feat(mobile): add measured cold-start home transitions

src/apps/mobile/android/app/src/main/kotlin/com/openbitfun/mobile/app/MainActivity.kt

@@ -5,6 +5,16 @@ import androidx.compose.foundation.layout.Box
 import androidx.compose.runtime.mutableStateOf
 import androidx.compose.runtime.setValue
 import com.openbitfun.mobile.app.ui.shell.StartupBrandReveal
+import com.openbitfun.mobile.app.ui.shell.ColdStartHomeTransition
+import com.openbitfun.mobile.app.ui.shell.LocalColdStartTarget
+import androidx.compose.runtime.CompositionLocalProvider
+import androidx.compose.runtime.remember
+import androidx.compose.ui.Modifier
+import androidx.compose.ui.geometry.Offset
+import androidx.compose.ui.layout.onGloballyPositioned
+import androidx.compose.ui.layout.positionInRoot
+import androidx.compose.ui.semantics.hideFromAccessibility
+import androidx.compose.ui.semantics.semantics
 import androidx.activity.ComponentActivity
 import androidx.activity.compose.setContent
 import androidx.activity.enableEdgeToEdge
@@ -23,12 +33,16 @@ import com.openbitfun.mobile.app.viewmodel.AppThemeMode
 
 class MainActivity : ComponentActivity() {
     private var showStartupBrand by mutableStateOf(true)
+    private var showColdStart by mutableStateOf(false)
+    private var allowColdStart by mutableStateOf(false)
     override fun onCreate(savedInstanceState: Bundle?) {
         AppLocaleController.applySaved(this)
         super.onCreate(savedInstanceState)
-        showStartupBrand = savedInstanceState == null
+        val coldStartCandidate = !processLaunchClaimed
             && !intent.getBooleanExtra(DESIGN_PREVIEW_EXTRA, false)
-            && StartupRevealPreference.claim(this)
+        processLaunchClaimed = true
+        showStartupBrand = coldStartCandidate && StartupRevealPreference.claim(this)
+        allowColdStart = coldStartCandidate && !showStartupBrand
         enableEdgeToEdge()
         setContent {
             if (intent.getBooleanExtra(DESIGN_PREVIEW_EXTRA, false)) {
@@ -44,11 +58,30 @@ class MainActivity : ComponentActivity() {
                 AppThemeMode.DARK -> true
             }
             OpenBitFunTheme(dark = dark) {
-                Box {
-                    MobileScreen()
+                val target = remember { mutableStateOf<androidx.compose.ui.geometry.Rect?>(null) }
+                var origin by remember { mutableStateOf(Offset.Zero) }
+                Box(Modifier.onGloballyPositioned { origin = it.positionInRoot() }) {
+                    CompositionLocalProvider(LocalColdStartTarget provides target) {
+                        Box(Modifier.semantics {
+                            if (showStartupBrand || showColdStart) hideFromAccessibility()
+                        }) {
+                        MobileScreen(onAccountRestored = { signedIn ->
+                            if (allowColdStart) {
+                                allowColdStart = false
+                                showColdStart = signedIn
+                            }
+                        })
+                        }
+                    }
                     if (showStartupBrand) StartupBrandReveal { showStartupBrand = false }
+                    val bounds = target.value
+                    if (showColdStart) {
+                        ColdStartHomeTransition(bounds?.translate(-origin)) { showColdStart = false }
+                    }
+                }
+                if (!showStartupBrand && !showColdStart && !allowColdStart) {
+                    com.openbitfun.mobile.app.ui.shell.NotificationOnboarding()
                 }
-                if (!showStartupBrand) com.openbitfun.mobile.app.ui.shell.NotificationOnboarding()
             }
         }
     }
@@ -60,6 +93,8 @@ class MainActivity : ComponentActivity() {
 
     override fun onStop() {
         showStartupBrand = false
+        showColdStart = false
+        allowColdStart = false
         if (!intent.getBooleanExtra(DESIGN_PREVIEW_EXTRA, false)) accountModel().setBackground(true)
         super.onStop()
     }
@@ -68,6 +103,7 @@ class MainActivity : ComponentActivity() {
         com.openbitfun.mobile.app.viewmodel.AccountViewModel.Factory)[com.openbitfun.mobile.app.viewmodel.AccountViewModel::class.java]
 
     private companion object {
+        var processLaunchClaimed = false
         const val DESIGN_PREVIEW_EXTRA = "openbitfun.design_preview"
         const val DESIGN_SCENARIO_EXTRA = "openbitfun.design_scenario"
     }

src/apps/mobile/android/app/src/main/kotlin/com/openbitfun/mobile/app/ui/remote/PairingScreen.kt

