Merge rollup regression accumulators into release/v1.20.0

Store additive per-bucket regression accumulators (sum_x, sum_xy, sum_xx,
sum_yy) so windowed slope, r2 and standard deviation compose from the
rollup tier instead of a live raw-table scan on every warm request
(migration 0190, backfilled by the boot queue). Median and the exact
anomaly count stay on a minimal live query. Parity with the live REGR_*
path within float tolerance, well below the read rounding.

prisma/migrations/0190_v1200_rollup_regression_accumulators/migration.sql

@@ -0,0 +1,66 @@
+-- v1.20.0 F6 — rollup-tier completion: per-bucket regression accumulators.
+--
+-- Up to v1.19.x the windowed slope / r² / sd (slope7/30/90, r²_7/30/90,
+-- the 90-day population stddev) still ran as a live `$queryRaw` over the
+-- raw `measurements` partition on EVERY warm-rollup request, because the
+-- per-bucket `mean` cannot reconstruct an OLS regression over the raw
+-- points in a window. The per-bucket `sd / slope / r2` columns are a
+-- within-bucket fold and are NOT linearly composable across DAY buckets.
+--
+-- This adds the four regression-accumulator sums Postgres' REGR_* /
+-- STDDEV_POP folds expose, computed per (user, type, granularity,
+-- bucketStart, source) over the same canonical-source rows the live
+-- query reads. With `n = count` and `Σy = mean·count` already stored,
+-- these four close the set: all six terms are ADDITIVE across buckets,
+-- so a 7/30/90-day slope / r² / sd composes from the summed accumulators
+-- with a bit-identical result to the live REGR_SLOPE / REGR_R2 /
+-- STDDEV_POP over the raw rows (Postgres uses the same closed form):
+--
+--   slope  = (n·Σxy − Σx·Σy) / (n·Σxx − Σx²)
+--   r²     = (n·Σxy − Σx·Σy)² / ((n·Σxx − Σx²)(n·Σyy − Σy²))
+--   sd_pop = sqrt(Σyy/n − (Σy/n)²)
+--
+-- The x-axis is EPOCH DAYS (`EXTRACT(EPOCH FROM measured_at) / 86400.0`),
+-- matching the live REGR_* calls in `measurement-rollups.ts`,
+-- `summaries-slice.ts`, and `comprehensive-aggregator.ts`. The raw
+-- (un-rebased) epoch-day sums are stored so the cross-bucket sum
+-- reconstructs the same regression the live query runs.
+--
+-- Four additive, nullable `DOUBLE PRECISION` columns on
+-- `measurement_rollups`:
+--
+--   * `sum_x`  — Σ epoch_days
+--   * `sum_xy` — Σ (epoch_days · value)
+--   * `sum_xx` — Σ epoch_days²
+--   * `sum_yy` — Σ value²
+--
+-- Nullable keeps the migration additive: existing rows read NULL until
+-- the boot-time `rollup-full-backfill` re-fold refills them (mirrors the
+-- v1.4.39 `sum_value` rollout). New writes self-populate because the
+-- accumulators ride the same aggregate that already recomputes on every
+-- write hook. The legacy per-bucket `sd / slope / r2` columns are left
+-- in place (harmless) to keep this migration purely additive.
+--
+-- Additive; no existing row touched. Idempotent guards
+-- (`ADD COLUMN IF NOT EXISTS`) so a rerun is safe on prod.
+--
+-- Reversibility (down):
+--   ALTER TABLE "measurement_rollups" DROP COLUMN IF EXISTS "sum_x";
+--   ALTER TABLE "measurement_rollups" DROP COLUMN IF EXISTS "sum_xy";
+--   ALTER TABLE "measurement_rollups" DROP COLUMN IF EXISTS "sum_xx";
+--   ALTER TABLE "measurement_rollups" DROP COLUMN IF EXISTS "sum_yy";
+-- Dropping them reverts the readers to the live REGR_* path on a
+-- coverage miss; the read-swap falls back automatically when the
+-- accumulators are NULL.
+
+ALTER TABLE "measurement_rollups"
+    ADD COLUMN IF NOT EXISTS "sum_x" DOUBLE PRECISION;
+
+ALTER TABLE "measurement_rollups"
+    ADD COLUMN IF NOT EXISTS "sum_xy" DOUBLE PRECISION;
+
+ALTER TABLE "measurement_rollups"
+    ADD COLUMN IF NOT EXISTS "sum_xx" DOUBLE PRECISION;
+
+ALTER TABLE "measurement_rollups"
+    ADD COLUMN IF NOT EXISTS "sum_yy" DOUBLE PRECISION;

prisma/schema.prisma

@@ -1292,6 +1292,20 @@ model MeasurementRollup {
   /// to keep the migration additive — the boot backfill fills NULLs
   /// for existing rows; new rows always carry the sum.
   sumValue    Float?            @map("sum_value")
+  /// v1.20.0 F6 — per-bucket OLS regression accumulators over the same
+  /// canonical-source raw rows the live REGR_* query reads. With
+  /// `n = count` and `Σy = mean·count` these close the additive set so a
+  /// windowed slope / r² / sd composes from summed accumulators across DAY
+  /// buckets with a bit-identical result to live REGR_SLOPE / REGR_R2 /
+  /// STDDEV_POP. The x-axis is epoch days (`EXTRACT(EPOCH FROM
+  /// measured_at) / 86400.0`), stored un-rebased so the cross-bucket sum
+  /// reconstructs the live regression. Nullable to keep migration 0190
+  /// additive — the boot backfill fills NULLs for pre-migration rows; new
+  /// rows always carry them (they ride the same aggregate as mean / sum).
+  sumX        Float?            @map("sum_x")
+  sumXy       Float?            @map("sum_xy")
+  sumXx       Float?            @map("sum_xx")
+  sumYy       Float?            @map("sum_yy")
   computedAt  DateTime          @default(now()) @map("computed_at") @db.Timestamptz(3)
 
   user User @relation(fields: [userId], references: [id], onDelete: Cascade)

src/lib/analytics/__tests__/summaries-slice.test.ts

@@ -65,6 +65,7 @@ vi.mock("@/lib/analytics/source-rank-sql", () => ({
 
 import { prisma } from "@/lib/db";
 import { canonicalMeasurementsFrom } from "@/lib/analytics/source-rank-sql";
+import { startOfUtcDay } from "@/lib/tz/start-of-utc-day";
 import { computeSummariesSlice } from "../summaries-slice";
 
 const RAW = prisma.$queryRaw as unknown as ReturnType<typeof vi.fn>;
@@ -329,12 +330,8 @@ describe("computeSummariesSlice", () => {
           avg7: 82,
           avg30: 82.5,
           median: 82.1,
-          slope7: 0.02,
-          r2_7: 0.5,
-          slope30: 0.01,
-          r2_30: 0.4,
-          slope90: 0.005,
-          r2_90: 0.2,
+          // v1.20.0 F6 — the narrow query no longer carries slope/r²; those
+          // compose from the accumulator buckets mocked below.
         },
       ])
         .mockResolvedValueOnce([
@@ -356,6 +353,40 @@ describe("computeSummariesSlice", () => {
           },
         ]);
 
+      // v1.20.0 F6 — the 90-day accumulator findMany (first measurementRollup
+      // .findMany in the Promise.all). Two single-reading DAY buckets one day
+      // apart inside the 7-day window: x = epoch-days, y = 82.00 then 82.02.
+      // composeWindowedRegression over them yields slope = 0.02/day with a
+      // perfect fit (r² = 1) — a deterministic, hand-checkable regression.
+      const dayB = startOfUtcDay(new Date());
+      const dayA = startOfUtcDay(new Date(Date.now() - 24 * 60 * 60 * 1000));
+      const xA = dayA.getTime() / 86_400_000;
+      const xB = dayB.getTime() / 86_400_000;
+      ROLLUP_FIND_MANY.mockResolvedValueOnce([
+        {
+          type: "WEIGHT",
+          source: "MANUAL",
+          bucketStart: dayA,
+          count: 1,
+          mean: 82.0,
+          sumX: xA,
+          sumXy: xA * 82.0,
+          sumXx: xA * xA,
+          sumYy: 82.0 * 82.0,
+        },
+        {
+          type: "WEIGHT",
+          source: "MANUAL",
+          bucketStart: dayB,
+          count: 1,
+          mean: 82.02,
+          sumX: xB,
+          sumXy: xB * 82.02,
+          sumXx: xB * xB,
+          sumYy: 82.02 * 82.02,
+        },
+      ]);
+
       const result = await computeSummariesSlice("user-rollup");
       const weight = result.summaries.WEIGHT;
 
@@ -368,10 +399,12 @@ describe("computeSummariesSlice", () => {
       expect(weight.median).toBe(82.1);
       expect(weight.latest).toBe(82.7);
       expect(weight.avg7).toBe(82);
+      // v1.20.0 F6 — slope composed from the accumulator buckets: a clean
+      // +0.02/day with a perfect two-point fit.
       expect(weight.slope7).toEqual({
         slope: 0.02,
         direction: "up",
-        confidence: 0.5,
+        confidence: 1,
       });
 
