fix(sleep-score): publish the rhythm floor and name it in the few-nights note

The note hard-coded "of 3" in every locale. SleepScoreValue now carries
rhythmMinNights, and the sheet reads the floor from it.

messages/de.json

@@ -4397,7 +4397,7 @@
             "composition": "Zusammensetzung"
           },
           "gap": {
-            "fewNights": "noch nicht genug Nächte ({count} von 3)",
+            "fewNights": "noch nicht genug Nächte ({count} von {needed})",
             "noMainSleep": "letzter Tag nur mit Nickerchen"
           }
         },

messages/en.json

@@ -4397,7 +4397,7 @@
             "composition": "Composition"
           },
           "gap": {
-            "fewNights": "not enough nights yet ({count} of 3)",
+            "fewNights": "not enough nights yet ({count} of {needed})",
             "noMainSleep": "latest day had only a nap"
           }
         },

messages/es.json

@@ -4397,7 +4397,7 @@
             "composition": "Composición"
           },
           "gap": {
-            "fewNights": "aún no hay suficientes noches ({count} de 3)",
+            "fewNights": "aún no hay suficientes noches ({count} de {needed})",
             "noMainSleep": "el último día solo tuvo una siesta"
           }
         },

messages/fr.json

@@ -4397,7 +4397,7 @@
             "composition": "Composition"
           },
           "gap": {
-            "fewNights": "pas encore assez de nuits ({count} sur 3)",
+            "fewNights": "pas encore assez de nuits ({count} sur {needed})",
             "noMainSleep": "le dernier jour n'a eu qu'une sieste"
           }
         },

messages/it.json

@@ -4397,7 +4397,7 @@
             "composition": "Composizione"
           },
           "gap": {
-            "fewNights": "notti ancora insufficienti ({count} su 3)",
+            "fewNights": "notti ancora insufficienti ({count} su {needed})",
             "noMainSleep": "l'ultimo giorno solo un pisolino"
           }
         },

messages/ko.json

@@ -4397,7 +4397,7 @@
             "composition": "구성"
           },
           "gap": {
-            "fewNights": "아직 밤이 부족함 ({count}/3)",
+            "fewNights": "아직 밤이 부족함 ({count}/{needed})",
             "noMainSleep": "최근 하루는 낮잠만 있음"
           }
         },

messages/pl.json

@@ -4397,7 +4397,7 @@
             "composition": "Struktura"
           },
           "gap": {
-            "fewNights": "za mało nocy ({count} z 3)",
+            "fewNights": "za mało nocy ({count} z {needed})",
             "noMainSleep": "ostatni dzień tylko z drzemką"
           }
         },

src/components/insights/derived/__tests__/composite-score-anatomy-gap.test.tsx

@@ -0,0 +1,62 @@
+import { describe, expect, it, vi } from "vitest";
+import { renderToStaticMarkup } from "react-dom/server";
+
+/**
+ * A rhythm sub-score withheld for too few nights names the floor the server
+ * published (`rhythmMinNights`), not a number the sheet carries itself.
+ */
+
+const anatomy = vi.fn();
+vi.mock("../score-anatomy-view", () => ({
+  ScoreAnatomyView: (props: Record<string, unknown>) => {
+    anatomy(props);
+    return null;
+  },
+}));
+vi.mock("@/components/insights/insight-status-card", () => ({
+  InsightStatusCard: () => null,
+}));
+vi.mock("../score-history", () => ({
+  ScoreHistoryChart: () => null,
+  ScoreTrendChartDynamic: () => null,
+}));
+vi.mock("@/lib/i18n/context", () => ({
+  useTranslations: () => ({
+    t: (key: string, vars?: Record<string, string | number>) =>
+      vars ? `${key}:${JSON.stringify(vars)}` : key,
+  }),
+}));
+vi.mock("../use-derived-metric", () => ({
+  useDerivedMetric: () => ({
+    isLoading: false,
+    data: {
+      status: "ok",
+      value: {
+        score: 70,
+        band: "yellow",
+        subScores: [
+          { key: "consistency", value: null, weight: 0.2, gap: "few_nights" },
+        ],
+        rhythmNights: 2,
+        rhythmMinNights: 5,
+      },
+      coverage: 1,
+      confidence: "high",
+      provenance: {},
+    },
+  }),
+}));
+
+import { CompositeScoreAnatomy } from "../composite-score-anatomy";
+
+describe("sleep score sheet — the few-nights gap", () => {
+  it("names the published floor", () => {
+    renderToStaticMarkup(<CompositeScoreAnatomy metric="SLEEP_SCORE" />);
+    const props = anatomy.mock.calls.at(-1)![0] as {
+      contributors: Array<{ key: string; missingLabel?: string }>;
+    };
+    const consistency = props.contributors.find((c) => c.key === "consistency");
+    expect(consistency?.missingLabel).toContain('"count":2');
+    expect(consistency?.missingLabel).toContain('"needed":5');
+  });
+});

src/components/insights/derived/composite-score-anatomy.tsx

@@ -243,6 +243,7 @@ export function CompositeScoreAnatomy({
             s.gap === "few_nights"
               ? t("insights.derived.composite.SLEEP_SCORE.gap.fewNights", {
                   count: v.rhythmNights ?? 0,
+                  needed: v.rhythmMinNights,
                 })
               : s.gap === "no_main_sleep"
                 ? t("insights.derived.composite.SLEEP_SCORE.gap.noMainSleep")

src/lib/insights/derived/sleep-score.ts

@@ -115,6 +115,11 @@ export interface SleepScoreValue {
    * `RHYTHM_MIN_NIGHTS` both are withheld with `gap: "few_nights"`.
    */
   rhythmNights: number;
+  /**
+   * `RHYTHM_MIN_NIGHTS`, published so a client names the floor it shows
+   * ("2 of 3 nights") from the server instead of carrying its own copy.
+   */
+  rhythmMinNights: number;
   /**
    * v1.42 — the score of every scorable night in the window (oldest → newest,
    * capped to `SPARKLINE_MAX_POINTS`), so a surface can show the score's
@@ -640,6 +645,7 @@ export async function computeSleepScore(
       subScores,
       windowNights: scorableNights.length,
       rhythmNights: midpoints.length,
+      rhythmMinNights: RHYTHM_MIN_NIGHTS,
       series,
     },
     coverage,

src/lib/openapi/routes/insights/schemas.ts

@@ -325,7 +325,7 @@ export const sleepScoreValue = z
             .enum(["few_nights", "no_main_sleep"])
             .optional()
             .describe(
-              "Only on a null `consistency` / `timing`: why it is withheld. `few_nights` — fewer than three nights in the window have a main sleep on the clock (count in `rhythmNights`); `no_main_sleep` — the latest day had only a daytime nap. Absent otherwise.",
+              "Only on a null `consistency` / `timing`: why it is withheld. `few_nights` — fewer than `rhythmMinNights` nights in the window have a main sleep on the clock (count in `rhythmNights`); `no_main_sleep` — the latest day had only a daytime nap. Absent otherwise.",
             ),
         }),
       )
@@ -337,6 +337,12 @@ export const sleepScoreValue = z
       .describe(
         "Nights in the window with a main sleep placed on the clock — what consistency and timing are computed from. A daytime nap is not one; a short night is.",
       ),
+    rhythmMinNights: z
+      .number()
+      .int()
+      .describe(
+        'How many `rhythmNights` consistency and timing need before they are scored; below it they carry `gap: "few_nights"`.',
+      ),
     series: z
       .array(z.number())
       .describe(