@@ -249,7 +249,7 @@ internal fun RemoteCompactHome(
                 .verticalScroll(rememberScrollState())
                 .padding(horizontal = MobileDesignGeometry.RecentHomeGutter, vertical = 24.dp),
         ) {
-            WelcomeBrandFlow(Modifier.align(Alignment.CenterHorizontally).size(MobileDesignGeometry.RecentHomeMarkSize), sweep = true)
+            com.openbitfun.mobile.app.ui.shell.ColdStartHomeMark(Modifier.align(Alignment.CenterHorizontally).size(MobileDesignGeometry.RecentHomeMarkSize))
             Text(stringResource(R.string.home_recent_title), fontSize = 25.sp,
                 fontWeight = FontWeight.Medium, textAlign = androidx.compose.ui.text.style.TextAlign.Center,
                 modifier = Modifier.fillMaxWidth().padding(top = 10.dp, bottom = 32.dp))

src/apps/mobile/android/app/src/main/kotlin/com/openbitfun/mobile/app/ui/shell/ColdStartHomeTransition.kt

@@ -0,0 +1,72 @@
+package com.openbitfun.mobile.app.ui.shell
+
+import androidx.compose.animation.core.Animatable
+import androidx.compose.animation.core.LinearEasing
+import androidx.compose.animation.core.tween
+import androidx.compose.foundation.background
+import androidx.compose.foundation.layout.BoxWithConstraints
+import androidx.compose.foundation.layout.fillMaxSize
+import androidx.compose.foundation.layout.offset
+import androidx.compose.foundation.layout.size
+import androidx.compose.runtime.Composable
+import androidx.compose.runtime.LaunchedEffect
+import androidx.compose.runtime.remember
+import androidx.compose.ui.Alignment
+import androidx.compose.ui.Modifier
+import androidx.compose.ui.graphics.graphicsLayer
+import androidx.compose.ui.layout.onGloballyPositioned
+import androidx.compose.ui.layout.boundsInRoot
+import androidx.compose.ui.unit.dp
+import androidx.compose.ui.input.pointer.pointerInput
+import androidx.compose.ui.semantics.clearAndSetSemantics
+import com.openbitfun.mobile.app.ui.theme.generated.MobileDesignMotion
+import kotlin.math.*
+
+/** Logged-in cold-start transition. The underlying home is already laid out. */
+@Composable
+internal fun ColdStartHomeTransition(target: androidx.compose.ui.geometry.Rect?, onFinished: () -> Unit) {
+    val progress = remember { Animatable(0f) }
+    LaunchedEffect(Unit) {
+        progress.animateTo(1f, tween(MobileDesignMotion.ColdStartHome, easing = LinearEasing))
+        onFinished()
+    }
+    val density = androidx.compose.ui.platform.LocalDensity.current
+    val p = progress.value
+    val travel = smooth((p - .16f) / .52f)
+    val overlayAlpha = 1f - smooth((p - .68f) / .32f)
+    BoxWithConstraints(
+        Modifier.fillMaxSize()
+            .graphicsLayer { alpha = overlayAlpha }
+            .background(androidx.compose.material3.MaterialTheme.colorScheme.background)
+            .pointerInput(Unit) { awaitPointerEventScope { while (true) awaitPointerEvent().changes.forEach { it.consume() } } }
+            .clearAndSetSemantics { },
+        contentAlignment = Alignment.TopCenter,
+    ) {
+        val targetY = target?.let { with(density) { it.center.y.toDp() } } ?: (maxHeight * .53f)
+        val targetX = target?.let { with(density) { it.center.x.toDp() } } ?: (maxWidth / 2)
+        val targetSize = target?.let { with(density) { it.width.toDp() } } ?: 56.dp
+        val centerY = maxHeight * .53f
+        val y = centerY + (targetY - centerY) * travel - (if (target != null) 9.dp else 0.dp) * sin(travel * PI).toFloat()
+        val size = 56.dp + (targetSize - 56.dp) * travel
+        WelcomeBrandFlow(
+            Modifier.size(size)
+                .offset(x = (targetX - maxWidth / 2) * travel, y = y - size / 2)
+                .graphicsLayer { alpha = (p / .13f).coerceIn(0f, 1f) },
+            sweep = true,
+        )
+    }
+}
+
+private fun smooth(value: Float): Float {
+    val p = value.coerceIn(0f, 1f)
+    return p * p * (3f - 2f * p)
+}
+
+internal val LocalColdStartTarget = androidx.compose.runtime.staticCompositionLocalOf<androidx.compose.runtime.MutableState<androidx.compose.ui.geometry.Rect?>?> { null }
+
+@Composable
+internal fun ColdStartHomeMark(modifier: Modifier) {
+    val target = LocalColdStartTarget.current
+    androidx.compose.runtime.DisposableEffect(target) { onDispose { target?.value = null } }
+    WelcomeBrandFlow(modifier.onGloballyPositioned { target?.value = it.boundsInRoot() }, sweep = true)
+}

