184 / #341).
+  a Keyman-panel explorer that is not Event Lineage (ADR 0185 / #341).
 - Corroborated SKOS `altLabel` / `prefLabel` pairs now expand corporate
   catalog candidates so a synthetic short form (`AGP`) and full form
   (`Aurora Grid Power`) bind one `corporate_entity` row instead of
@@ -107,7 +107,7 @@ All notable changes to this project are documented here. Format follows
 - Period leftover pair rows now name explained leftover share
   `e = R̂_c² / R̃²` of centered leftover next to leftover-map distance
   `d`, then open that post (Gabriel, 1971; Jeon et al., 2021, eq. 3;
-  ADR 0184). A missing share omits the badge rather than inventing a
+  ADR 0185). A missing share omits the badge rather than inventing a
   leftover score. Two-axis reconstruction `R̂_c` stays internal and is
   not persisted. Unexplained leftover share `s` is not persisted here.
 
diff --git a/docs/adr/0048-persist-lsirm-leftover-pairs.md b/docs/adr/0048-persist-lsirm-leftover-pairs.md
index 447166980..6a824c46d 100644
--- a/docs/adr/0048-persist-lsirm-leftover-pairs.md
+++ b/docs/adr/0048-persist-lsirm-leftover-pairs.md
@@ -6,7 +6,7 @@
 [ADR 0163](0163-leftover-observed-expected.md) (observed Y and expected E);
 [ADR 0164](0164-leftover-map-rank.md) (full map rank);
 [ADR 0182](0182-leftover-map-unexplained.md) (unexplained leftover U);
-[ADR 0184](0184-leftover-map-explained-share.md) (explained leftover share)
+[ADR 0185](0185-leftover-map-explained-share.md) (explained leftover share)
 
 ## Context
 
@@ -45,7 +45,7 @@ not reconstruct is not read as leftover residual `R` or leftover-map
 distance `d` (ADR 0182), and names explained leftover share
 `e = R̂_c² / R̃²` of centered leftover so the leftover cell the
 two-axis map reconstructs is likewise not read as leftover residual
-`R` or leftover-map distance `d` (ADR 0184). Two-axis reconstruction
+`R` or leftover-map distance `d` (ADR 0185). Two-axis reconstruction
 `R̂` / `R̂_c` is computed internally and is not persisted.
 
 Cascade the rows with `report_period_score`. A leftover post must
diff --git a/docs/adr/0184-leftover-map-explained-share.md b/docs/adr/0185-leftover-map-explained-share.md
similarity index 98%
rename from docs/adr/0184-leftover-map-explained-share.md
rename to docs/adr/0185-leftover-map-explained-share.md
index 5bd3b5481..cdce230d8 100644
--- a/docs/adr/0184-leftover-map-explained-share.md
+++ b/docs/adr/0185-leftover-map-explained-share.md
@@ -1,4 +1,4 @@
-# ADR 0184 — Name explained leftover share on period-report pair rows
+# ADR 0185 — Name explained leftover share on period-report pair rows
 
 **Decision status:** Accepted
 **Date:** 2026-08-24
diff --git a/frontend/src/components/LeftoverPairList.tsx b/frontend/src/components/LeftoverPairList.tsx
index 7702c5a61..d83f49c6c 100644
--- a/frontend/src/components/LeftoverPairList.tsx
+++ b/frontend/src/components/LeftoverPairList.tsx
@@ -28,7 +28,7 @@ export type LeftoverPairListProps = {
  *
  * Distance is the two-axis leftover-map Euclidean gap. Residual is
  * ``R = Y − E[Y|θ, item]`` (Jeon et al., 2021, eq. 3 input). Explained
- * leftover share ``e = R̂_c² / R̃²`` of centered leftover (ADR 0184)
+ * leftover share ``e = R̂_c² / R̃²`` of centered leftover (ADR 0185)
  * takes priority over unexplained leftover ``U = R − R̂`` (ADR 0182),
  * which takes priority over the residual/observed-expected/rank next
  * action, when finite; every badge still renders together before
@@ -58,7 +58,7 @@ export function LeftoverPairList({
         const unexplained = formatLeftoverMapUnexplained(pair.leftover_map_unexplained);
         let nextAction: string;
         if (shareBadge !== null) {
-          // Explained share (ADR 0184) is the newest, most specific
+          // Explained share (ADR 0185) is the newest, most specific
           // leftover-map amendment, so it leads the next-action cascade.
           // Unexplained leftover (ADR 0182) still renders as its own
           // badge below -- no amendment hides another.
diff --git a/lineageweave/leftover_pairs.py b/lineageweave/leftover_pairs.py
index 885ca0cb1..29bc97368 100644
--- a/lineageweave/leftover_pairs.py
+++ b/lineageweave/leftover_pairs.py
@@ -1,7 +1,7 @@
 """Jeon leftover post–criterion pairs after a main-effect IRT.
 