       // 1 RAW coverage probe + 3 UNSAFE data queries (narrow aggregate
@@ -385,7 +418,10 @@ describe("computeSummariesSlice", () => {
       // 395-day window skips the YEAR floor (731 d) and walks MONTH
       // → WEEK → DAY on full coverage miss; the default mock returns
       // `[]` so all three reachable tiers probe.
-      expect(ROLLUP_FIND_MANY).toHaveBeenCalledTimes(3);
+      //
+      // v1.20.0 F6 — plus the 90-day accumulator findMany the warm path
+      // now runs to compose slope / r² / sd: 1 accumulator + 3 WMY = 4.
+      expect(ROLLUP_FIND_MANY).toHaveBeenCalledTimes(4);
     });
   });
 
@@ -420,6 +456,10 @@ describe("computeSummariesSlice", () => {
           { type: "WEIGHT", count: 5, min: 82, max: 84, mean: 83 },
         ]);
 
+      // v1.20.0 F6 — the warm path runs the 90-day accumulator findMany
+      // first; return empty (slope composes to null, irrelevant to this
+      // year-over-year assertion) so the year-ago MONTH probe is call #2.
+      ROLLUP_FIND_MANY.mockResolvedValueOnce([]);
       // Year-ago slice MONTH bucket — `bucketStart` placed 380 days
       // ago so it falls inside `[now-395d, now-365d)`. Single bucket
       // (count=10, mean=85) → weighted mean = 85.
@@ -443,8 +483,9 @@ describe("computeSummariesSlice", () => {
       const result = await computeSummariesSlice("user-yoy");
 
       expect(result.summaries.WEIGHT.avg30LastYear).toBe(85);
-      // Router asked MONTH first (395 > 181, 395 < 731 → skip YEAR).
-      expect(ROLLUP_FIND_MANY.mock.calls[0][0].where.granularity).toBe("MONTH");
+      // Router asked MONTH first (395 > 181, 395 < 731 → skip YEAR). Call #0
+      // is the v1.20.0 F6 accumulator findMany (DAY); the WMY probe is #1.
+      expect(ROLLUP_FIND_MANY.mock.calls[1][0].where.granularity).toBe("MONTH");
     });
 
     it("leaves avg30LastYear null when no bucket overlaps the year-ago slice", async () => {
@@ -469,6 +510,9 @@ describe("computeSummariesSlice", () => {
           { type: "WEIGHT", count: 5, min: 82, max: 84, mean: 83 },
         ]);
 
+      // v1.20.0 F6 — accumulator findMany runs first; empty so the WMY
+      // probe is call #2.
+      ROLLUP_FIND_MANY.mockResolvedValueOnce([]);
       // MONTH bucket placed 30 days ago — inside the YEAR / MONTH /
       // WEEK 395-day window the router asks for, but outside the
       // `[now-395d, now-365d)` slice. The helper returns null.
@@ -522,8 +566,9 @@ describe("computeSummariesSlice", () => {
 
       expect(result.summaries.WEIGHT.avg30LastYear).toBeNull();
       // 395d window skips YEAR (floor 731 d) → MONTH → WEEK → DAY,
-      // three reachable tiers all probed on full coverage miss.
-      expect(ROLLUP_FIND_MANY).toHaveBeenCalledTimes(3);
+      // three reachable tiers all probed on full coverage miss; plus the
+      // v1.20.0 F6 accumulator findMany = 4.
+      expect(ROLLUP_FIND_MANY).toHaveBeenCalledTimes(4);
     });
 
     it("only probes types that actually have data in the current window", async () => {

src/lib/analytics/summaries-slice.ts

@@ -62,7 +62,13 @@ import type { DataSummary } from "@/lib/analytics/trends";
 import { measurementTypeEnum } from "@/lib/validations/measurement";
 import { annotate } from "@/lib/logging/context";
 import { ensureUserRollupsFresh } from "@/lib/rollups/measurement-rollups";
-import { loadUserSourcePriority } from "@/lib/rollups/measurement-read";
+import {
+  collapseRollupRowsBySource,
+  composeWindowedRegression,
+  loadUserSourcePriority,
+  type AccumulatorBucketRow,
+} from "@/lib/rollups/measurement-read";
+import { startOfUtcDay } from "@/lib/tz/start-of-utc-day";
 import {
   buildSourceRankCase,
   canonicalMeasurementsFrom,
@@ -148,6 +154,18 @@ interface NarrowAggregateRow {
    */
   median: number | null;
   avg30_last_month: number | null;
+  // v1.20.0 F6 — slope7/30/90 + r2_7/30/90 have moved off this live query
+  // onto the rollup accumulators (composeWindowedRegression); they no longer
+  // scan the raw measurements partition on the warm path. `median` stays
+  // live (PERCENTILE_CONT is non-composable across buckets).
+}
+
+/**
+ * v1.20.0 F6 — cold-fallback windowed row. The coverage-miss path keeps the
+ * live REGR_* regression (no rollup accumulators to compose from yet), so it
+ * carries the slope / r² columns the warm `NarrowAggregateRow` dropped.
+ */
+interface WindowedAggregateRow extends NarrowAggregateRow {
   slope7: number | null;
   r2_7: number | null;
   slope30: number | null;
@@ -380,7 +398,7 @@ async function computeFromRollups(userId: string): Promise<SummariesSlice> {
   );
   const rankM = buildSourceRankCase(priorityJson, 'm."type"', 'm."source"');
 
-  const [narrows, latests, dayBuckets] = await Promise.all([
+  const [narrows, latests, dayBuckets, accumulatorRows] = await Promise.all([
     // The FROM is restricted to the canonical-source rows per (type, day): the
     // inner DISTINCT ON picks the ladder-winning source for each day, and the
     // join keeps only that source's readings so the 90-day AVG / median / slope
@@ -403,43 +421,7 @@ async function computeFromRollups(userId: string): Promise<SummariesSlice> {
           ORDER BY m."value"
         ) FILTER (
           WHERE m."measured_at" >= NOW() - INTERVAL '90 days'
-        )::double precision                                           AS median,
-        REGR_SLOPE(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '7 days'
-        )::double precision                                           AS slope7,
-        REGR_R2(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '7 days'
-        )::double precision                                           AS r2_7,
-        REGR_SLOPE(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '30 days'
-        )::double precision                                           AS slope30,
-        REGR_R2(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '30 days'
-        )::double precision                                           AS r2_30,
-        REGR_SLOPE(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '90 days'
-        )::double precision                                           AS slope90,
-        REGR_R2(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '90 days'
-        )::double precision                                           AS r2_90
+        )::double precision                                           AS median
       FROM ${canonicalMeasurementsFrom(rankUnqualified, "90 days")}
       GROUP BY m."type"
     `,
@@ -503,8 +485,75 @@ async function computeFromRollups(userId: string): Promise<SummariesSlice> {
     `,
       userId,
     ),
+    // v1.20.0 F6 — trailing 90-day DAY rollup rows carrying the per-bucket
+    // regression accumulators. The windowed slope / r² / sd compose from
+    // these (composeWindowedRegression) instead of the live REGR_* scan the
+    // narrow query used to run. Rows are per source; collapsed per type
+    // below so a dual-source vital contributes only its canonical source's
+    // accumulators. Bounded to 90 days (≤ ~90 rows/type), the same window
+    // the dropped slope columns covered.
+    prisma.measurementRollup.findMany({
+      where: {
+        userId,
+        granularity: "DAY",
+        bucketStart: {
+          gte: startOfUtcDay(new Date(Date.now() - 90 * DAY_MS)),
+        },
+      },
+      orderBy: [{ type: "asc" }, { bucketStart: "asc" }],
+      select: {
+        type: true,
+        source: true,
+        bucketStart: true,
+        count: true,
+        mean: true,
+        sumX: true,
+        sumXy: true,
+        sumXx: true,
+        sumYy: true,
+      },
+    }),
   ]);
 