src/apps/mobile/android/app/src/main/kotlin/com/openbitfun/mobile/app/ui/shell/MobileScreen.kt

@@ -126,7 +126,7 @@ private fun PaneSeparator(gapWidth: Int) {
  */
 @OptIn(ExperimentalMaterial3Api::class)
 @Composable
-internal fun MobileScreen() {
+internal fun MobileScreen(onAccountRestored: (Boolean) -> Unit = {}) {
     var compactDrawerOpen by rememberSaveable { mutableStateOf(false) }
     val shell = rememberAppShellState()
 
@@ -137,6 +137,11 @@ internal fun MobileScreen() {
     val accountPhase by accountViewModel.connectionPhase.collectAsStateWithLifecycle()
     val accountWorkspaceDirectory by accountViewModel.workspaceDirectory.collectAsStateWithLifecycle()
     val readyAccount = accountState as? AccountUiState.Ready
+    LaunchedEffect(accountState) {
+        if (accountState !is AccountUiState.Idle && accountState !is AccountUiState.Restoring) {
+            onAccountRestored(readyAccount?.userId?.isNotBlank() == true)
+        }
+    }
     val linkContext = androidx.compose.ui.platform.LocalContext.current
     var pendingDeviceLink by rememberSaveable { mutableStateOf<String?>(null) }
     val connectDeviceLink: (String) -> Unit = { url ->

src/apps/mobile/android/app/src/main/kotlin/com/openbitfun/mobile/app/ui/shell/WelcomeBrandFlow.kt

@@ -61,7 +61,9 @@ internal fun WelcomeBrandFlow(modifier: Modifier, sweep: Boolean = false) {
     ) else remember { mutableFloatStateOf(0f) }
     val ink=MaterialTheme.colorScheme.onBackground
     Canvas(modifier) {
-        val phase = animatedPhase.value
+        val framePhase = animatedPhase.value
+        // Keep the cover and measured home mark on the same sweep during handoff.
+        val phase = if (sweep && moving) (android.os.SystemClock.uptimeMillis() % 5000L) / 5000f else framePhase
         drawIntoCanvas { canvas ->
             val c=canvas.nativeCanvas;c.save();c.scale(size.width/256,size.height/256);paint.color=ink.toArgb()
             if(sweep) {

src/apps/mobile/android/app/src/main/kotlin/com/openbitfun/mobile/app/ui/theme/generated/MobileDesignTokens.kt

@@ -271,4 +271,5 @@ internal object MobileDesignMotion {
     const val Quick: Int = 180
     const val Structure: Int = 220
     const val StartupBrand: Int = 6800
+    const val ColdStartHome: Int = 2400
 }

src/apps/mobile/design-system/README.md

@@ -210,3 +210,18 @@ The recent-home brand and headline are centered above the leading-aligned sessio
 HarmonyOS welcome occupies the full window when signed out without an active remote target. It suppresses the workspace sidebar without changing retained selection. At 600vp and above, the brand, phrase and constrained action group are centered without the compact dock; smaller windows retain the stacked dock. The welcome mark is 156vp compact and 184vp wide, using the diagonal sweep. Size changes update this layout in place.
 
 For HarmonyOS welcome windows at least 840vp wide with width/height at least 1.2, a centered composition capped at 1000vp places the brand and actions side by side. This follows available window geometry rather than a device model or fold count.
+
+### Authenticated cold-start home transition
+
+After the persisted first-install reveal has already been claimed, an
+authenticated process launch uses `cold_start_home` (2400 ms). The home shell
+mounts immediately so restoration and remote loading continue underneath the
+cover. The contour mark starts at 56 logical units, then moves to the mark's
+measured native bounds during 16%–68% of the timeline; the cover fades from
+68%–100%. Each platform measures the actual compact or wide home layout, so
+safe-area insets, split windows, and foldable posture changes do not rely on a
+fixed coordinate. Signed-out restore, manual login after launch, activity or
+scene recreation, foreground resume, and a second root do not claim the
+transition. If the home mark is unavailable, the mark remains centered and the
+cover still fades on the same clock. Reduced motion finishes immediately, and
+accessibility and pointer interaction stay with the cover until it completes.

