feat(router): rubber-duck idea capture + feed

The rubber-duck path emits a fenced {"ideas":[…]} block; Ideas.parse strips it
from the chat turn and onUserInput records an IdeaCapturedEvent each (CHAT only).
IdeaReader folds eventStore.allEvents() into the active cross-session board, and
DefaultRouterContextBuilder injects a capped "## Ideas" entry — router-only, so
workflow stages never see it. Extended SYSTEM_PROMPT option (d) to capture ideas.

testing/deterministic/src/test/kotlin/RouterFacadeTest.kt

@@ -33,6 +33,7 @@ import com.correx.core.router.ChatMode
 import com.correx.core.router.DefaultRouterContextBuilder
 import com.correx.core.router.DefaultRouterFacade
 import com.correx.core.router.DefaultRouterReducer
+import com.correx.core.router.IdeaReader
 import com.correx.core.router.RouterContextBuilder
 import com.correx.core.router.RouterFacade
 import com.correx.core.router.RouterProjector
@@ -664,6 +665,50 @@ class RouterFacadeTest {
         assertTrue(store.appendedEvents.map { it.payload }.filterIsInstance<WorkflowProposedEvent>().isEmpty())
     }
 
+    @Test
+    fun `rubber-duck ideas are captured, readable cross-session, and removed by a discard`(): Unit = runBlocking {
+        val store = mockEventStore()
+        val reply = "Right — worth keeping.\n```json\n{\"ideas\":[\"cache the repo map\",\"add --dry-run\"]}\n```"
+        val facade = facadeProposing(store, reply, emptyList())
+
+        facade.onUserInput(SessionId("chat-1"), "how do we speed this up?")
+
+        val reader = IdeaReader(store)
+        val ideas = reader.activeIdeas()
+        assertEquals(2, ideas.size)
+        assertTrue(ideas.any { it.text == "cache the repo map" } && ideas.any { it.text == "add --dry-run" })
+
+        // The visible chat turn must not leak the json block.
+        val routerTurn = store.appendedEvents.map { it.payload }
+            .filterIsInstance<ChatTurnEvent>().first { it.role == ChatTurnRole.ROUTER }
+        assertFalse(routerTurn.content.contains("```"))
+
+        // Discard one (from a *different* session) → it drops off the board, the other stays.
+        val drop = ideas.first { it.text == "add --dry-run" }
+        store.append(
+            NewEvent(
+                metadata = EventMetadata(
+                    eventId = EventId("disc-1"), sessionId = SessionId("chat-2"),
+                    timestamp = Instant.parse("2026-01-01T00:00:00Z"), schemaVersion = 1, causationId = null, correlationId = null,
+                ),
+                payload = com.correx.core.events.events.IdeaDiscardedEvent(ideaId = drop.id, sessionId = SessionId("chat-2")),
+            ),
+        )
+        val after = reader.activeIdeas()
+        assertEquals(listOf("cache the repo map"), after.map { it.text })
+    }
+
+    @Test
+    fun `a steering turn never captures ideas`(): Unit = runBlocking {
+        val store = mockEventStore()
+        val reply = "x\n```json\n{\"ideas\":[\"nope\"]}\n```"
+        val facade = facadeProposing(store, reply, emptyList())
+
+        facade.onUserInput(SessionId("s"), "steer", ChatMode.STEERING)
+
+        assertTrue(IdeaReader(store).activeIdeas().isEmpty())
+    }
+
     // --------------------------------------------------------------------------
     // Helpers
     // --------------------------------------------------------------------------