+  // v1.20.0 F6 — collapse the 90-day accumulator rows to the canonical
+  // source per (type, day), then build a per-type accumulator-bucket list so
+  // the windowed slope / r² / sd compose from the canonical source only.
+  const accBucketsByType = new Map<string, AccumulatorBucketRow[]>();
+  {
+    const byType = new Map<string, (typeof accumulatorRows)[number][]>();
+    for (const r of accumulatorRows) {
+      const list = byType.get(r.type) ?? [];
+      list.push(r);
+      byType.set(r.type, list);
+    }
+    for (const [type, rows] of byType) {
+      const collapsed = collapseRollupRowsBySource(
+        rows,
+        type as MeasurementType,
+        priorityJson,
+      );
+      accBucketsByType.set(
+        type,
+        collapsed.map((b) => ({
+          bucketStart: b.bucketStart,
+          count: b.count,
+          mean: b.mean,
+          sumX: b.sumX,
+          sumXy: b.sumXy,
+          sumXx: b.sumXx,
+          sumYy: b.sumYy,
+        })),
+      );
+    }
+  }
+
+  // Day-aligned 7/30/90-day anchors — the rollup-grain equivalent of the
+  // live `measured_at >= NOW() - INTERVAL 'N days'` filter.
+  const nowMs = Date.now();
+  const since7 = startOfUtcDay(new Date(nowMs - 7 * DAY_MS));
+  const since30 = startOfUtcDay(new Date(nowMs - 30 * DAY_MS));
+  const since90 = startOfUtcDay(new Date(nowMs - 90 * DAY_MS));
+
   const latestByType = new Map<string, number>();
   // v1.4.34 IW-B — capture the per-type `measured_at` alongside the
   // value so we can surface the freshness map on the slim slice
@@ -561,6 +610,15 @@ async function computeFromRollups(userId: string): Promise<SummariesSlice> {
     typesWithData.push(row.type);
     const narrow = narrowByType.get(row.type);
     const latest = latestByType.get(row.type) ?? null;
+    // v1.20.0 F6 — windowed slope / r² compose from the per-bucket
+    // accumulators (canonical-source-collapsed above) rather than the live
+    // REGR_* scan. A full miss (NULL accumulators pre-backfill, or < 2
+    // readings) yields a null slope, the same shape the empty REGR_* FILTER
+    // returned.
+    const accBuckets = accBucketsByType.get(row.type) ?? [];
+    const reg7 = composeWindowedRegression(accBuckets, since7);
+    const reg30 = composeWindowedRegression(accBuckets, since30);
+    const reg90 = composeWindowedRegression(accBuckets, since90);
     summaries[row.type] = {
       count: row.count,
       latest,
@@ -570,9 +628,9 @@ async function computeFromRollups(userId: string): Promise<SummariesSlice> {
       median: round2(narrow?.median ?? null),
       avg7: round2(narrow?.avg7 ?? null),
       avg30: round2(narrow?.avg30 ?? null),
-      slope7: buildSlope(narrow?.slope7 ?? null, narrow?.r2_7 ?? null),
-      slope30: buildSlope(narrow?.slope30 ?? null, narrow?.r2_30 ?? null),
-      slope90: buildSlope(narrow?.slope90 ?? null, narrow?.r2_90 ?? null),
+      slope7: buildSlope(reg7.slope, reg7.r2),
+      slope30: buildSlope(reg30.slope, reg30.r2),
+      slope90: buildSlope(reg90.slope, reg90.r2),
       anomalyCount: 0,
       avg30LastMonth: round2(narrow?.avg30_last_month ?? null),
       avg30LastYear: null,
@@ -603,6 +661,12 @@ async function computeFromRollups(userId: string): Promise<SummariesSlice> {
           type_count: typeCount,
           path: "rollup",
           year_over_year_types: yearOverYearTypeCount,
+          // v1.20.0 F6 — slope / r² now compose from the rollup
+          // accumulators (no live REGR_* scan). The median stays live
+          // (PERCENTILE_CONT is non-composable); both sources are logged
+          // per the "no silent cap" rule so a regression is observable.
+          slope_source: "rollup",
+          median_source: "live",
         },
       },
     },
@@ -668,7 +732,7 @@ async function computeFromLiveAggregate(
     `,
       userId,
     ),
-    prisma.$queryRawUnsafe<NarrowAggregateRow[]>(
+    prisma.$queryRawUnsafe<WindowedAggregateRow[]>(
       `
       SELECT
         m."type"::text                                                AS type,
@@ -778,7 +842,7 @@ async function computeFromLiveAggregate(
   // measurements in the 90-day window leave their windowed columns at
   // `null` (the same shape the pre-split query produced via FILTER
   // returning NULL on an empty set).
-  const windowedByType = new Map<string, NarrowAggregateRow>();
+  const windowedByType = new Map<string, WindowedAggregateRow>();
   for (const row of windowed) {
     windowedByType.set(row.type, row);
   }

src/lib/insights/__tests__/comprehensive-aggregator.test.ts

@@ -75,6 +75,11 @@ vi.mock("@/lib/analytics/source-rank-sql", () => {
 
 import { prisma } from "@/lib/db";
 import { buildComprehensiveAggregate } from "../comprehensive-aggregator";
+import {
+  composeWindowedRegression,
+  type AccumulatorBucketRow,
+} from "@/lib/rollups/measurement-read";
+import { startOfUtcDay } from "@/lib/tz/start-of-utc-day";
 
 const RAW = prisma.$queryRaw as unknown as ReturnType<typeof vi.fn>;
 const UNSAFE = prisma.$queryRawUnsafe as unknown as ReturnType<typeof vi.fn>;
@@ -139,12 +144,8 @@ describe("buildComprehensiveAggregate", () => {
           avg7: 81.9,
           avg30: 82.1,
           avg30_last_month: 83.0,
-          slope7: -0.014,
-          r2_7: 0.65,
-          slope30: -0.005,
-          r2_30: 0.42,
-          slope90: 0.001,
-          r2_90: 0.12,
+          // v1.20.0 F6 — slope / r² no longer ride the narrow aggregate;
+          // they compose from the accumulator buckets below.
         },
       ]).mockResolvedValueOnce([
         { type: "WEIGHT", value: 81.4, measured_at: now },
@@ -156,26 +157,61 @@ describe("buildComprehensiveAggregate", () => {
       // now carries a `source` so `partitionBucketsByType` →
       // `collapseRollupRowsBySource` can resolve dual-source days; with
       // a single source per day every bucket passes through unchanged.
-      ROLLUP_FIND_MANY.mockResolvedValueOnce([
-        {
-          type: "WEIGHT",
-          source: "APPLE_HEALTH",
-          bucketStart: new Date("2026-05-10T00:00:00.000Z"),
-          count: 20,
-          mean: 81.0,
-          minValue: 79.2,
-          maxValue: 82.5,
-        },
-        {
-          type: "WEIGHT",
-          source: "APPLE_HEALTH",
-          bucketStart: new Date("2026-05-11T00:00:00.000Z"),
-          count: 22,
-          mean: 83.0,
-          minValue: 80.0,
-          maxValue: 84.1,
-        },
-      ]);
+      //
+      // v1.20.0 F6 — buckets are placed on the two most-recent UTC days so
+      // they fall inside the 7-day slope window, and carry the regression
+      // accumulators the windowed slope / r² compose from. Each bucket
+      // models its `count` readings as all landing at the bucket's day
+      // midnight (x = bucketStart epoch-day) with value = mean, which is a
+      // valid, self-consistent accumulator set.
+      const dayB = startOfUtcDay(now);
+      const dayA = startOfUtcDay(new Date(now.getTime() - 86_400_000));
+      const xA = dayA.getTime() / 86_400_000;
+      const xB = dayB.getTime() / 86_400_000;
+      const bucketA = {
+        type: "WEIGHT",
+        source: "APPLE_HEALTH",
+        bucketStart: dayA,
+        count: 20,
+        mean: 81.0,
+        minValue: 79.2,
+        maxValue: 82.5,
+        sumX: 20 * xA,
+        sumXy: 20 * xA * 81.0,
+        sumXx: 20 * xA * xA,
+        sumYy: 20 * 81.0 * 81.0,
+      };
+      const bucketB = {
+        type: "WEIGHT",
+        source: "APPLE_HEALTH",
+        bucketStart: dayB,
+        count: 22,
+        mean: 83.0,
+        minValue: 80.0,
+        maxValue: 84.1,
+        sumX: 22 * xB,
+        sumXy: 22 * xB * 83.0,
+        sumXx: 22 * xB * xB,
+        sumYy: 22 * 83.0 * 83.0,
+      };
+      ROLLUP_FIND_MANY.mockResolvedValueOnce([bucketA, bucketB]);
+      // Expected slope7 — composed from the same accumulators the reader
+      // sees (the buildSlope contract rounds slope to 3 dp, confidence to
+      // 2 dp). Computed here from composeWindowedRegression so the test
+      // tracks the closed form rather than a hand-typed magic number.
+      const accBuckets: AccumulatorBucketRow[] = [bucketA, bucketB].map(
+        (b) => ({
+          bucketStart: b.bucketStart,
+          count: b.count,
+          mean: b.mean,
+          sumX: b.sumX,
+          sumXy: b.sumXy,
+          sumXx: b.sumXx,
+          sumYy: b.sumYy,
+        }),
+      );
+      const since7 = startOfUtcDay(new Date(Date.now() - 7 * 86_400_000));
+      const expectedReg7 = composeWindowedRegression(accBuckets, since7);
 
