diff --git a/src/lib/measurements/day-mean.ts b/src/lib/measurements/day-mean.ts
index 38b2e2970..9d90908bc 100644
--- a/src/lib/measurements/day-mean.ts
+++ b/src/lib/measurements/day-mean.ts
@@ -245,34 +245,32 @@ function weightedRowsSql(
   if (!/^[a-z_][a-z0-9_]*$/.test(source)) {
     throw new Error(`source must be a CTE name: ${source}`);
   }
-  const hourOf = (alias: string) =>
-    `date_trunc('hour', ${frameTs(frame, `${alias}."measured_at"`)})`;
-  const dayOf = (alias: string) =>
-    `date_trunc('day', ${frameTs(frame, `${alias}."measured_at"`)})`;
-  const src = bySource ? `, t."source"` : "";
-  const part = bySource ? `, x."source"` : "";
-  const join = bySource ? ` AND hw."source" = s."source"` : "";
+  // One scan of the CTE and window functions only. The earlier shape joined
+  // the CTE to an hour grouping of itself; with stale or missing statistics
+  // (a fresh import below the autoanalyze threshold) the planner ran that
+  // join as a nested loop and a year of pulse ran into the statement timeout.
+  //
+  // `dm_hour_n` counts the readings in a row's hour and `dm_hour_first` marks
+  // one row per hour, so the sum of `dm_hour_first` over a day is the day's
+  // hour count. Both columns ride along on the row; every caller aggregates.
+  const partition = (alias: string, unit: "hour" | "day") => {
+    const keys = bySource
+      ? `${alias}."type", ${alias}."source"`
+      : `${alias}."type"`;
+    const ts = frameTs(frame, `${alias}."measured_at"`);
+    return `PARTITION BY ${keys}, date_trunc('${unit}', ${ts})`;
+  };
   return `(
       SELECT s.*,
         (CASE WHEN ${isHourlyMeanTypeSql('s."type"')}
-              THEN 1.0 / (hw.n * hw.hours)
+              THEN 1.0 / (s.dm_hour_n * SUM(s.dm_hour_first) OVER (${partition("s", "day")}))
               ELSE 1.0 END)::double precision AS day_weight
-      FROM ${source} s
-      LEFT JOIN (
-        SELECT x."type"${part}, x.local_hour, x.n,
-               COUNT(*) OVER (PARTITION BY x."type"${part}, x.local_day) AS hours
-        FROM (
-          SELECT t."type"${src},
-                 ${hourOf("t")} AS local_hour,
-                 ${dayOf("t")} AS local_day,
-                 COUNT(*) AS n
-          FROM ${source} t
-          WHERE ${isHourlyMeanTypeSql('t."type"')}
-          GROUP BY ${bySource ? "1, 2, 3, 4" : "1, 2, 3"}
-        ) x
-      ) hw
-        ON hw."type" = s."type"${join}
-       AND hw.local_hour = ${hourOf("s")}
+      FROM (
+        SELECT t.*,
+               COUNT(*) OVER (${partition("t", "hour")}) AS dm_hour_n,
+               (ROW_NUMBER() OVER (${partition("t", "hour")}) = 1)::int AS dm_hour_first
+        FROM ${source} t
+      ) s
     )`;
 }
 
diff --git a/tests/integration/day-weight-unanalysed-scale.test.ts b/tests/integration/day-weight-unanalysed-scale.test.ts
new file mode 100644
index 000000000..977f32575
--- /dev/null
+++ b/tests/integration/day-weight-unanalysed-scale.test.ts
@@ -0,0 +1,232 @@
+/**
+ * The shared pulse day weight (`dayWeightedRows`) must not depend on planner
+ * statistics. A new account importing a year of pulse lands below the
+ * autoanalyze threshold, so the first reads run against a table the planner
+ * believes is empty. The earlier shape joined the CTE to an hour grouping of
+ * itself; on such a table the planner chose a nested loop and the all-time
+ * pulse aggregate ran into the 60 s production statement timeout.
+ *
+ * This file seeds a year of dense pulse (well over 100k rows) with autovacuum
+ * off for the table and no ANALYZE, then:
+ *
+ *   - times the real all-time reader (`readAllTimeExtremes`) and a bare
+ *     day-weighted mean, each well under the timeout;
+ *   - after ANALYZE, compares the weights per day, per frame and per source
+ *     against the earlier self-join SQL kept below as the oracle.
