Add an iOS Demo with Signin With Apple

.licenseignore

@@ -37,4 +37,5 @@ Package.resolved
 **/frontend/*
 **/*.code-snippets
 .DS_Store
-.licenseignore
+.licenseignore
+**/*.entitlements

Examples/ios-math-solver/.gitignore

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+.DS_Store
+/.build
+/Packages
+xcuserdata/
+DerivedData/
+.swiftpm/configuration/registries.json
+.swiftpm/xcode/package.xcworkspace/contents.xcworkspacedata
+.netrc

Examples/ios-math-solver/README.md

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+# Math Problem Solver
+
+An iOS application that uses AWS Bedrock and Claude to solve math and physics problems from images.
+
+## Features
+
+- Take a photo or select an image from your photo library
+- Analyze math and physics problems using Claude AI
+- Get step-by-step solutions with explanations
+- Secure authentication using Sign in with Apple (SIWA) and AWS STS
+
+## Screenshot
+
+![Math Problem Solver App Screenshot](screenshot.png)
+
+## Technology Stack
+
+- Swift bedrock Library for AI image analysis and problem solving
+- Swift and SwiftUI for the iOS app
+- Claude 3 Sonnet model for high-quality responses
+- Sign in with Apple (SIWA) for authentication
+- Streaming responses for real-time feedback
+
+## How It Works
+
+1. The app captures or selects an image containing a math or physics problem
+2. The image is processed and sent to AWS Bedrock
+3. Claude analyzes the problem and generates a step-by-step solution
+4. The solution is streamed back to the app in real-time
+5. The app displays the formatted solution with mathematical notation
+
+## Requirements
+
+- iOS 16.0+
+- Xcode 15.0+
+- AWS account with Bedrock configured
+- Sign in with Apple enabled in your Apple Developer account
+
+## License
+
+This project is licensed under the Apache License 2.0 - see the LICENSE file for details.

Examples/ios-math-solver/Sources/Assets.xcassets/AccentColor.colorset/Contents.json

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+{
+  "colors" : [
+    {
+      "idiom" : "universal"
+    }
+  ],
+  "info" : {
+    "author" : "xcode",
+    "version" : 1
+  }
+}

Examples/ios-math-solver/Sources/Assets.xcassets/AppIcon.appiconset/Contents.json

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+{
+  "images" : [
+    {
+      "idiom" : "universal",
+      "platform" : "ios",
+      "size" : "1024x1024"
+    },
+    {
+      "appearances" : [
+        {
+          "appearance" : "luminosity",
+          "value" : "dark"
+        }
+      ],
+      "idiom" : "universal",
+      "platform" : "ios",
+      "size" : "1024x1024"
+    },
+    {
+      "appearances" : [
+        {
+          "appearance" : "luminosity",
+          "value" : "tinted"
+        }
+      ],
+      "idiom" : "universal",
+      "platform" : "ios",
+      "size" : "1024x1024"
+    }
+  ],
+  "info" : {
+    "author" : "xcode",
+    "version" : 1
+  }
+}

Examples/ios-math-solver/Sources/Assets.xcassets/Contents.json

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+{
+  "info" : {
+    "author" : "xcode",
+    "version" : 1
+  }
+}

Examples/ios-math-solver/Sources/AuthenticationManager.swift

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+//===----------------------------------------------------------------------===//
+//
+// This source file is part of the Swift Bedrock Library open source project
+//
+// Copyright (c) 2025 Amazon.com, Inc. or its affiliates
+//                    and the Swift Bedrock Library project authors
+// Licensed under Apache License v2.0
+//
+// See LICENSE.txt for license information
+// See CONTRIBUTORS.txt for the list of Swift Bedrock Library project authors
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+//===----------------------------------------------------------------------===//
+
+import AuthenticationServices
+import Foundation
+import SwiftUI
+
+class AuthenticationManager: ObservableObject {
+    @Published var isAuthenticated = false  // FIXME: check if the token is still valid
+    @Published var userId: String? = nil
+    @Published var error: String? = nil
+
+    var jwtToken: String? = nil
+
+    // Trigger for credential changes
+    @Published var credentialsUpdated = false
+
+    func signOut() {
+        isAuthenticated = false
+        userId = nil
+    }
+
+    func authenticate(with userIdentifier: String, identityToken: Data) {
+        userId = userIdentifier
+
+        // Convert identity token to string
+        guard let tokenString = String(data: identityToken, encoding: .utf8) else {
+            handleAuthError(
+                NSError(
+                    domain: "AuthenticationError",
+                    code: 1001,
+                    userInfo: [NSLocalizedDescriptionKey: "Failed to convert identity token to string"]
+                )
+            )
+            return
+        }
+
+        self.jwtToken = tokenString
+
+        // Get AWS credentials using the Apple identity token
+        Task {
+            // Update UI on main thread
+            await MainActor.run {
+                self.isAuthenticated = true
+                self.error = nil
+            }
+        }
+    }
+
+    func handleAuthError(_ error: Error) {
+        self.error = error.localizedDescription
+        isAuthenticated = false
+    }
+}