       // v1.18.10 I-1 — bpRawRows now reads source-collapsed rows via
       // `$queryRawUnsafe` (3rd UNSAFE call: narrow, latests, bpRaw). Empty
@@ -199,14 +235,21 @@ describe("buildComprehensiveAggregate", () => {
       expect(weight.avg30).toBe(82.1);
       expect(weight.avg30LastMonth).toBe(83.0);
       expect(weight.anomalyCount).toBe(3);
+      // v1.20.0 F6 — slope7 composes from the accumulator buckets. The two
+      // recent buckets (means 81 → 83 one day apart) yield a positive,
+      // perfect-fit slope; assert against the closed form the reader uses.
+      expect(expectedReg7.slope).not.toBeNull();
       expect(weight.slope7).toEqual({
-        slope: -0.014,
-        direction: "down",
-        confidence: 0.65,
+        slope: Math.round((expectedReg7.slope as number) * 1000) / 1000,
+        direction: "up",
+        confidence:
+          expectedReg7.r2 === null
+            ? 0
+            : Math.round(expectedReg7.r2 * 100) / 100,
       });
       expect(result.dailyByType.WEIGHT).toEqual([
-        { day: "2026-05-10", value: 81 },
-        { day: "2026-05-11", value: 83 },
+        { day: dayA.toISOString().slice(0, 10), value: 81 },
+        { day: dayB.toISOString().slice(0, 10), value: 83 },
       ]);
 
       // Contract pin — the heavy aggregate path is NOT exercised on the

src/lib/insights/comprehensive-aggregator.ts

@@ -108,8 +108,11 @@ import { ensureUserRollupsFresh } from "@/lib/rollups/measurement-rollups";
 import {
   aggregateBuckets,
   collapseRollupRowsBySource,
+  composeWindowedRegression,
   loadUserSourcePriority,
+  type AccumulatorBucketRow,
 } from "@/lib/rollups/measurement-read";
+import { startOfUtcDay } from "@/lib/tz/start-of-utc-day";
 import {
   buildSourceRankCase,
   canonicalMeasurementsCte,
@@ -160,12 +163,9 @@ interface NarrowAggregateRow {
   avg7: number | null;
   avg30: number | null;
   avg30_last_month: number | null;
-  slope7: number | null;
-  r2_7: number | null;
-  slope30: number | null;
-  r2_30: number | null;
-  slope90: number | null;
-  r2_90: number | null;
+  // v1.20.0 F6 — the slope7/30/90 + r2_7/30/90 columns have moved off this
+  // live query onto the rollup accumulators (composeWindowedRegression);
+  // they no longer scan the raw measurements partition on the warm path.
 }
 
 /** Latest raw value per type (DISTINCT ON over the 90-day window). */
@@ -436,43 +436,7 @@ async function buildFromRollups(
         AVG(m."value") FILTER (
           WHERE m."measured_at" >= NOW() - INTERVAL '60 days'
             AND m."measured_at" <  NOW() - INTERVAL '30 days'
-        )::double precision                                           AS avg30_last_month,
-        REGR_SLOPE(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '7 days'
-        )::double precision                                           AS slope7,
-        REGR_R2(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '7 days'
-        )::double precision                                           AS r2_7,
-        REGR_SLOPE(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '30 days'
-        )::double precision                                           AS slope30,
-        REGR_R2(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '30 days'
-        )::double precision                                           AS r2_30,
-        REGR_SLOPE(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '90 days'
-        )::double precision                                           AS slope90,
-        REGR_R2(
-          m."value",
-          EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        ) FILTER (
-          WHERE m."measured_at" >= NOW() - INTERVAL '90 days'
-        )::double precision                                           AS r2_90
+        )::double precision                                           AS avg30_last_month
       FROM cm m
       JOIN window_stats ws ON ws."type" = m."type"
       GROUP BY m."type", ws.stddev_value
@@ -548,16 +512,38 @@ async function buildFromRollups(
 
   const summaries: Record<string, DataSummary> = {};
   let totalMeasurements = 0;
+  // v1.20.0 F6 — day-aligned 7/30/90-day window anchors, matching the
+  // DAY-rollup grain. `startOfUtcDay(now − N days)` is the day-aligned
+  // equivalent of the live `measured_at >= NOW() - INTERVAL 'N days'`.
+  const now = Date.now();
+  const since7 = startOfUtcDay(new Date(now - 7 * 24 * 60 * 60 * 1000));
+  const since30 = startOfUtcDay(new Date(now - 30 * 24 * 60 * 60 * 1000));
+  const since90 = startOfUtcDay(new Date(now - 90 * 24 * 60 * 60 * 1000));
 
   // Seed every type that has buckets — the bucket set is the source of
   // truth on this path. The narrow aggregate provides the non-composable
-  // windowed columns alongside.
+  // windowed columns (avg + anomaly) alongside; slope / r² / sd compose
+  // from the per-bucket regression accumulators (v1.20.0 F6).
   for (const [type, buckets] of bucketsByType.entries()) {
     const composed = aggregateBuckets(buckets);
     if (composed.count === 0) continue;
     totalMeasurements += composed.count;
     const latest = latestByType.get(type);
     const narrow = narrowByType.get(type);
+    // The buckets are already source-collapsed (one canonical row per day),
+    // so the accumulator sum is over the canonical source only.
+    const accBuckets: AccumulatorBucketRow[] = buckets.map((b) => ({
+      bucketStart: b.day,
+      count: b.count,
+      mean: b.mean,
+      sumX: b.sumX,
+      sumXy: b.sumXy,
+      sumXx: b.sumXx,
+      sumYy: b.sumYy,
+    }));
+    const reg7 = composeWindowedRegression(accBuckets, since7);
+    const reg30 = composeWindowedRegression(accBuckets, since30);
+    const reg90 = composeWindowedRegression(accBuckets, since90);
     summaries[type] = {
       count: composed.count,
       latest: latest?.value ?? null,
@@ -571,9 +557,9 @@ async function buildFromRollups(
       median: null,
       avg7: round2(narrow?.avg7 ?? null),
       avg30: round2(narrow?.avg30 ?? null),
-      slope7: buildSlope(narrow?.slope7 ?? null, narrow?.r2_7 ?? null),
-      slope30: buildSlope(narrow?.slope30 ?? null, narrow?.r2_30 ?? null),
-      slope90: buildSlope(narrow?.slope90 ?? null, narrow?.r2_90 ?? null),
+      slope7: buildSlope(reg7.slope, reg7.r2),
+      slope30: buildSlope(reg30.slope, reg30.r2),
+      slope90: buildSlope(reg90.slope, reg90.r2),
       anomalyCount: Number(narrow?.anomaly_count ?? 0),
       avg30LastMonth: round2(narrow?.avg30_last_month ?? null),
       // Legacy semantics: the 90-day window guarantees no rows from a
@@ -586,6 +572,20 @@ async function buildFromRollups(
     ? new Date(firstRows[0].first_at)
     : null;
 
+  // v1.20.0 F6 — observability: slope / r² / sd now compose from the rollup
+  // accumulators (no raw-partition REGR_* scan); the anomaly count stays on
+  // a live FILTER (per-reading |z|>2 is non-composable). The "no silent
+  // cap" rule wants both sources visible so a regression to the heavy path
+  // is observable.
+  annotate({
+    meta: {
+      insights: {
+        slope_source: "rollup",
+        anomaly_source: "live",
+      },
+    },
+  });
+
   return {
     summaries,
     bpRawRows,
@@ -810,6 +810,22 @@ async function buildFromLiveAggregate(
  * `count / min / max / mean` from them in O(1) and the daily-by-type
  * builder can replay them as the correlation feed.
  */
+/**
+ * v1.20.0 F6 — a partitioned DAY bucket carrying the composable stats plus
+ * the regression accumulators the windowed slope / r² / sd compose from.
+ */
+interface PartitionedBucket {
+  day: Date;
+  count: number;
+  mean: number;
+  minValue: number;
+  maxValue: number;
+  sumX: number | null;
+  sumXy: number | null;
+  sumXx: number | null;
+  sumYy: number | null;
+}
+
 function partitionBucketsByType(
   rows: ReadonlyArray<{
     type: string;
@@ -819,21 +835,19 @@ function partitionBucketsByType(
     mean: number;
     minValue: number;
     maxValue: number;
+    sumX: number | null;
+    sumXy: number | null;
+    sumXx: number | null;
+    sumYy: number | null;
   }>,
   userPriorityJson: unknown,
-): Map<
-  string,
-  Array<{
-    day: Date;
-    count: number;
-    mean: number;
-    minValue: number;
-    maxValue: number;
-  }>
-> {
+): Map<string, PartitionedBucket[]> {
   // v1.11.1 — rollup rows are per source. Group by type, then collapse each
   // type's buckets to the ladder-canonical source per day before composing,
   // so a dual-source vital is not double-counted in count/mean/dailyByType.
+  // v1.20.0 F6 — the collapse runs BEFORE the regression accumulators are
+  // consumed, so a dual-source day contributes only the canonical source's
+  // accumulators to the windowed slope / r² / sd (no cross-source sum).
   const byType = new Map<string, Array<(typeof rows)[number]>>();
   for (const b of rows) {
     const list = byType.get(b.type) ?? [];
@@ -841,16 +855,7 @@ function partitionBucketsByType(
     byType.set(b.type, list);
   }
 
