seonghobae · Aug 23, 2026 · Aug 23, 2026 · Aug 24, 2026 · Aug 24, 2026 · Aug 24, 2026
diff --git 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 / 0183) 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
+unexplained leftover share `s = U_c² / R̃²` of centered leftover next
+to leftover-map distance `d` so a click opens that post. Centered
+leftover `U_c` and two-axis reconstruction `R̂_c` are 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
@@ -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 / 0183) persist to
+`report_leftover_pair` with unexplained leftover share `s = U_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/2.12.27-leftover-map-unexplained-share.md b/CHANGELOG.d/2.12.27-leftover-map-unexplained-share.md
@@ -0,0 +1,9 @@
+## 2.12.27 — Leftover-map unexplained leftover share
+
+- Persist unexplained leftover share `s = U_c² / R̃²` of centered
+  leftover on leftover post–criterion pairs (ADR 0183). After
+  `make seed`, closest and farthest leftover pairs sit above the
+  member list with `U²/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 `U` or reconstruction `R̂`.
diff --git 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.
 
+## [2.12.27] - 2026-08-24
+
+### Added
+
+- Period leftover pair rows now name unexplained leftover share
+  `s = U_c² / R̃²` of centered leftover next to leftover-map distance
+  `d`, then open that post (Gabriel, 1971; Jeon et al., 2021, eq. 3;
+  ADR 0183). A missing share omits the badge rather than inventing a
+  leftover score. Centered leftover `U_c` and two-axis reconstruction
+  `R̂_c` stay internal and are not persisted.
+
 ## [2.12.6] - 2026-08-20
 
 ### Added

diff --git 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 unexplained leftover share `U²/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
@@ -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_unexplained_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_unexplained_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_unexplained_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_unexplained_share": (
+                            None
+                            if row["leftover_map_unexplained_share"] is None
+                            else float(row["leftover_map_unexplained_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
@@ -113,6 +113,11 @@
     / "migrations"
     / "0102_project_bound_summary_event.sql"
 )
+_LEFTOVER_MAP_UNEXPLAINED_SHARE_MIGRATION = (
+    Path(__file__).resolve().parents[2]
+    / "migrations"
+    / "0183_report_leftover_map_unexplained_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_UNEXPLAINED_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 +4524,13 @@ 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_unexplained_share")
+        assert share is None or isinstance(share, (int, float))
+        if share is not None:
+            assert share >= 0
+        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
@@ -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_*|0183_*) ;;
         *) 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
@@ -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 / 0183): 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 unexplained leftover share
+   `s = U_c² / R̃²` of centered leftover when Gabriel coordinates exist
+   so the leftover cell the two-axis map does not reconstruct is not
+   read as leftover residual or leftover-map distance. Do not persist
+   leftover-map unexplained leftover `U` 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
@@ -30,7 +30,13 @@ 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 unexplained leftover share `s = U_c² / R̃²` of
+centered leftover when Gabriel coordinates exist so the leftover
+cell the two-axis map does not reconstruct is not read as leftover
+residual `R` or leftover-map distance `d` (ADR 0183). Centered leftover
+`U_c` and two-axis reconstruction `R̂_c` are computed internally and
+are 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
@@ -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.”). Unexplained leftover share next
+action: leftover map leaves unexplained share `s` 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. Unexplained leftover share naming is
+[ADR 0183](0183-leftover-map-unexplained-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/0183-leftover-map-unexplained-share.md b/docs/adr/0183-leftover-map-unexplained-share.md
@@ -0,0 +1,100 @@
+# ADR 0183 — Name unexplained 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 unexplained leftover
+share `s = U_c² / R̃²` (`U_c = R̃ − R̂_c`) lets a buyer read leftover
+residual `R` or leftover-map distance `d` as the leftover the two-axis
+map does not reconstruct. Subtracting reconstruction from raw `R`
+(or dividing by `R²`) leaves the grand mean inside the named leftover,
+so a fully reconstructed rank-1 cell would look unexplained whenever
+`center ≠ 0`.
+
+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 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. Centered leftover `U_c` and reconstruction `R̂_c` are
+computed internally so `s` is honest, then discarded.
+
+The unprotected-stack reconstructions for neighbouring leftover facts
+use 0162–0182. This protected-main increment uses **0183** so it does
+not collide with 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_unexplained_share` — unexplained
+leftover share `s = U_c² / R̃²` of centered leftover after two-axis
+Gabriel reconstruction `R̂_c = ξ_{1:2} · ζ_{1:2}`. Migration `0183`
+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 `U_c = 0`), not a
+missing value. A fully reconstructed rank-1 cell stores `0.0` 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_unexplained_share_nonnegative_chk` rejects a stored
+negative share. Do not persist `leftover_map_unexplained` or
+`leftover_map_reconstruction`.
+
+The pair button shows `U²/R̃² {share}` next to leftover-map distance
+`d` when the value is a finite non-negative number. Next action:
+leftover map leaves unexplained share `s` 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_unexplained_share`. After `make seed`, closest and
+farthest leftover pairs sit above the member list with named
+`U²/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,
+and leftover-map unexplained leftover.
+
+## 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
@@ -1,7 +1,7 @@
 {
   "name": "frontend",
   "private": true,
-  "version": "2.12.6",
+  "version": "2.12.27",
   "type": "module",
   "scripts": {
     "dev": "vite",

diff --git 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_unexplained_share: 0.12,
                   },
                   {
                     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_unexplained_share: 0.45,
                   },
                 ],
                 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.",
+      "Leftover map leaves unexplained share 0.12 of centered leftover after IRT main effects. Open this post to read sales-lead.",
     );
+    expect(closestPair).toHaveTextContent("U²/R̃² 0.12");
     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.",
+      "Leftover map leaves unexplained share 0.45 of centered leftover after IRT main effects. Open this post to read negative.",
     );
+    expect(farthestPair).toHaveTextContent("U²/R̃² 0.45");
     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();