+ */
+import { afterAll, beforeAll, describe, expect, it } from "vitest";
+
+import { getPrismaClient, truncateAllTables } from "./setup";
+import type { Prisma } from "@/generated/prisma/client";
+import { readAllTimeExtremes } from "@/lib/insights/feature-blocks";
+import {
+  SESSION_DAY_FRAME,
+  dayWeightedRows,
+  zoneDayFrame,
+  type DayFrame,
+} from "@/lib/measurements/day-mean";
+
+const prisma = getPrismaClient();
+const USER = "day-weight-scale";
+const DAY = 86_400_000;
+const MINUTE = 60_000;
+const DAYS = 365;
+/** Generous against a 60 s production timeout, far above what one scan takes. */
+const BOUND_MS = 15_000;
+
+const start =
+  Date.UTC(
+    new Date().getUTCFullYear(),
+    new Date().getUTCMonth(),
+    new Date().getUTCDate(),
+  ) -
+  DAYS * DAY;
+
+/**
+ * About 330 readings a day, unevenly spread so hours carry different counts,
+ * plus a second source on every fifth day so the per-source weights differ.
+ */
+function seedRows(): Prisma.MeasurementCreateManyInput[] {
+  const rows: Prisma.MeasurementCreateManyInput[] = [];
+  let i = 0;
+  for (let d = 0; d < DAYS; d += 1) {
+    for (let m = 0; m < 24 * 60; m += 4) {
+      if ((m + d) % 13 === 0) continue;
+      const hour = Math.floor(m / 60);
+      // Night hours sparse, day hours dense.
+      if (hour < 6 && m % 12 !== 0) continue;
+      rows.push({
+        id: `${USER}-a-${i}`,
+        userId: USER,
+        type: "PULSE",
+        unit: "bpm",
+        source: "APPLE_HEALTH",
+        value: 55 + ((i * 7 + d) % 50),
+        measuredAt: new Date(start + d * DAY + m * MINUTE + (i % 3) * 1000),
+      });
+      i += 1;
+    }
+    if (d % 5 === 0) {
+      for (const h of [7, 7, 13, 22]) {
+        rows.push({
+          id: `${USER}-w-${i}`,
+          userId: USER,
+          type: "PULSE",
+          unit: "bpm",
+          source: "WITHINGS",
+          value: 60 + (i % 20),
+          measuredAt: new Date(
+            start + d * DAY + h * 3_600_000 + (i % 50) * MINUTE,
+          ),
+        });
+        i += 1;
+      }
+    }
+  }
+  return rows;
+}
+
+/** The earlier self-join, kept verbatim as the oracle for the weights. */
+function oracleWeightedRows(
+  source: string,
+  frame: DayFrame,
+  bySource: boolean,
+): string {
+  const ts = (column: string) =>
+    frame.kind === "session"
+      ? column
+      : `((${column} AT TIME ZONE 'UTC') AT TIME ZONE ${frame.tzSql})`;
+  const hourOf = (alias: string) =>
+    `date_trunc('hour', ${ts(`${alias}."measured_at"`)})`;
+  const dayOf = (alias: string) =>
+    `date_trunc('day', ${ts(`${alias}."measured_at"`)})`;
+  const src = bySource ? `, t."source"` : "";
+  const part = bySource ? `, x."source"` : "";
+  const join = bySource ? ` AND hw."source" = s."source"` : "";
+  return `(
+      SELECT s.*,
+        (CASE WHEN (s."type")::text IN ('PULSE')
+              THEN 1.0 / (hw.n * hw.hours)
+              ELSE 1.0 END)::double precision AS day_weight
+      FROM ${source} s
+      LEFT JOIN (
+        SELECT x."type"${part}, x.local_hour, x.n,
+               COUNT(*) OVER (PARTITION BY x."type"${part}, x.local_day) AS hours
+        FROM (
+          SELECT t."type"${src},
+                 ${hourOf("t")} AS local_hour,
+                 ${dayOf("t")} AS local_day,
+                 COUNT(*) AS n
+          FROM ${source} t
+          WHERE (t."type")::text IN ('PULSE')
+          GROUP BY ${bySource ? "1, 2, 3, 4" : "1, 2, 3"}
+        ) x
+      ) hw
+        ON hw."type" = s."type"${join}
+       AND hw.local_hour = ${hourOf("s")}
+    )`;
+}
+
+const SRC_CTE = `WITH src AS (
+  SELECT m."id", m."type", m."source", m."measured_at", m."value"
+  FROM measurements m
+  WHERE m."user_id" = $1 AND m."deleted_at" IS NULL AND m."type" = 'PULSE'
+)`;
+
+async function timed<T>(fn: () => Promise<T>): Promise<[T, number]> {
+  const t0 = performance.now();
+  const out = await fn();
+  return [out, performance.now() - t0];
+}
+
+let rowCount = 0;
+
+beforeAll(async () => {
+  await truncateAllTables(prisma);
+  await prisma.$executeRawUnsafe(
+    "ALTER TABLE measurements SET (autovacuum_enabled = false)",
+  );
+  await prisma.user.create({ data: { id: USER, username: USER } });
+  const rows = seedRows();
+  rowCount = rows.length;
