feat(cache-warming): manual POST /chat/warm trigger endpoint

A frontend 'warm now' button (and fast tests) can trigger a warm on demand
instead of waiting for the automatic timer.
- transport-contract: WarmRequest / WarmResponse wire types
- transport-http: POST /chat/warm → cacheWarmHandle.warm(); 200 with cachePct,
  409 when the conversation is generating, 400 on missing conversationId

Live-verified vs claude haiku: seed turn cacheWrite=6799 → POST /chat/warm
returns cacheReadTokens=6799 cachePct=100 (100% hit). 760 vitest + 109 bun green.

1 files changed, 6 insertions, 2 deletions

diff --git a/tasks.md b/tasks.md
index 0bde08f..9409fff 100644
--- a/tasks.md
+++ b/tasks.md
@@ -156,8 +156,12 @@ arm-on-settle/cancel-on-start; `pct = round(clamp(cacheRead/input,0,1)*100)`).
     calls `warm()`, computes `lastPct`, persists `{enabled,intervalMs}` (default on/240s) in
     host.storage; registers a controls Surface. 19 tests.
   - [x] **host-bin** — registered cache-warming; **transport-http** HostAPI stub fixed for `emit`.
-- **Live-verified:** full-graph `tsc -b` EXIT 0, biome clean (boot smoke + live Claude warm pending
-  a restart with the cache-warming ext loaded).
+- **Manual trigger endpoint:** `POST /chat/warm {conversationId, model?, cwd?}` → `WarmResponse`
+  `{inputTokens,outputTokens,cacheReadTokens,cacheWriteTokens,cachePct}` (409 if generating). Powers a
+  FE "warm now" button + fast tests. Types in `@dispatch/transport-contract`; route in transport-http.
+- **LIVE-VERIFIED against Claude haiku:** automatic timer warm → journal `warm complete pct:100`;
+  manual `POST /chat/warm` → `cacheReadTokens:6799, cachePct:100` (100% hit), HTTP 200. The external
+  `../claude` provider-anthropic is loaded via `bin/up` (`DISPATCH_EXTERNAL_EXTENSIONS`).
 - **OPEN — surface-system limits (CR from cache-warming):** the surface system has (a) NO
   per-conversation context (surface reflects most-recently-active conversation; invoke carries
   conversationId), and (b) NO numeric-input field kind, so the **interval ("set time to refresh")