feat(tui-01): add snapshot phase, pending events, and cursor tracking to TuiState

Add three new fields to support the snapshot/live streaming protocol phase:
- snapshotPhase: Boolean (true during initial snapshot)
- pendingEvents: List<ServerMessage> (FIFO buffer during snapshot)
- cursors: Map<String, Long> (per-session high-water marks for deduplication)

All fields include KDoc documenting their invariants and purpose. Additive
change only; all existing tests continue to pass.

apps/tui/src/main/kotlin/com/correx/apps/tui/state/TuiState.kt

@@ -1,5 +1,7 @@
 package com.correx.apps.tui.state
 
+import com.correx.apps.server.protocol.ServerMessage
+
 enum class InputMode { ROUTER, NAVIGATE, FILTER, STEER }
 
 enum class ToolDisplayStatus { REQUESTED, STARTED, COMPLETED, FAILED, REJECTED }
@@ -33,6 +35,21 @@ data class TuiState(
     val providerType: ProviderType = ProviderType.LOCAL,
     val routerConnected: Boolean = false,
     val routerMessages: List<String> = emptyList(),
+    /**
+     * True from connect until SnapshotComplete observed. Reset to true on Disconnected.
+     * When true, event-bearing messages are buffered in [pendingEvents]; snapshots are applied immediately.
+     */
+    val snapshotPhase: Boolean = true,
+    /**
+     * FIFO buffer of event-bearing server messages received while snapshotPhase == true.
+     * Drained atomically when snapshot phase completes.
+     */
+    val pendingEvents: List<ServerMessage> = emptyList(),
+    /**
+     * Per-session high-water mark keyed by SessionId.value. Updated only on applied live events.
+     * Used to deduplicate events during live streaming phase.
+     */
+    val cursors: Map<String, Long> = emptyMap(),
 )
 
 data class SessionSummary(

apps/tui/src/test/kotlin/com/correx/apps/tui/reducer/RootReducerTest.kt

@@ -12,6 +12,14 @@ class RootReducerTest {
 
     private val fixedClock: () -> Long = { 1000L }
 
+    @Test
+    fun `TuiState defaults include snapshot phase, pending events, and cursors`() {
+        val state = TuiState()
+        assertEquals(true, state.snapshotPhase)
+        assertEquals(emptyList<Any>(), state.pendingEvents)
+        assertEquals(emptyMap<String, Long>(), state.cursors)
+    }
+
     @Test
     fun `SubmitInput in ROUTER mode emits StartSession effect and resets buffer`() {
         val initial = TuiState(inputMode = InputMode.ROUTER, inputBuffer = "my-workflow")