Examples/ios-math-solver/Sources/Content.swift

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+//===----------------------------------------------------------------------===//
+//
+// This source file is part of the Swift Bedrock Library open source project
+//
+// Copyright (c) 2025 Amazon.com, Inc. or its affiliates
+//                    and the Swift Bedrock Library project authors
+// Licensed under Apache License v2.0
+//
+// See LICENSE.txt for license information
+// See CONTRIBUTORS.txt for the list of Swift Bedrock Library project authors
+//
+// SPDX-License-Identifier: Apache-2.0
+//
+//===----------------------------------------------------------------------===//
+
+let content = """
+    ### Solution
+
+    #### Concepts Involved
+    This problem involves the Doppler effect, which describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. In this case, the source is a rotating sound emitter, and the observer is a microphone.
+
+    #### Given Data
+    - Frequency of the sound source, \\( f_0 = 1500 \\, \\text{Hz} \\)
+    - Radius of the circular path, \\( r = 40.0 \\, \\text{cm} = 0.4 \\, \\text{m} \\)
+    - The sound source is rotating in an anti-clockwise direction.
+
+    #### Steps to Solve the Problem
+
+    1. **Determine the angular velocity (\\( \\omega \\)) of the source:**
+
+    Since the source is rotating, we need to find its angular velocity. However, the problem does not provide the rotational speed directly. We will assume the tangential velocity \\( v \\) at the point of the source is given by \\( v = r \\omega \\).
+
+    2. **Calculate the Doppler shift for each position (a, b, c):**
+
+    The Doppler effect formula for sound is given by:
+
+    \\(f = f_0 \\left( \\frac{v + v_o}{v + v_s} \\right)\\)
+
+    where:
+    - \\( f \\) is the observed frequency.
+    - \\( f_0 \\) is the source frequency.
+    - \\( v \\) is the speed of sound in the medium.
+    - \\( v_o \\) is the observer's velocity relative to the medium.
+    - \\( v_s \\) is the source's velocity relative to the medium.
+
+    Since the observer (microphone) is stationary, \\( v_o = 0 \\).
+
+    3. **Frequency at point a:**
+
+    At point a, the source is moving towards the observer.
+    \\[f_a = f_0 \\left( \\frac{v}{v - v_s} \\right)\\]
+    where \\( v_s = r \\omega \\).
+
+    4. **Frequency at point b:**
+
+    At point b, the source is moving perpendicular to the line of sight of the observer.
+    \\[f_b = f_0\\]
+    There is no Doppler shift because the component of the velocity towards the observer is zero.
+
+    5. **Frequency at point c:**
+
+    At point c, the source is moving away from the observer.
+    \\[f_c = f_0 \\left( \\frac{v}{v + v_s} \\right)\\]
+    where \\( v_s = r \\omega \\).
+
+    6. **Compare the frequencies:**
+
+    From the Doppler effect formulas:
+    - \\( f_a > f_0 \\) because the source is moving towards the observer.
+    - \\( f_b = f_0 \\) because there is no relative motion towards or away from the observer.
+    - \\( f_c < f_0 \\) because the source is moving away from the observer.
+
+    Therefore, the relationship between the frequencies is:
+    \\(f_a > f_b = f_c\\)
+
+    ### Conclusion
+    The frequencies perceived by the microphone are such that \\( f_a > f_b = f_c \\).
+    """