fix: repair decayBeliefs CTE so belief decay actually runs

The CTE was `WITH halflives AS (SELECT profile, CASE profile ...)` with no
FROM clause. Postgres rejects it with 42703 (column "profile" does not
exist) on every hourly invocation, so the temporal dimension of the
recommendation engine had never executed once — obsession (14d half-life)
and contextual (7d) never faded.

Rewritten as `WITH halflives(profile, halflife_sec) AS (VALUES ...)`,
half-lives preserved exactly.

One deliberate semantic change: the broken CASE had an `ELSE 30 * 86400`
fallback, so an unrecognised profile would have decayed on a 30-day
half-life. The VALUES join leaves unknown profiles undecayed instead.
Today that is a no-op (only `forgotten`, already excluded by the WHERE),
but a future profile added without a half-life will now conspicuously not
decay rather than quietly decaying at an arbitrary rate.

Verified against a scratch PG16 with one belief per profile aged exactly
one half-life: UPDATE 2, obsession and contextual halved, forgotten and a
fresh longterm untouched. Against the live DB (in a rolled-back
transaction) the fix reports UPDATE 843.

NOTE ON ROLLOUT: the first successful run applies ~23 days of accrued
decay at once, cutting obsession beliefs to ~0.32x. That is correct
behaviour, but recommendations will shift visibly. Expected, not a
regression.

REVIEW-2026-07-30.md finding 3.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

backend/src/services/db.service.ts

@@ -1790,16 +1790,16 @@ export class DbService {
    */
   async decayBeliefs(): Promise<number> {
     const res = await this.pgClient.query(`
-      WITH halflives AS (
+      -- NOTE: this MUST be a VALUES list, not "SELECT profile, CASE profile ...",
-        SELECT profile,
+      -- which has no FROM clause and is rejected by Postgres with 42703
-          CASE profile
+      -- (column "profile" does not exist) on every single run.
-            WHEN 'longterm'   THEN 365 * 86400
+      WITH halflives(profile, halflife_sec) AS (
-            WHEN 'obsession'  THEN 14 * 86400
+        VALUES
-            WHEN 'discovery'  THEN 30 * 86400
+          ('longterm',   365 * 86400),
-            WHEN 'negative'   THEN 180 * 86400
+          ('obsession',   14 * 86400),
-            WHEN 'contextual' THEN 7 * 86400
+          ('discovery',   30 * 86400),
-            ELSE 30 * 86400
+          ('negative',   180 * 86400),
-          END AS halflife_sec
+          ('contextual',   7 * 86400)
       )
       UPDATE listener_beliefs lb
       SET value = GREATEST(-1.0, LEAST(1.0, lb.value * POWER(0.5,