feat(api): add concept temperature bands and expose in stats

apps/api/src/srs.ts

@@ -1,6 +1,6 @@
 /**
- * SRS domain: ET dates, the work week, the interval ladder, deterministic
- * sampling, and the one write path for attempts.
+ * SRS domain: ET dates, the work week, the interval ladder, concept
+ * temperature, deterministic sampling, and the one write path for attempts.
  *
  * D1 is the single source of truth. The stage names the review a problem must
  * pass NEXT (`+3` = due 3 working days after the last clean solve). Passing
@@ -128,14 +128,20 @@ export function prettyDate(date: string): string {
 
 export const SCHEDULE: Record<string, number> = scheduleJson;
 
-/** Week in which a topic was (or will be) taught. */
-export function topicWeek(topic: number): number | undefined {
+/** Date the schedule teaches a topic on, if it teaches it at all. */
+export function topicDate(topic: number): string | undefined {
   for (const [date, t] of Object.entries(SCHEDULE)) {
-    if (t === topic) return campaignWeek(date);
+    if (t === topic) return date;
   }
   return undefined;
 }
 
+/** Week in which a topic was (or will be) taught. */
+export function topicWeek(topic: number): number | undefined {
+  const date = topicDate(topic);
+  return date === undefined ? undefined : campaignWeek(date);
+}
+
 // ── deterministic sampling ───────────────────────────────────────
 
 /** FNV-1a → mulberry32: seeded PRNG so re-runs pick identical problems. */
@@ -182,6 +188,45 @@ export const STAGES: Stage[] = ["new", "+3", "+7", "retired"];
 export type Result = "pass" | "fail";
 export type Kind = "first" | "review" | "drill" | "gate";
 
+/**
+ * Catalog vocabulary, carried by the `diff:*` / `set:*` issue labels and
+ * stored verbatim in `problems`. Listed low to high / most to least required,
+ * which is the order every chart, table and digest section prints them in.
+ */
+export const DIFFICULTIES = ["easy", "medium", "hard"] as const;
+export type Difficulty = (typeof DIFFICULTIES)[number];
+export const SETS = ["core", "optional", "deferred"] as const;
+export type SetLabel = (typeof SETS)[number];
+
+/**
+ * How warm a concept is: the age of a topic's most recent attempt, bucketed by
+ * the ladder's own windows so the two cannot drift. Touched inside the first
+ * window it is `hot`, inside the second `fresh`, inside one more full second
+ * window `fading`; older than that — or never attempted — it is `cold`.
+ *
+ * A read-side label only: nothing is scheduled off it. It answers the question
+ * the ladder cannot, because the ladder tracks problems and a topic can go
+ * quiet for a fortnight while not one of its problems comes due.
+ */
+export const TEMPERATURES = ["hot", "fresh", "fading", "cold"] as const;
+export type Temperature = (typeof TEMPERATURES)[number];
+
+/** Warmest band first, with the age it tolerates. Past the last one is cold. */
+const TEMPERATURE_MAX_AGE: [Temperature, number][] = [
+  ["hot", WINDOWS[0]],
+  ["fresh", WINDOWS[1]],
+  ["fading", WINDOWS[1] * 2],
+];
+
+/** Days since a topic's last attempt → its band; null (never) is cold. */
+export function temperatureOf(age: number | null): Temperature {
+  if (age === null) return "cold";
+  for (const [temperature, max] of TEMPERATURE_MAX_AGE) {
+    if (age <= max) return temperature;
+  }
+  return "cold";
+}
+
 export interface ProblemRow {
   lc_number: number;
   issue: number;