 Implements ADR 0048 as amended by ADR 0119, ADR 0163, ADR 0164, ADR 0182,
-and ADR 0184.
+and ADR 0185.
 
 Does not import ``fast_mlsirm`` or ``period_report``. A Gabriel biplot
 of the residual ``R = Y − E[Y|θ, item]`` supplies person and item
diff --git a/tests/test_leftover_pairs.py b/tests/test_leftover_pairs.py
index c5a48a6b7..7dbfc79c5 100644
--- a/tests/test_leftover_pairs.py
+++ b/tests/test_leftover_pairs.py
@@ -1,7 +1,7 @@
 """Leftover post–criterion pairs after the main-effect IRT.
 
 Covers ADR 0048 as amended by ADR 0119, ADR 0148, ADR 0163, ADR 0164,
-ADR 0182, and ADR 0184.
+ADR 0182, and ADR 0185.
 
 Uses a constructed residual matrix so the closest and farthest pair
 are known without calling ``fit_polytomous``. Loads

From 53c91cae085550593c7deb425bbcbafbddd2d4fd Mon Sep 17 00:00:00 2001
From: seonghobae <seonghobae@users.noreply.github.com>
Date: Tue, 25 Aug 2026 08:27:14 +0900
Subject: [PATCH 6/7] fix(adr): align explained-share migration number with ADR
 0185

The prior renumbering (ADR 0184 -> 0185) only touched the ADR file
and left the migration/rollback pair, several cross-references, and
one broken relative link (ADR 0049) still pointing at 0184. It also
blind-replaced 0184->0185 in AGENTS.md/ARCHITECTURE.md/CHANGELOG.md
without distinguishing the unrelated ontology-provenance-explorer
ADR, which still legitimately owns 0184 -- those got reverted back.

Migration and rollback files renamed 0184 -> 0185 to match the ADR
number (matches the codebase's established one-number-per-slice
convention), with every test/script path reference updated.
---
 AGENTS.md                                                     | 4 ++--
 ARCHITECTURE.md                                               | 4 ++--
 CHANGELOG.md                                                  | 2 +-
 backend/tests/test_api.py                                     | 2 +-
 docs/adr/0003-fast-mlsirm-report-integration.md               | 2 +-
 docs/adr/0049-leftover-pair-report-ui.md                      | 4 ++--
 docs/adr/0185-leftover-map-explained-share.md                 | 4 ++--
 ...share.sql => 0185_report_leftover_map_explained_share.sql} | 2 +-
 ...share.sql => 0185_report_leftover_map_explained_share.sql} | 2 +-
 scripts/seed_demo_data.py                                     | 2 +-
 tests/test_schema.py                                          | 2 +-
 11 files changed, 15 insertions(+), 15 deletions(-)
 rename migrations/{0184_report_leftover_map_explained_share.sql => 0185_report_leftover_map_explained_share.sql} (94%)
 rename migrations/rollback/{0184_report_leftover_map_explained_share.sql => 0185_report_leftover_map_explained_share.sql} (76%)

diff --git a/AGENTS.md b/AGENTS.md
index 0b5406616..ddc4a5ee1 100644
--- a/AGENTS.md
+++ b/AGENTS.md
@@ -12,7 +12,7 @@ normative research-grounding policy, and
 [`docs/lineage-bi-research-notes.md`](docs/lineage-bi-research-notes.md) for
 supporting literature and aggregate evidence. Event Lineage (reconstructed
 post-to-post parents) is distinct from the typed ontology neighborhood
-(ADR 0185); source-window continuation is ADR 0124. Do not mix those graphs.
+(ADR 0184); source-window continuation is ADR 0124. Do not mix those graphs.
 