+  for (let k = 0; k < rows.length; k += 20_000) {
+    await prisma.measurement.createMany({ data: rows.slice(k, k + 20_000) });
+  }
+}, 180_000);
+
+afterAll(async () => {
+  await prisma.$executeRawUnsafe(
+    "ALTER TABLE measurements RESET (autovacuum_enabled)",
+  );
+});
+
+describe("day weight on an unanalysed table", () => {
+  it("seeds a year of dense pulse", () => {
+    expect(rowCount).toBeGreaterThan(100_000);
+  });
+
+  it("answers the all-time pulse aggregate well under the timeout", async () => {
+    const [out, ms] = await timed(() => readAllTimeExtremes(USER, ["PULSE"]));
+    console.info(`[day-weight] readAllTimeExtremes ${ms.toFixed(0)} ms`);
+    expect(out.get("PULSE")?.mean).toBeGreaterThan(55);
+    expect(ms).toBeLessThan(BOUND_MS);
+  });
+
+  it("answers a bare day-weighted mean well under the timeout", async () => {
+    const [rows, ms] = await timed(() =>
+      prisma.$queryRawUnsafe<Array<{ mean: number }>>(
+        `${SRC_CTE}
+         SELECT (SUM(w."value" * w.day_weight) / SUM(w.day_weight))::double precision AS mean
+         FROM ${dayWeightedRows("src", zoneDayFrame("$2"), { bySource: true })} w`,
+        USER,
+        "Europe/Berlin",
+      ),
+    );
+    console.info(`[day-weight] zone + bySource mean ${ms.toFixed(0)} ms`);
+    expect(rows[0].mean).toBeGreaterThan(55);
+    expect(ms).toBeLessThan(BOUND_MS);
+  });
+});
+
+describe("day weight against the earlier self-join", () => {
+  beforeAll(async () => {
+    // Statistics now, so the oracle plans the way it did in production.
+    await prisma.$executeRawUnsafe("ANALYZE measurements");
+  }, 120_000);
+
+  const cases: Array<[string, DayFrame, boolean, unknown[]]> = [
+    ["session frame", SESSION_DAY_FRAME, false, []],
+    ["session frame by source", SESSION_DAY_FRAME, true, []],
+    ["Berlin frame", zoneDayFrame("$2"), false, ["Europe/Berlin"]],
+    ["Kolkata frame by source", zoneDayFrame("$2"), true, ["Asia/Kolkata"]],
+  ];
+
+  it.each(cases)(
+    "%s gives every row the same weight",
+    async (_label, frame, bySource, extra) => {
+      const query = (sub: string) =>
+        prisma.$queryRawUnsafe<Array<{ id: string; w: number }>>(
+          `${SRC_CTE}
+           SELECT w."id" AS id, w.day_weight AS w
+           FROM ${sub} w
+           ORDER BY w."id"`,
+          USER,
+          ...extra,
+        );
+      const fresh = await query(dayWeightedRows("src", frame, { bySource }));
+      const oracle = await query(oracleWeightedRows("src", frame, bySource));
+      expect(fresh.length).toBe(rowCount);
+      expect(fresh.length).toBe(oracle.length);
+      let mismatches = 0;
+      for (let k = 0; k < fresh.length; k += 1) {
+        if (
+          fresh[k].id !== oracle[k].id ||
+          Math.abs(fresh[k].w - oracle[k].w) > 1e-12
+        ) {
+          mismatches += 1;
+        }
+      }
+      expect(mismatches).toBe(0);
+    },
+  );
+});
diff --git a/tests/integration/mcp-metric-series-source-snapshot.test.ts b/tests/integration/mcp-metric-series-source-snapshot.test.ts
index 3759189dc..ab95bc21a 100644
--- a/tests/integration/mcp-metric-series-source-snapshot.test.ts
+++ b/tests/integration/mcp-metric-series-source-snapshot.test.ts
@@ -218,13 +218,10 @@ beforeAll(async () => {
   // The mood feature warms its rollup tier fire-and-forget on first read;
   // settle it now so both builds read the same tier.
   await ensureUserMoodRollupsFresh(userId);
-  // Planner statistics for the rows just written. Without them the
-  // all-time pulse aggregate (`readAllTimeExtremes`, day-weighted for pulse)
-  // plans against an empty table and runs for ~14 s per call until
-  // autovacuum's analyze happens to land, which on a loaded runner took the
-  // first case past its 60 s budget. A production table always has
-  // statistics, so this measures what production runs.
-  await prisma.$executeRawUnsafe("ANALYZE measurements, measurement_rollups");
+  // No ANALYZE here, on purpose: a fresh import below the autoanalyze
+  // threshold is what production runs too, and the all-time pulse aggregate
+  // must not depend on planner statistics
+  // (`day-weight-unanalysed-scale.test.ts`).
 }, 120_000);
 
 describe("get_metric_series built from one source's rows", () => {