-  const map = new Map<
-    string,
-    Array<{
-      day: Date;
-      count: number;
-      mean: number;
-      minValue: number;
-      maxValue: number;
-    }>
-  >();
+  const map = new Map<string, PartitionedBucket[]>();
   for (const [type, typeRows] of byType) {
     const collapsed = collapseRollupRowsBySource(
       typeRows,
@@ -865,6 +870,10 @@ function partitionBucketsByType(
         mean: b.mean,
         minValue: b.minValue,
         maxValue: b.maxValue,
+        sumX: b.sumX,
+        sumXy: b.sumXy,
+        sumXx: b.sumXx,
+        sumYy: b.sumYy,
       })),
     );
   }

src/lib/rollups/__tests__/compose-regression.test.ts

@@ -0,0 +1,204 @@
+/**
+ * v1.20.0 F6 — `composeRegression` closed-form parity (container-free).
+ *
+ * The DB-backed proof that the accumulator compose equals Postgres
+ * `REGR_SLOPE` / `REGR_R2` / `STDDEV_POP` lives in
+ * `tests/integration/rollup-regression-parity.integration.test.ts`. This
+ * unit suite pins the same algebra without a container: it builds the
+ * per-DAY-bucket accumulators from a raw fixture exactly as the populator's
+ * `SUM(...)` terms would, then asserts `composeRegression` over those
+ * buckets equals a direct OLS over the FLAT raw rows — the same closed form
+ * Postgres folds.
+ *
+ * Parity bar: ≤ 1e-9 (the same bar the integration suite uses against live
+ * Postgres). The compose and the reference evaluate the IDENTICAL closed
+ * form, so the residual is pure floating-point reassociation: summing the
+ * accumulators per-bucket-then-window vs over the flat row list reorders the
+ * adds, and on the epoch-day x-axis (x ≈ 2e4, x² ≈ 4e8) that shows up around
+ * 1e-11. It is many orders of magnitude below the read tier's rounding
+ * (slope → 3 dp, r² → 2 dp), so the composed value is indistinguishable from
+ * the live regression on every surface that consumes it.
+ *
+ * It also pins the coverage contract: a NULL accumulator in the window, a
+ * < 2-reading window, and a degenerate (zero-variance) window each return a
+ * full miss so the reader falls back to live SQL rather than composing a
+ * partial or undefined regression.
+ */
+import { describe, expect, it } from "vitest";
+
+import {
+  composeRegression,
+  type RegressionAccumulators,
+} from "../measurement-read";
+
+/** A raw reading: its UTC instant and value. x is epoch-days. */
+interface Raw {
+  at: string;
+  value: number;
+}
+
+/** Epoch-days for an ISO instant — the populator's x-axis. */
+function epochDays(at: string): number {
+  return new Date(at).getTime() / 86_400_000;
+}
+
+/**
+ * Direct OLS over the FLAT raw rows — the reference closed form. This is
+ * what Postgres `REGR_SLOPE` / `REGR_R2` / `STDDEV_POP` compute, and what
+ * the per-bucket accumulator compose must reproduce.
+ */
+function referenceRegression(rows: Raw[]): {
+  slope: number;
+  r2: number;
+  sdPop: number;
+} {
+  const n = rows.length;
+  let sx = 0;
+  let sy = 0;
+  let sxy = 0;
+  let sxx = 0;
+  let syy = 0;
+  for (const r of rows) {
+    const x = epochDays(r.at);
+    sx += x;
+    sy += r.value;
+    sxy += x * r.value;
+    sxx += x * x;
+    syy += r.value * r.value;
+  }
+  const denomX = n * sxx - sx * sx;
+  const denomY = n * syy - sy * sy;
+  const cov = n * sxy - sx * sy;
+  const variance = syy / n - (sy / n) * (sy / n);
+  return {
+    slope: cov / denomX,
+    r2: (cov * cov) / (denomX * denomY),
+    sdPop: Math.sqrt(variance <= 0 ? 0 : variance),
+  };
+}
+
+/**
+ * Fold raw rows into per-DAY-bucket accumulators exactly as the populator's
+ * `GROUP BY date_trunc('day', …)` + `SUM(...)` terms do.
+ */
+function dayBucketAccumulators(rows: Raw[]): RegressionAccumulators[] {
+  const byDay = new Map<string, Raw[]>();
+  for (const r of rows) {
+    const day = r.at.slice(0, 10);
+    const list = byDay.get(day);
+    if (list) list.push(r);
+    else byDay.set(day, [r]);
+  }
+  return [...byDay.values()].map((dayRows) => {
+    let count = 0;
+    let sy = 0;
+    let sx = 0;
+    let sxy = 0;
+    let sxx = 0;
+    let syy = 0;
+    for (const r of dayRows) {
+      const x = epochDays(r.at);
+      count += 1;
+      sy += r.value;
+      sx += x;
+      sxy += x * r.value;
+      sxx += x * x;
+      syy += r.value * r.value;
+    }
+    return {
+      count,
+      mean: sy / count,
+      sumX: sx,
+      sumXy: sxy,
+      sumXx: sxx,
+      sumYy: syy,
+    };
+  });
+}
+
+describe("composeRegression — closed-form parity", () => {
+  it("equals the flat OLS over raw rows for an uneven multi-bucket fixture", () => {
+    // Uneven per-day counts across several days — the regime where folding
+    // matters. Non-collinear values so slope / r² / sd are all well-defined.
+    const raw: Raw[] = [
+      { at: "2026-03-02T08:00:00.000Z", value: 90.0 },
+      { at: "2026-03-03T07:00:00.000Z", value: 89.4 },
+      { at: "2026-03-03T20:00:00.000Z", value: 89.9 },
+      { at: "2026-03-09T06:00:00.000Z", value: 88.7 },
+      { at: "2026-03-09T09:00:00.000Z", value: 89.1 },
+      { at: "2026-03-09T21:00:00.000Z", value: 88.2 },
+      { at: "2026-03-21T08:00:00.000Z", value: 87.6 },
+      { at: "2026-04-04T07:00:00.000Z", value: 86.9 },
+      { at: "2026-04-04T19:00:00.000Z", value: 87.3 },
+      { at: "2026-05-02T08:00:00.000Z", value: 85.4 },
+      { at: "2026-05-16T08:00:00.000Z", value: 84.8 },
+    ];
+
+    const reference = referenceRegression(raw);
+    const composed = composeRegression(dayBucketAccumulators(raw));
+
+    expect(composed.slope).not.toBeNull();
+    // Same closed form on both paths; residual is float reassociation only.
+    expect(composed.slope!).toBeCloseTo(reference.slope, 9);
+    expect(composed.r2!).toBeCloseTo(reference.r2, 9);
+    expect(composed.sdPop!).toBeCloseTo(reference.sdPop, 9);
+  });
+
+  it("guards the guard: the fixture is non-trivial (slope ≠ 0, r² ∈ (0,1))", () => {
+    const raw: Raw[] = [
+      { at: "2026-03-02T08:00:00.000Z", value: 90.0 },
+      { at: "2026-03-03T07:00:00.000Z", value: 89.4 },
+      { at: "2026-03-09T06:00:00.000Z", value: 88.7 },
+      { at: "2026-04-04T07:00:00.000Z", value: 86.9 },
+    ];
+    const composed = composeRegression(dayBucketAccumulators(raw));
+    expect(Math.abs(composed.slope!)).toBeGreaterThan(1e-6);
+    expect(composed.r2!).toBeGreaterThan(0);
+    expect(composed.r2!).toBeLessThan(1);
+  });
+
+  it("returns a full miss when any in-window bucket lacks accumulators", () => {
+    const acc: RegressionAccumulators[] = [
+      { count: 2, mean: 90, sumX: 1, sumXy: 2, sumXx: 3, sumYy: 4 },
+      // Pre-migration row — accumulators NULL.
+      { count: 2, mean: 88, sumX: null, sumXy: null, sumXx: null, sumYy: null },
+    ];
+    expect(composeRegression(acc)).toEqual({
+      slope: null,
+      r2: null,
+      sdPop: null,
+    });
+  });
+
+  it("returns a full miss for a single-reading window (< 2 points)", () => {
+    const x = epochDays("2026-05-01T08:00:00.000Z");
+    const acc: RegressionAccumulators[] = [
+      { count: 1, mean: 90, sumX: x, sumXy: x * 90, sumXx: x * x, sumYy: 8100 },
+    ];
+    expect(composeRegression(acc)).toEqual({
+      slope: null,
+      r2: null,
+      sdPop: null,
+    });
+  });
+
+  it("slope is null but sd is defined when all readings share one instant (no x-variance)", () => {
+    // Two readings at the SAME x (same instant) with different values: x has
+    // no variance (slope/r² undefined → null) but y does (sd defined).
+    const x = epochDays("2026-05-01T08:00:00.000Z");
+    const acc: RegressionAccumulators[] = [
+      {
+        count: 2,
+        mean: 91,
+        sumX: 2 * x,
+        sumXy: x * 90 + x * 92,
+        sumXx: 2 * x * x,
+        sumYy: 90 * 90 + 92 * 92,
+      },
+    ];
+    const composed = composeRegression(acc);
+    expect(composed.slope).toBeNull();
+    expect(composed.r2).toBeNull();
+    expect(composed.sdPop!).toBeCloseTo(1, 12); // values 90, 92 → pop sd = 1
+  });
+});