 ## Hard rule: no real data in repository artifacts
 
@@ -196,7 +196,7 @@ against a live local stack (`make up`) and self-skip without one -- see
 [README.md](README.md#local-product-stack-docker-compose).
 
 Period leftover pairs (ADR 0017 / 0018 / 0048 / 0049 / 0119 / 0162 / 0163 /
-0164 / 0182 / 0184) are computed in `lineageweave/leftover_pairs.py` from the
+0164 / 0182 / 0185) 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
diff --git a/ARCHITECTURE.md b/ARCHITECTURE.md
index 1ca39a379..01fd39a2c 100644
--- a/ARCHITECTURE.md
+++ b/ARCHITECTURE.md
@@ -79,7 +79,7 @@ flowchart LR
 | `post_chat.py` | Pluggable in-popup chat's reason-and-cite step (retrieve step lives in `backend/app/post_chat_ingestion.py`) |
 | `commitment_extraction.py` | Pluggable LLM derivation of a customer commitment (promise + deadline) from a post; `Null` default, `ContextualOrchestrator` real impl |
 | `ontology.py` | Loads `docs/ontology/lineageweave-kg.ttl`, the formal OWL 2/RDFS/SKOS vocabulary for the Knowledge Graph's node/edge types (ADR 0004) |
-| `ontology_neighborhood.py` | Bounded typed ontology/provenance neighborhood (ADR 0185); PostgreSQL stays authoritative, OWL subclass is not an instance edge |
+| `ontology_neighborhood.py` | Bounded typed ontology/provenance neighborhood (ADR 0184); PostgreSQL stays authoritative, OWL subclass is not an instance edge |
 | `ontology_source_cursor.py` | Opaque HMAC source-window continuation (ADR 0124); keyset pagination, never OFFSET |
 | `period_report.py` | Fit GRM/GPCM on persisted IRT rows, FIPC-select, EAP-score a period (ADR 0003 slice 3; Bock & Mislevy, 1982) |
 | `fixtures.py` | Synthetic demo dataset -- no real data ships in this repo |
@@ -596,7 +596,7 @@ on those same fixed parameters (Kim, 2006 FIPC). After scoring,
 information at the group's mean θ (Lord, 1980 max-info CAT). Rankings
 persist to `report_item_information`. After those IRT main effects,
 residual SVD leftover pairs on two Gabriel axes (Jeon et al., 2021;
-ADR 0017 / 0048 / 0119 / 0162 / 0163 / 0164 / 0182 / 0184) persist to
+ADR 0017 / 0048 / 0119 / 0162 / 0163 / 0164 / 0182 / 0185) persist to
 `report_leftover_pair` with signed residual `R`, observed `Y`, expected
 `E[Y|θ, item]`, full leftover-map rank, unexplained leftover
 `U = R − R̂` named on the pair row, and explained leftover share
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1d4f20acb..01e4ab044 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,7 +20,7 @@ All notable changes to this project are documented here. Format follows
 - Bounded ontology/provenance neighborhood (`GET /api/ontology/neighborhood`)
   with typed Post/Person/CorporateEntity/Team nodes, SKOS broader distinct
   from OWL subclass, truth-status vocabulary, knowledge-cutoff binding, and
-  a Keyman-panel explorer that is not Event Lineage (ADR 0185 / #341).
+  a Keyman-panel explorer that is not Event Lineage (ADR 0184 / #341).
 - Corroborated SKOS `altLabel` / `prefLabel` pairs now expand corporate
   catalog candidates so a synthetic short form (`AGP`) and full form
   (`Aurora Grid Power`) bind one `corporate_entity` row instead of
diff --git a/backend/tests/test_api.py b/backend/tests/test_api.py
index 14d21d74f..319a374ba 100644
--- a/backend/tests/test_api.py
+++ b/backend/tests/test_api.py
@@ -155,7 +155,7 @@
 _LEFTOVER_MAP_EXPLAINED_SHARE_MIGRATION = (
     Path(__file__).resolve().parents[2]
     / "migrations"
-    / "0184_report_leftover_map_explained_share.sql"
+    / "0185_report_leftover_map_explained_share.sql"
 )
 