src/apps/mobile/design-system/components/mobile-components.json

@@ -225,6 +225,13 @@
       "tokens": ["page_bg", "ink", "brand_dot", "startup_brand"],
       "platformNotes": "Native first-launch-only overlay on HarmonyOS, Android and iOS. Claim a persisted installation-local flag before playback; account changes, process restarts and upgrades do not reset it. Design previews do not consume it. Existing installs without the flag show it once after upgrade; 6800ms timeline independent of network readiness. A cyan dot hops ahead of ten 42-unit letters with subtle letter bounce. At normalized text time 0.70–0.86 it arcs back to the dotless i, settling at 7.35 units diameter with one fading halo. Text time is min(progress / 0.65 * 0.9, 0.9). Logo expands from 0.65 to 1 with a small overshoot during progress 0.66–0.85 as the word moves down 42 units. Use a centered 280×240 stage, scaled down for narrow windows, 92-unit contour mark on Android/iOS and a 156vp mark on HarmonyOS, with platform-native soft sans typography. HarmonyOS positions the mark at (62, -34) to preserve separation from the settled wordmark. Fade the overlay over the last 3%. Reserve full glyph slots; no layout changes during reveal. Remove on completion or background and do not replay on activity recreation/foreground. Skip for reduced motion. Notification onboarding follows completion. The dedicated brand_dot token preserves identity independently of action/status colors."
     },
+    "cold_start_home_transition": {
+      "purpose": "Covers a normal authenticated process launch while the measured home brand mark moves into its final position and the page fades in.",
+      "anatomy": ["home_surface", "moving_contour_brand_mark", "measured_home_mark_anchor", "page_fade"],
+      "states": ["authenticated_process_launch", "signed_out", "background_resume", "reduce_motion", "compact", "wide"],
+      "tokens": ["page_bg", "recent_home_mark_size", "cold_start_home"],
+      "platformNotes": "Only the first authenticated restore in a new process may claim this presentation. The existing installation-local startup_brand_reveal takes precedence and remains unchanged. The home shell mounts underneath; no network request gates the 2400ms timeline. Start the mark at 56 logical units, measure the rendered home mark in the native layout, and interpolate to that measured rect so compact, wide, safe-area, and foldable layouts share the same endpoint. Move through the measured target during 16%–68% of the timeline, then fade the cover from 68%–100%. Signed-out restore, later manual login, foreground resume, activity recreation, and a second scene root do not replay it. Reduced motion completes immediately. If the target is unavailable, keep the mark centered and fade the cover without inventing an endpoint. Hide the underlying shell from accessibility while the cover is active; preserve pointer blocking until completion."
+    },
     "permission_request_panel": {
       "purpose": "Answers an independent runtime permission request below the conversation header, outside the transcript, matching mobile-web.",
       "anatomy": [

src/apps/mobile/design-system/tokens/mobile-tokens.json

@@ -430,6 +430,7 @@
   "motion": {
     "quick": 180,
     "structure": 220,
-    "startup_brand": 6800
+    "startup_brand": 6800,
+    "cold_start_home": 2400
   }
 }

src/apps/mobile/harmonyos/AGENTS.md

@@ -150,6 +150,15 @@ removing the running action. Test both postures and restore normal App afterward
 
 ## Theme and device verification
 
+For cold-start home animation geometry, launch the isolated design preview with
+`hdc shell aa start -a EntryAbility -b <bundle-id> --ps openbitfunDesignPreview cold-start-home`
+(or `cold-start-home-dark`). Use **Replay** to run the production 2400 ms
+transition over the production recent-home component and **Resize** during
+playback to remeasure its anchor. This fixture does not load account or remote
+state. Check compact and wide windows separately, then force-stop and start the
+normal EntryAbility without preview arguments. A fixture check does not replace
+authenticated cold-process, signed-out, and background/foreground verification.
+
 - Use existing semantic colors from `Theme.ets`; do not hard-code a light-only foreground or surface color.
 - For changes to navigation controls, menus, or responsive presentation, verify compact and wide behavior, light and dark theme legibility, and capture a real-device screenshot before completion when a device is connected.
 - Run the smallest matching HarmonyOS build/check plus `pnpm run theme:color-audit:all` for theme or color-related changes.