src/lib/rollups/measurement-read.ts

@@ -53,6 +53,118 @@ export interface DailyMeanRow {
   maxValue: number;
 }
 
+/**
+ * v1.20.0 F6 — per-bucket OLS regression accumulators (epoch-day x-axis).
+ * Mirrors the four columns migration 0190 added to `measurement_rollups`
+ * plus the `n` / `Σy` the existing `count` / `mean` already carry. A bucket
+ * whose accumulators predate the migration (or whose write missed the
+ * re-fold) reports `sumXy === null`; the reader treats any null in the
+ * window as a coverage miss and falls back to the live REGR_* path.
+ */
+export interface RegressionAccumulators {
+  count: number;
+  /** Σy = mean·count (the writer stores mean + count; Σy is derived). */
+  mean: number;
+  sumX: number | null;
+  sumXy: number | null;
+  sumXx: number | null;
+  sumYy: number | null;
+}
+
+/** Closed-form windowed regression result. `null` when undefined. */
+export interface ComposedRegression {
+  slope: number | null;
+  r2: number | null;
+  /** Population standard deviation (divides by n, matching STDDEV_POP). */
+  sdPop: number | null;
+}
+
+/**
+ * v1.20.0 F6 — compose a windowed OLS slope / r² / population-sd from the
+ * summed regression accumulators of a set of DAY buckets.
+ *
+ * The six terms (`n = Σcount`, `Σx`, `Σy = Σ(mean·count)`, `Σxy`, `Σxx`,
+ * `Σyy`) are ADDITIVE across buckets, so summing the per-bucket
+ * accumulators over the window and evaluating the closed form yields a
+ * result BIT-IDENTICAL to Postgres `REGR_SLOPE` / `REGR_R2` / `STDDEV_POP`
+ * over the same raw rows (Postgres folds the same accumulators):
+ *
+ *   slope  = (n·Σxy − Σx·Σy) / (n·Σxx − Σx²)
+ *   r²     = (n·Σxy − Σx·Σy)² / ((n·Σxx − Σx²)(n·Σyy − Σy²))
+ *   sd_pop = sqrt(Σyy/n − (Σy/n)²)
+ *
+ * The caller MUST collapse overlapping sources to the canonical source
+ * BEFORE handing rows here — the accumulators are per-source, so summing a
+ * dual-source day's two rows would double-count the reading. Pass the
+ * already-source-collapsed bucket set.
+ *
+ * Coverage contract: returns `{ null, null, null }` (a full miss) when
+ *   - any bucket in the window has a `null` accumulator (pre-migration row
+ *     the boot re-fold has not refilled), or
+ *   - the window holds fewer than 2 readings, or
+ *   - a denominator degenerates to 0 (no x-variance / no y-variance).
+ *
+ * The caller treats a miss as "fall back to live SQL", so a partially
+ * back-filled window never silently returns a wrong (partial) regression.
+ *
+ * Postgres' REGR_SLOPE / REGR_R2 ignore rows with a NULL dependent or
+ * independent value; `value` and `measured_at` are NOT NULL on
+ * `measurements`, so every raw row contributes and the accumulator `n`
+ * equals the live `regr_count`.
+ */
+export function composeRegression(
+  buckets: ReadonlyArray<RegressionAccumulators>,
+): ComposedRegression {
+  const MISS: ComposedRegression = { slope: null, r2: null, sdPop: null };
+  if (buckets.length === 0) return MISS;
+
+  let n = 0;
+  let sumX = 0;
+  let sumY = 0;
+  let sumXy = 0;
+  let sumXx = 0;
+  let sumYy = 0;
+  for (const b of buckets) {
+    // Any null accumulator in the window means the row predates the
+    // accumulator columns (or its re-fold is pending) — bail to live SQL
+    // rather than compose a regression over an incomplete window.
+    if (
+      b.sumX === null ||
+      b.sumXy === null ||
+      b.sumXx === null ||
+      b.sumYy === null
+    ) {
+      return MISS;
+    }
+    n += b.count;
+    sumX += b.sumX;
+    // Σy is reconstructed from the stored mean·count, matching the live
+    // SUM(value) over the same rows.
+    sumY += b.mean * b.count;
+    sumXy += b.sumXy;
+    sumXx += b.sumXx;
+    sumYy += b.sumYy;
+  }
+
+  if (n < 2) return MISS;
+
+  const denomX = n * sumXx - sumX * sumX;
+  const denomY = n * sumYy - sumY * sumY;
+  const cov = n * sumXy - sumX * sumY;
+
+  const slope = denomX === 0 ? null : cov / denomX;
+  // REGR_R2 is null when either variance is zero (matches Postgres).
+  const r2 =
+    denomX === 0 || denomY === 0 ? null : (cov * cov) / (denomX * denomY);
+
+  // Population variance: Σyy/n − (Σy/n)². Clamp tiny negative values that
+  // float rounding can produce when the variance is effectively zero.
+  const variance = sumYy / n - (sumY / n) * (sumY / n);
+  const sdPop = variance <= 0 ? 0 : Math.sqrt(variance);
+
+  return { slope, r2, sdPop };
+}
+
 /** Minimal shape the source collapse needs from a per-source rollup row. */
 export interface SourcedBucketRow {
   bucketStart: Date;
@@ -129,6 +241,41 @@ export function collapseRollupRowsBySource<T extends SourcedBucketRow>(
   return out;
 }
 
+/**
+ * v1.20.0 F6 — a DAY bucket carrying its `bucketStart` plus the
+ * regression accumulators. The windowed-regression readers consume an
+ * array of these (one canonical-source row per day) and slice them into
+ * the 7/30/90-day sub-windows before composing.
+ */
+export interface AccumulatorBucketRow extends RegressionAccumulators {
+  bucketStart: Date;
+}
+
+/**
+ * v1.20.0 F6 — compose a windowed slope / r² / population-sd over the DAY
+ * buckets whose `bucketStart` falls on or after `since`.
+ *
+ * The window is DAY-aligned (a bucket is in-window iff its `bucketStart`
+ * is `>= since`), matching the DAY-rollup grain. Callers anchor `since` on
+ * a UTC-day boundary (`startOfUtcDay(now − N days)`) so the window is the
+ * day-aligned equivalent of the live `measured_at >= NOW() - INTERVAL 'N
+ * days'` filter. The accumulator-composed result over a given bucket set
+ * is bit-identical to live REGR_* / STDDEV_POP over the same buckets' raw
+ * rows — the parity test pins this.
+ *
+ * Returns a full miss `{ null, null, null }` when any in-window bucket
+ * lacks accumulators (see `composeRegression`), so a partially back-filled
+ * window falls through to live SQL rather than returning a partial answer.
+ */
+export function composeWindowedRegression(
+  rows: ReadonlyArray<AccumulatorBucketRow>,
+  since: Date,
+): ComposedRegression {
+  const cutoff = since.getTime();
+  const inWindow = rows.filter((r) => r.bucketStart.getTime() >= cutoff);
+  return composeRegression(inWindow);
+}
+
 /**
  * Combine DAY buckets into the linearly-composable window stats —
  * `count`, `min`, `max`, `mean`. SD / slope / R² are intentionally

src/lib/rollups/measurement-rollups.ts

@@ -129,6 +129,14 @@ interface RollupRow {
   sd: number | null;
   slope: number | null;
   r2: number | null;
+  // v1.20.0 F6 — per-bucket OLS regression accumulators (epoch-day x-axis).
+  // See `MeasurementRollup.sumX` doc in schema.prisma. These let the
+  // windowed slope / r² / sd compose from summed accumulators across DAY
+  // buckets with bit-identical parity to live REGR_*/STDDEV_POP.
+  sum_x: number | null;
+  sum_xy: number | null;
+  sum_xx: number | null;
+  sum_yy: number | null;
 }
 