 
diff --git a/docs/adr/0003-fast-mlsirm-report-integration.md b/docs/adr/0003-fast-mlsirm-report-integration.md
index b0c549f8f..c2d8ae19d 100644
--- a/docs/adr/0003-fast-mlsirm-report-integration.md
+++ b/docs/adr/0003-fast-mlsirm-report-integration.md
@@ -100,7 +100,7 @@ than one large PR:
    `information_polytomous` (Lord, 1980 max-info). Persist the ranking
    (`report_item_information`) and show the rank-1 item on the Period
    reports panel. Do not reimplement an information function here.
-7. **Leftover-pair slice** (shipped in 0.71.2; ADR 0017 / 0018 / 0048 / 0049 / 0182 / 0184): after
+7. **Leftover-pair slice** (shipped in 0.71.2; ADR 0017 / 0018 / 0048 / 0049 / 0182 / 0185): after
    IRT main effects, persist closest and farthest post–criterion pairs
    from the residual leftover map, and name unexplained leftover
    `U = R − R̂` and explained leftover share `e = R̂_c² / R̃²` of
diff --git a/docs/adr/0049-leftover-pair-report-ui.md b/docs/adr/0049-leftover-pair-report-ui.md
index 5160edb34..08723eeb1 100644
--- a/docs/adr/0049-leftover-pair-report-ui.md
+++ b/docs/adr/0049-leftover-pair-report-ui.md
@@ -6,7 +6,7 @@
 [ADR 0163](0163-leftover-observed-expected.md) (observed Y and expected E);
 [ADR 0164](0164-leftover-map-rank.md) (full map rank);
 [ADR 0182](0182-leftover-map-unexplained.md) (unexplained leftover U);
-[ADR 0184](0184-leftover-map-explained-share.md) (explained leftover share)
+[ADR 0185](0185-leftover-map-explained-share.md) (explained leftover share)
 
 ## Context
 
@@ -41,7 +41,7 @@ row. Residual naming is [ADR 0162](0162-leftover-residual-disclosure.md),
 observed/expected naming is [ADR 0163](0163-leftover-observed-expected.md),
 rank naming is [ADR 0164](0164-leftover-map-rank.md), unexplained
 leftover naming is [ADR 0182](0182-leftover-map-unexplained.md),
-explained-share naming is [ADR 0184](0184-leftover-map-explained-share.md).
+explained-share naming is [ADR 0185](0185-leftover-map-explained-share.md).
 
 After `make seed`, closest and farthest leftover pairs sit above the
 member list. Click a pair to open that post.
diff --git a/docs/adr/0185-leftover-map-explained-share.md b/docs/adr/0185-leftover-map-explained-share.md
index cdce230d8..76dc7b53a 100644
--- a/docs/adr/0185-leftover-map-explained-share.md
+++ b/docs/adr/0185-leftover-map-explained-share.md
@@ -38,7 +38,7 @@ Euclidean. Reconstruction `R̂_c` is computed internally so `e` is
 honest, then discarded.
 
 The unprotected-stack reconstructions for neighbouring leftover facts
-use 0162–0183. This protected-main increment uses **0184** so it does
+use 0162–0184. This protected-main increment uses **0185** so it does
 not collide with leftover-map unexplained leftover share (0183),
 leftover-map unexplained leftover (0182), leftover-map reconstruction
 (0181), leftover-map length (0181 on the length stack), leftover-map
@@ -52,7 +52,7 @@ leftover interaction-map persistence (0121).
 
