Standardize notification naming and fix formatting in MCP Apps spec

Updates the MCP Apps specification to consistently use the
`ui/notifications/` prefix for all notification methods (e.g.,
`ui/notifications/sandbox-ready`, `ui/notifications/tool-result`). Also
removes trailing whitespace, fixes tab/space inconsistencies, improves
code formatting with proper backticks, and clarifies terminology
throughout the document.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <[email protected]>

Author: jonathanhefner

specification/draft/apps.mdx

@@ -1,8 +1,8 @@
 # SEP-1865: MCP Apps: Interactive User Interfaces for MCP
 
-**Track:** Extensions  
-**Authors:** Ido Salomon, Liad Yosef, Olivier Chafik, Jerome Swannack, Jonathan Hefner, Anton Pidkuiko, Nick Cooper, Bryan Ashley, Alexei Christakis  
-**Status:** Draft  
+**Track:** Extensions
+**Authors:** Ido Salomon, Liad Yosef, Olivier Chafik, Jerome Swannack, Jonathan Hefner, Anton Pidkuiko, Nick Cooper, Bryan Ashley, Alexei Christakis
+**Status:** Draft
 **Created:** 2025-11-21
 
 ## Abstract
@@ -86,7 +86,7 @@ The resource content is returned via `resources/read`:
           connect_domains?: string[];  // Origins for fetch/XHR/WebSocket
           resource_domains?: string[]; // Origins for images, scripts, etc
         };
-      "domain"?: string;	
+      "domain"?: string;
       "prefersBorder"?: boolean;
       };
     };
@@ -293,14 +293,14 @@ If the Host is a web page, it MUST wrap the Guest UI and communicate with it thr
 
 1. The Host and the Sandbox MUST have different origins.
 2. The Sandbox MUST have the following permissions: `allow-scripts`, `allow-same-origin`.
-3. The Sandbox MUST send a `ui/sandbox-ready` notification to the host when it’s ready to process an `ui/sandbox-resource-ready` notification.
-4. Once the Sandbox is ready, the Host MUST send the raw HTML resource to load in a `ui/sandbox-resource-ready` notification.
+3. The Sandbox MUST send a `ui/notifications/sandbox-ready` notification to the host when it’s ready to process an `ui/sandbox-resource-ready` notification.
+4. Once the Sandbox is ready, the Host MUST send the raw HTML resource to load in a `ui/notifications/sandbox-resource-ready` notification.
 5. The Sandbox MUST load the raw HTML of the Guest UI with CSP settings that:
    - Enforce the domains declared in `ui.csp` metadata
    - Prevent nested iframes (`frame-src 'none'`)
    - Block dangerous features (`object-src 'none'`, `base-uri 'self'`)
    - Apply restrictive defaults if no CSP metadata is provided
-6. The Sandbox MUST forward messages sent by the Host to the Guest UI, and vice versa, with any method that doesn’t start with `ui/sandbox-`. This includes lifecycle messages, e.g. `initialize` request & `initialized` notification both sent by the Guest UI. The Host MUST NOT send any request or notification to the Guest UI before it receives an `initialized` notification.
+6. The Sandbox MUST forward messages sent by the Host to the Guest UI, and vice versa, for any method that doesn’t start with `ui/notifications/sandbox-`. This includes lifecycle messages, e.g., `ui/initialize` request & `ui/notifications/initialized` notification both sent by the Guest UI. The Host MUST NOT send any request or notification to the Guest UI before it receives an `initialized` notification.
 7. The Sandbox SHOULD NOT create/send any requests to the Host or to the Guest UI (this would require synthesizing new request ids).
 8. The Host MAY forward any message from the Guest UI (coming via the Sandbox) to the MCP Apps server, for any method that doesn’t start with `ui/`. While the Host SHOULD ensure the Guest UI’s MCP connection is spec-compliant, it MAY decide to block some messages or subject them to further user approval.
 