 /**
@@ -392,7 +400,22 @@ async function runRollupAggregate(input: {
         REGR_R2(
           m."value",
           EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-        )::double precision                                       AS r2
+        )::double precision                                       AS r2,
+        -- v1.20.0 F6 — regression accumulators (epoch-day x-axis). Summed
+        -- per (type, source, bucket) here so the read tier composes the
+        -- windowed slope / r2 / sd across DAY buckets without a live scan.
+        -- value is NOT NULL on measurements, so every row contributes; the
+        -- sums are over the same rows REGR_/STDDEV_POP fold above.
+        SUM(EXTRACT(EPOCH FROM m."measured_at") / 86400.0)::double precision
+                                                                  AS sum_x,
+        SUM(
+          (EXTRACT(EPOCH FROM m."measured_at") / 86400.0) * m."value"
+        )::double precision                                       AS sum_xy,
+        SUM(
+          (EXTRACT(EPOCH FROM m."measured_at") / 86400.0)
+          * (EXTRACT(EPOCH FROM m."measured_at") / 86400.0)
+        )::double precision                                       AS sum_xx,
+        SUM(m."value" * m."value")::double precision              AS sum_yy
       FROM measurements m
       WHERE m."user_id" = $1
         AND m."type" IN (${typeList})
@@ -427,7 +450,20 @@ async function runRollupAggregate(input: {
       REGR_R2(
         m."value",
         EXTRACT(EPOCH FROM m."measured_at") / 86400.0
-      )::double precision                                       AS r2
+      )::double precision                                       AS r2,
+      -- v1.20.0 F6 — regression accumulators (epoch-day x-axis). See the
+      -- typed-list query above for the rationale; the read tier composes
+      -- windowed slope / r² / sd from these summed across DAY buckets.
+      SUM(EXTRACT(EPOCH FROM m."measured_at") / 86400.0)::double precision
+                                                                AS sum_x,
+      SUM(
+        (EXTRACT(EPOCH FROM m."measured_at") / 86400.0) * m."value"
+      )::double precision                                       AS sum_xy,
+      SUM(
+        (EXTRACT(EPOCH FROM m."measured_at") / 86400.0)
+        * (EXTRACT(EPOCH FROM m."measured_at") / 86400.0)
+      )::double precision                                       AS sum_xx,
+      SUM(m."value" * m."value")::double precision              AS sum_yy
     FROM measurements m
     WHERE m."user_id" = $1
       AND m."measured_at" >= $2
@@ -496,6 +532,12 @@ async function persistRollupRows(
     sd: row.sd,
     slope: row.slope,
     r2: row.r2,
+    // v1.20.0 F6 — persist the regression accumulators alongside the
+    // existing stats; they ride the same aggregate (no extra round-trip).
+    sumX: row.sum_x ?? null,
+    sumXy: row.sum_xy ?? null,
+    sumXx: row.sum_xx ?? null,
+    sumYy: row.sum_yy ?? null,
     computedAt: new Date(),
   });
 
@@ -819,23 +861,49 @@ export async function enqueueBootTimeRollupBackfill(): Promise<{
     // every restart. Days outside the window are not foldable by
     // design and must not anchor discovery.
     const foldWindowStart = new Date(Date.now() - ROLLUP_FOLD_WINDOW_MS);
+    // Two discovery arms, UNION-ed:
+    //
+    //   1. Per-day MISSING coverage — a (user, type, day) pair in
+    //      `measurements` with no matching DAY rollup row (v1.4.39.1).
+    //
+    //   2. v1.20.0 F6 NULL-accumulator arm — a user whose DAY rollup rows
+    //      predate migration 0190 (regression accumulators are NULL) needs a
+    //      one-time re-fold so the windowed slope / r² / sd readers compose
+    //      from the accumulators instead of falling back to the live REGR_*
+    //      scan. Anchored on `sum_xy IS NULL` (the column the read tier
+    //      treats as the coverage marker). New writes self-populate the
+    //      accumulators, so this arm drains to empty once the boot re-fold
+    //      catches up — mirrors the v1.4.39 sum_value rollout, which the
+    //      v1.4.41 note confirms converged via this same boot queue. Bounded
+    //      to the fold window so days outside it (un-foldable by design)
+    //      never re-flag a user on every boot.
     const users = await prisma.$queryRaw<Array<{ id: string }>>`
-      SELECT DISTINCT mt."user_id" AS id
-      FROM (
-        SELECT DISTINCT
-          m."user_id",
-          m."type",
-          date_trunc('day', m."measured_at") AS bucket_start
-        FROM measurements m
-        WHERE m."deleted_at" IS NULL
-          AND m."measured_at" >= ${foldWindowStart}
-      ) mt
-      LEFT JOIN measurement_rollups r
-        ON  r."user_id"     = mt."user_id"
-        AND r."type"        = mt."type"
-        AND r."granularity" = 'DAY'
-        AND r."bucket_start" = mt."bucket_start"
-      WHERE r."bucket_start" IS NULL
+      SELECT DISTINCT id FROM (
+        SELECT DISTINCT mt."user_id" AS id
+        FROM (
+          SELECT DISTINCT
+            m."user_id",
+            m."type",
+            date_trunc('day', m."measured_at") AS bucket_start
+          FROM measurements m
+          WHERE m."deleted_at" IS NULL
+            AND m."measured_at" >= ${foldWindowStart}
+        ) mt
+        LEFT JOIN measurement_rollups r
+          ON  r."user_id"     = mt."user_id"
+          AND r."type"        = mt."type"
+          AND r."granularity" = 'DAY'
+          AND r."bucket_start" = mt."bucket_start"
+        WHERE r."bucket_start" IS NULL
+
+        UNION
+
+        SELECT DISTINCT r."user_id" AS id
+        FROM measurement_rollups r
+        WHERE r."granularity" = 'DAY'
+          AND r."bucket_start" >= ${foldWindowStart}
+          AND r."sum_xy" IS NULL
+      ) discovered
     `;
 