 Each leftover pair names `leftover_map_explained_share` — explained
 leftover share `e = R̂_c² / R̃²` of centered leftover after two-axis
-Gabriel reconstruction `R̂_c = ξ_{1:2} · ζ_{1:2}`. Migration `0184`
+Gabriel reconstruction `R̂_c = ξ_{1:2} · ζ_{1:2}`. Migration `0185`
 is the single source of the column on every install path, fresh or
 existing -- shipped migrations (`0001` / `0012`) are never edited after
 the fact. The column is nullable so older leftover rows keep distance
diff --git a/migrations/0184_report_leftover_map_explained_share.sql b/migrations/0185_report_leftover_map_explained_share.sql
similarity index 94%
rename from migrations/0184_report_leftover_map_explained_share.sql
rename to migrations/0185_report_leftover_map_explained_share.sql
index 3cfa40d84..c3d40b804 100644
--- a/migrations/0184_report_leftover_map_explained_share.sql
+++ b/migrations/0185_report_leftover_map_explained_share.sql
@@ -1,4 +1,4 @@
--- ADR 0184: persist explained leftover share e = R̂_c² / R̃² of the
+-- ADR 0185: persist explained leftover share e = R̂_c² / R̃² of the
 -- centered leftover the two-axis leftover map reconstructs
 -- (R̃ = R − center, R̂_c = ξ_{1:2} · ζ_{1:2}).
 -- Distance stays Euclidean leftover-map d. Centered leftover U_c and
diff --git a/migrations/rollback/0184_report_leftover_map_explained_share.sql b/migrations/rollback/0185_report_leftover_map_explained_share.sql
similarity index 76%
rename from migrations/rollback/0184_report_leftover_map_explained_share.sql
rename to migrations/rollback/0185_report_leftover_map_explained_share.sql
index 9a1b554d2..d7758bf69 100644
--- a/migrations/rollback/0184_report_leftover_map_explained_share.sql
+++ b/migrations/rollback/0185_report_leftover_map_explained_share.sql
@@ -1,4 +1,4 @@
--- Reverse 0184. Leftover distance and residual stay on the pair row.
+-- Reverse 0185. Leftover distance and residual stay on the pair row.
 
 alter table report_leftover_pair
     drop constraint if exists leftover_pair_explained_share_nonnegative_chk;
diff --git a/scripts/seed_demo_data.py b/scripts/seed_demo_data.py
index 0d85107de..7845d6a35 100644
--- a/scripts/seed_demo_data.py
+++ b/scripts/seed_demo_data.py
@@ -123,7 +123,7 @@ def seed(
             cur.execute((migrations / "0168_report_leftover_map_coverage.sql").read_text())
             cur.execute((migrations / "0169_report_leftover_map_axis.sql").read_text())
             cur.execute((migrations / "0182_report_leftover_map_unexplained.sql").read_text())
-            cur.execute((migrations / "0184_report_leftover_map_explained_share.sql").read_text())
+            cur.execute((migrations / "0185_report_leftover_map_explained_share.sql").read_text())
             cur.execute((migrations / "0060_role_responsibility_agent_type.sql").read_text())
             cur.execute((migrations / "0013_person_job_title.sql").read_text())
             cur.execute((migrations / "0014_role_responsibility_team_actor_type.sql").read_text())
diff --git a/tests/test_schema.py b/tests/test_schema.py
index 3560fca99..1318a8356 100644
--- a/tests/test_schema.py
+++ b/tests/test_schema.py
@@ -71,7 +71,7 @@
 _LEFTOVER_MAP_EXPLAINED_SHARE_MIGRATION = (
     Path(__file__).resolve().parents[1]
     / "migrations"
-    / "0184_report_leftover_map_explained_share.sql"
+    / "0185_report_leftover_map_explained_share.sql"
 )
 
 

From e4dffe63cff2eb028bfb7e2a478d4aaf3cb187d6 Mon Sep 17 00:00:00 2001
From: seonghobae <seonghobae@users.noreply.github.com>
Date: Tue, 25 Aug 2026 10:57:36 +0900
Subject: [PATCH 7/7] test(leftover): full-width candidate row in the
 negative-rank test

The 7-element tuple passed only because the negative-rank guard raised
before _pair_from_candidate read row[7]; the row now carries all 8
elements so the test exercises the guard, not an IndexError shield.
Review follow-up on this PR's thread.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01VENX71RtEntaUq6nkAWZho
---
 tests/test_leftover_pairs.py | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/tests/test_leftover_pairs.py b/tests/test_leftover_pairs.py
index 7dbfc79c5..e4221bf1a 100644
--- a/tests/test_leftover_pairs.py
+++ b/tests/test_leftover_pairs.py
@@ -596,7 +596,9 @@ def test_leftover_map_rank_rejects_negative_rank() -> None:
     with pytest.raises(ValueError, match="non-negative integer"):
         leftover._pair_from_candidate(
             PAIR_KIND_CLOSEST,
-            (0.0, "public-post", "sales_lead_specificity", 0.0, 1.0, 1.0, None),
+            # Full 8-element candidate row: the guard must fire on the rank,
+            # not survive by short-circuiting before row[7] is read.
+            (0.0, "public-post", "sales_lead_specificity", 0.0, 1.0, 1.0, None, None),
             -1,
         )