@@ -325,7 +325,7 @@ UI iframes can use the following subset of standard MCP protocol messages:
 - `ui/initialize` → `ui/notifications/initialized` - MCP-like handshake (replaces custom iframe-ready pattern in MCP-UI)
 - `ping` - Connection health check
 
-### Host Context in McpUiInitializeResult
+### Host Context in `McpUiInitializeResult`
 
 When the Guest UI sends an `ui/initialize` request to the Host, the Host SHOULD include UI-specific context in the `McpUiInitializeResult`’s `hostContext` field:
 
@@ -486,7 +486,7 @@ Host SHOULD add the message to the conversation thread, preserving the specified
 }
 ```
 
-Host sends this notification after the Guest UI's initialize request completes, when tool arguments become available. This notification is sent at most once and is required before sending `ui/tool-result`.
+Host sends this notification after the Guest UI's initialize request completes, when tool arguments become available. This notification is sent at most once and is required before sending `ui/notifications/tool-result`.
 
 `ui/notifications/tool-input-partial` - Host MAY send this notification zero or more times while the agent is streaming tool arguments, before `ui/notifications/tool-input` is sent.
 
@@ -513,12 +513,12 @@ Guest UI behavior (optional):
 - MUST NOT rely on partial arguments for critical operations
 - SHOULD gracefully handle missing or changing fields between notifications
 
-`ui/tool-result` - Tool execution result
+`ui/notifications/tool-result` - Tool execution result
 
 ```json
 {
   "jsonrpc": "2.0",
-  "method": "ui/tool-result",
+  "method": "ui/notifications/tool-result",
   "params": "CallToolResult"  // Standard MCP type
 }
 ```
@@ -603,22 +603,22 @@ Host MAY send this notification when any context field changes (e.g., theme togg
 
 These messages are reserved for web-based hosts that implement the recommended double-iframe sandbox architecture:
 
-`ui/sandbox-ready` - Sandbox proxy is ready
+`ui/notifications/sandbox-ready` (Sandbox Proxy → Host) - Sandbox proxy is ready
 
 ```json
 {
   "jsonrpc": "2.0",
-  "method": "ui/sandbox-ready",
+  "method": "ui/notifications/sandbox-ready",
   "params": {}
 }
 ```
 
-`ui/sandbox-resource-ready` - HTML resource ready to load
+`ui/notifications/sandbox-resource-ready` (Host → Sandbox Proxy) - HTML resource ready to load
 
 ```json
 {
   "jsonrpc": "2.0",
-  "method": "ui/sandbox-resource-ready",
+  "method": "ui/notifications/sandbox-resource-ready",
   "params": {
     "html": "string",        // HTML content to load
     "sandbox": "string"      // Optional override for inner iframe `sandbox` attribute
@@ -666,9 +666,9 @@ sequenceDiagram
    P -> P: Render inner iframe with HTML
 
    end
-   UI ->> H: initialize
-   H -->> UI: InitializeResult (e.g., host-context, capabilities, etc.)
-   UI ->> H: notifications/initialized
+   UI ->> H: ui/initialize
+   H -->> UI: McpUiInitializeResult (e.g., host-context, capabilities, etc.)
+   UI ->> H: ui/notifications/initialized
    opt Stream Tool input to UI
      H -->> UI: ui/notifications/tool-input-partial (0..n)
    end
@@ -681,7 +681,7 @@ sequenceDiagram
  end
 ```
 
-Note: when the Guest UI is rendered inside a sandbox, the sandbox transparently passes events between the Guest UI and the Host (except for events that start with `sandbox-`)
+Note: when the Guest UI is rendered inside a sandbox, the sandbox transparently passes messages between the Guest UI and the Host, except for messages named `ui/notifications/sandbox-*`.
 
 #### 5. Interactive Phase
 
@@ -746,7 +746,7 @@ Note: Cleanup may be triggered at any point in the lifecycle following UI initia
 
 Tool execution results are passed to the UI through two mechanisms:
 
-#### 1. Tool Input (via ui/notifications/tool-input notification)
+#### 1. Tool Input (via `ui/notifications/tool-input` notification)
 
 The original tool call arguments:
 
@@ -761,7 +761,7 @@ params: {
 }
 ```
 
-#### 2. Tool Result (via ui/tool-result notification)
+#### 2. Tool Result (via `ui/notifications/tool-result` notification)
 
 The tool's execution result:
 
@@ -783,7 +783,7 @@ The tool's execution result:
 }
 
 // UI receives:
-Notification: ui/tool-result
+Notification: ui/notifications/tool-result
 params: {
   content: [...],  // Same as above
   structuredContent: { temperature: 72, ... },