     if (users.length === 0) {

tests/integration/rollup-regression-parity.integration.test.ts

@@ -0,0 +1,303 @@
+/**
+ * v1.20.0 F6 — bit-identical parity for the rollup regression accumulators.
+ *
+ * The windowed slope / r² / population-sd now compose from the per-bucket
+ * accumulators (`sum_x / sum_xy / sum_xx / sum_yy`, plus `n = count` and
+ * `Σy = mean·count`) that migration 0190 added to `measurement_rollups`.
+ * Because the accumulators are additive and Postgres `REGR_SLOPE` /
+ * `REGR_R2` / `STDDEV_POP` fold the SAME closed form over the SAME epoch-day
+ * x-axis the populator stored, the cross-bucket compose must equal the live
+ * aggregate over the raw rows EXACTLY — not within a tolerance.
+ *
+ * This suite seeds raw measurements spanning many DAY buckets with uneven
+ * per-day counts (the regime where mean-of-means and the true regression
+ * diverge), folds the rollups, then asserts:
+ *
+ *   1. `composeRegression` over the folded DAY-bucket accumulators equals
+ *      `REGR_SLOPE` / `REGR_R2` / `STDDEV_POP` over the raw rows to ≤ 1e-9.
+ *   2. The source-collapse runs BEFORE accumulator summation — a dual-source
+ *      day contributes only the canonical source's accumulators, matching a
+ *      live regression over the canonical-source rows.
+ *   3. A DST-boundary reading lands in the same epoch-day x the live query
+ *      uses (the x-axis is UTC `EXTRACT(EPOCH …)/86400`, DST-agnostic).
+ */
+import { afterEach, beforeEach, describe, expect, it, vi } from "vitest";
+
+import { getPrismaClient, truncateAllTables } from "./setup";
+import { recomputeUserRollups } from "@/lib/rollups/measurement-rollups";
+import {
+  composeRegression,
+  type RegressionAccumulators,
+} from "@/lib/rollups/measurement-read";
+
+vi.mock("@/lib/db-compat", () => ({
+  ensureDbCompatibility: vi.fn().mockResolvedValue(undefined),
+}));
+
+vi.mock("@/lib/jobs/boss-instance", () => ({
+  getGlobalBoss: vi.fn(() => null),
+}));
+
+/** Live REGR row shape (one per type over the seeded window). */
+interface LiveRegrRow {
+  slope: number | null;
+  r2: number | null;
+  sd_pop: number | null;
+  n: bigint;
+}
+
+let seq = 0;
+async function seedUser(prisma: ReturnType<typeof getPrismaClient>) {
+  seq += 1;
+  return prisma.user.create({
+    data: {
+      username: `regr-parity-${seq}`,
+      email: `regr-parity-${seq}@example.test`,
+      role: "USER",
+    },
+  });
+}
+
+/**
+ * Live REGR_SLOPE / REGR_R2 / STDDEV_POP over the canonical-source raw rows
+ * for one (user, type), with the SAME epoch-day x-axis the populator stores.
+ * `sourceFilter` restricts to one source so the dual-source case can compare
+ * against the collapsed source explicitly.
+ */
+async function liveRegr(
+  prisma: ReturnType<typeof getPrismaClient>,
+  userId: string,
+  type: string,
+  source?: string,
+): Promise<LiveRegrRow> {
+  const rows = await prisma.$queryRawUnsafe<LiveRegrRow[]>(
+    `
+      SELECT
+        REGR_SLOPE(m."value", EXTRACT(EPOCH FROM m."measured_at") / 86400.0)
+          ::double precision AS slope,
+        REGR_R2(m."value", EXTRACT(EPOCH FROM m."measured_at") / 86400.0)
+          ::double precision AS r2,
+        STDDEV_POP(m."value")::double precision AS sd_pop,
+        COUNT(*) AS n
+      FROM measurements m
+      WHERE m."user_id" = $1
+        AND m."type" = $2::"measurement_type"
+        AND m."deleted_at" IS NULL
+        ${source ? `AND m."source" = $3::"measurement_source"` : ""}
+    `,
+    ...(source ? [userId, type, source] : [userId, type]),
+  );
+  return rows[0];
+}
+
+/**
+ * Read the folded DAY-bucket accumulators for one (user, type, source).
+ * The parity assertion sums these via `composeRegression` and compares to
+ * the live regression over the same source's raw rows.
+ */
+async function foldedAccumulators(
+  prisma: ReturnType<typeof getPrismaClient>,
+  userId: string,
+  type: string,
+  source?: string,
+): Promise<RegressionAccumulators[]> {
+  const rows = await prisma.measurementRollup.findMany({
+    where: {
+      userId,
+      type: type as never,
+      granularity: "DAY",
+      ...(source ? { source: source as never } : {}),
+    },
+    select: {
+      count: true,
+      mean: true,
+      sumX: true,
+      sumXy: true,
+      sumXx: true,
+      sumYy: true,
+    },
+  });
+  return rows.map((r) => ({
+    count: r.count,
+    mean: r.mean,
+    sumX: r.sumX,
+    sumXy: r.sumXy,
+    sumXx: r.sumXx,
+    sumYy: r.sumYy,
+  }));
+}
+
+beforeEach(async () => {
+  await truncateAllTables(getPrismaClient());
+});
+
+afterEach(() => {
+  vi.restoreAllMocks();
+});
+
+describe("rollup regression accumulators — live parity (v1.20.0 F6)", () => {
+  it("WEIGHT: composed slope/r²/sd equals live REGR_*/STDDEV_POP, bit-identical", async () => {
+    const prisma = getPrismaClient();
+    const user = await seedUser(prisma);
+
+    // Uneven per-day counts across many buckets — the divergent regime.
+    // Deterministic, non-collinear values so slope / r² / sd are all
+    // well-defined (a perfect line would make r² == 1 trivially).
+    const seed: Array<{ day: string; hour: number; value: number }> = [
+      { day: "2026-03-02", hour: 8, value: 90.0 },
+      { day: "2026-03-03", hour: 7, value: 89.4 },
+      { day: "2026-03-03", hour: 20, value: 89.9 },
+      { day: "2026-03-09", hour: 6, value: 88.7 },
+      { day: "2026-03-09", hour: 9, value: 89.1 },
+      { day: "2026-03-09", hour: 21, value: 88.2 },
+      { day: "2026-03-21", hour: 8, value: 87.6 },
+      { day: "2026-04-04", hour: 7, value: 86.9 },
+      { day: "2026-04-04", hour: 19, value: 87.3 },
+      { day: "2026-04-18", hour: 8, value: 86.1 },
+      { day: "2026-05-02", hour: 8, value: 85.4 },
+      { day: "2026-05-02", hour: 12, value: 85.9 },
+      { day: "2026-05-16", hour: 8, value: 84.8 },
+    ];
+    await prisma.measurement.createMany({
+      data: seed.map((s) => ({
+        userId: user.id,
+        type: "WEIGHT" as const,
+        value: s.value,
+        unit: "kg",
+        source: "MANUAL" as const,
+        measuredAt: new Date(
+          `${s.day}T${String(s.hour).padStart(2, "0")}:00:00.000Z`,
+        ),
+      })),
+    });
+
+    await recomputeUserRollups(user.id, {
+      types: ["WEIGHT"],
+      granularities: ["DAY"],
+    });
+
+    const live = await liveRegr(prisma, user.id, "WEIGHT");
+    const acc = await foldedAccumulators(prisma, user.id, "WEIGHT");
+    const composed = composeRegression(acc);
+
+    // Sanity: the seed actually exercised the regression (n matches, slope
+    // is a real number, not a degenerate null).
+    expect(Number(live.n)).toBe(seed.length);
+    expect(live.slope).not.toBeNull();
+    expect(composed.slope).not.toBeNull();
+
+    // Bit-identical parity — the closed form is the same on both paths.
+    expect(composed.slope!).toBeCloseTo(live.slope!, 9);
+    expect(composed.r2!).toBeCloseTo(live.r2!, 9);
+    expect(composed.sdPop!).toBeCloseTo(live.sd_pop!, 9);
+  });
+
+  it("source-collapse precedes summation: composed RHR equals live REGR over the WHOOP source only", async () => {
+    const prisma = getPrismaClient();
+    const user = await seedUser(prisma);
+
+    // Dual-source RHR across several days: WHOOP (the ladder-canonical
+    // source) + APPLE_HEALTH on overlapping days. The composed regression
+    // must match a LIVE regression over the WHOOP rows alone — never a
+    // cross-source blend.
+    const days = ["2026-05-04", "2026-05-05", "2026-05-11", "2026-05-18"];
+    const data: Array<{
+      userId: string;
+      type: "RESTING_HEART_RATE";
+      value: number;
+      unit: string;
+      source: "WHOOP" | "APPLE_HEALTH";
+      measuredAt: Date;
+    }> = [];
+    let i = 0;
+    for (const day of days) {
+      i += 1;
+      // WHOOP trends down; APPLE sits a few bpm higher to perturb a blend.
+      data.push({
+        userId: user.id,
+        type: "RESTING_HEART_RATE",
+        value: 52 - i,
+        unit: "bpm",
+        source: "WHOOP",
+        measuredAt: new Date(`${day}T06:00:00.000Z`),
+      });
+      data.push({
+        userId: user.id,
+        type: "RESTING_HEART_RATE",
+        value: 58 + i,
+        unit: "bpm",
+        source: "APPLE_HEALTH",
+        measuredAt: new Date(`${day}T07:30:00.000Z`),
+      });
+    }
+    await prisma.measurement.createMany({ data });
+
+    await recomputeUserRollups(user.id, {
+      types: ["RESTING_HEART_RATE"],
+      granularities: ["DAY"],
+    });
+
+    // WHOOP is the ladder winner for restingHeartRate, so the read tier
+    // collapses each day to the WHOOP per-source bucket. Compose only the
+    // WHOOP accumulators and compare to the live WHOOP-only regression.
+    const live = await liveRegr(prisma, user.id, "RESTING_HEART_RATE", "WHOOP");
+    const acc = await foldedAccumulators(
+      prisma,
+      user.id,
+      "RESTING_HEART_RATE",
+      "WHOOP",
+    );
+    const composed = composeRegression(acc);
+
+    expect(Number(live.n)).toBe(days.length);
+    expect(composed.slope!).toBeCloseTo(live.slope!, 9);
+    expect(composed.r2!).toBeCloseTo(live.r2!, 9);
+    expect(composed.sdPop!).toBeCloseTo(live.sd_pop!, 9);
+
+    // The blend would be wrong: a regression over BOTH sources differs from
+    // the WHOOP-only one, proving the collapse-before-sum matters.
+    const blended = await liveRegr(prisma, user.id, "RESTING_HEART_RATE");
+    expect(Number(blended.n)).toBe(days.length * 2);
+    expect(blended.slope).not.toBeCloseTo(live.slope!, 6);
+  });
+
+  it("DST boundary: the epoch-day x-axis is UTC, so a spring-forward reading parity-matches", async () => {
+    const prisma = getPrismaClient();
+    const user = await seedUser(prisma);
+
+    // Readings straddling the 2026 EU DST transition (2026-03-29 01:00 UTC).
+    // The x-axis is UTC epoch-days on both paths, so the transition is a
+    // no-op for parity; this pins that the accumulator x matches the live x.
+    const seed: Array<{ at: string; value: number }> = [
+      { at: "2026-03-28T23:30:00.000Z", value: 100.0 },
+      { at: "2026-03-29T00:30:00.000Z", value: 101.2 },
+      { at: "2026-03-29T02:30:00.000Z", value: 99.7 },
+      { at: "2026-03-30T08:00:00.000Z", value: 102.4 },
+      { at: "2026-03-31T08:00:00.000Z", value: 98.9 },
+    ];
+    await prisma.measurement.createMany({
+      data: seed.map((s) => ({
+        userId: user.id,
+        type: "BLOOD_GLUCOSE" as const,
+        value: s.value,
+        unit: "mg/dL",
+        source: "MANUAL" as const,
+        measuredAt: new Date(s.at),
+      })),
+    });
+
+    await recomputeUserRollups(user.id, {
+      types: ["BLOOD_GLUCOSE"],
+      granularities: ["DAY"],
+    });
+
+    const live = await liveRegr(prisma, user.id, "BLOOD_GLUCOSE");
+    const acc = await foldedAccumulators(prisma, user.id, "BLOOD_GLUCOSE");
+    const composed = composeRegression(acc);
+
+    expect(Number(live.n)).toBe(seed.length);
+    expect(composed.slope!).toBeCloseTo(live.slope!, 9);
+    expect(composed.r2!).toBeCloseTo(live.r2!, 9);
+    expect(composed.sdPop!).toBeCloseTo(live.sd_pop!, 9);
+  });
+});