seonghobae · Aug 24, 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 / 0182) 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 `U = R − R̂` next to leftover-map distance `d`
+so a click opens that post. Two-axis reconstruction `R̂` 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
@@ -588,8 +588,8 @@ 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 / 0182) persist to
+`report_leftover_pair` with unexplained leftover `U = R − R̂` 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/2.12.26-leftover-map-unexplained.md b/CHANGELOG.d/2.12.26-leftover-map-unexplained.md
@@ -0,0 +1,8 @@
+## 2.12.26 — Leftover-map unexplained leftover
+
+- Persist unexplained leftover `U = R − R̂` on leftover post–criterion
+  pairs (ADR 0182). After `make seed`, closest and farthest leftover
+  pairs sit above the member list with `U` next to leftover-map
+  distance `d`; click opens that post. Omit the badge when unexplained
+  leftover is missing. Never invent a leftover score. Do not persist
+  leftover-map reconstruction `R̂`.
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -12,6 +12,16 @@ 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.
 
+## [2.12.26] - 2026-08-24
+
+### Added
+
+- Period leftover pair rows now name unexplained leftover `U = R − R̂`
+  next to leftover-map distance `d`, then open that post (Gabriel, 1971;
+  Jeon et al., 2021, eq. 3; ADR 0182). A missing unexplained leftover
+  omits the badge rather than inventing a leftover score. Two-axis
+  reconstruction `R̂` stays internal and is 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 `U` 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
+            ) 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,
         )
 
 
@@ -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,
+               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": (
+                            None
+                            if row["leftover_map_unexplained"] is None
+                            else float(row["leftover_map_unexplained"])
+                        ),
                         "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_MIGRATION = (
+    Path(__file__).resolve().parents[2]
+    / "migrations"
+    / "0182_report_leftover_map_unexplained.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_MIGRATION.read_text())
             cur.execute(
                 "insert into common_lookup_value (lookup_category, lookup_code, lookup_label) values "
                 "('corporate_entity_level', 'group', 'Group'), "
@@ -4518,6 +4524,10 @@ 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", []):
+        unexplained = pair.get("leftover_map_unexplained")
+        assert unexplained is None or isinstance(unexplained, (int, float))
+        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_*|0182_*) ;;
         *) 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 +100,13 @@ 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 / 0182): 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
+   `U = R − R̂` 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 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 +30,12 @@ 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 unexplained leftover `U = R − R̂` 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 0182). Two-axis reconstruction `R̂` 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
@@ -19,8 +19,12 @@ 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 next action:
+leftover map leaves unexplained `U` after IRT main effects; open this
+post to read the named criterion. A missing unexplained leftover keeps
+the existing closest/farthest next action. Clicking the button opens that
+post with the same handler as a member row. Unexplained leftover naming is
+[ADR 0182](0182-leftover-map-unexplained.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/0182-leftover-map-unexplained.md b/docs/adr/0182-leftover-map-unexplained.md
@@ -0,0 +1,92 @@
+# ADR 0182 — Name unexplained leftover 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 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 = ξ_{1:2} · ζ_{1:2}` is therefore the leftover cell the map
+shows. Hiding unexplained leftover `U = R − R̂` lets a buyer read
+leftover residual `R` or leftover-map distance `d` as the leftover
+the two-axis map does not reconstruct.
+
+This increment does not persist leftover-map reconstruction `R̂`, does
+not persist leftover-map coordinates, does not name leftover-map inner
+product as a separate full-rank column, does not name leftover-map
+cosine, does not name leftover-map 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` is computed internally so `U` is honest, then
+discarded.
+
+The unprotected-stack reconstructions for neighbouring leftover facts
+use 0162–0181. This protected-main increment uses **0182** so it does
+not collide with 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` (0177), leftover-map
+rank (0172), two-axis leftover-map distance (0166), leftover coverage
+(0168), leftover-map axis share (0148), or leftover interaction-map
+persistence (0121).
+
+## Decision
+
+Each leftover pair names `leftover_map_unexplained` — unexplained
+leftover `U = R − R̂` after two-axis Gabriel reconstruction
+`R̂ = ξ_{1:2} · ζ_{1:2}`. Migration `0182` 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 unexplained leftover. Fallback pairs that have no
+complete-case leftover map omit the value rather than inventing one.
+A rank-0 origin map stores `0.0` (`R = 0` and `R̂ = 0`), not a
+missing value. A non-finite unexplained leftover stores null rather
+than inventing a leftover score. Do not persist
+`leftover_map_reconstruction`.
+
+The pair button shows `U {signed}` next to leftover-map distance `d`
+when the value is finite. Next action: leftover map leaves unexplained
+`U` after IRT main effects; open this post to read the named criterion.
+A missing or non-finite unexplained leftover 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`. After `make seed`, closest and farthest
+leftover pairs sit above the member list with named `U` 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, and leftover-map
+reconstruction.
+
+## 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": "2.12.26",
   "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: 0.05,
                   },
                   {
                     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: -0.25,
                   },
                 ],
                 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 U +0.05 after IRT main effects. Open this post to read sales-lead.",
     );
+    expect(closestPair).toHaveTextContent("U +0.05");
     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 U −0.25 after IRT main effects. Open this post to read negative.",
     );
+    expect(farthestPair).toHaveTextContent("U −0.25");
     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();