docs(showcase): add docs/showcase/fact-dynamics.mdx for Fact Dynamics pr…

docs/showcase/fact-dynamics.mdx

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+---
+title: Fact Dynamics | Real-time Fact-Checking Flutter App
+description: Cross-platform app for real-time fact-checking of debates, speeches, and images using Perplexity's Sonar API
+sidebar_position: 2
+keywords: [Fact Dynamics, fact-checking, Flutter, Dart, real-time, speech-to-text, debate, image verification]
+---
+
+# Fact Dynamics | Real-time Fact-Checking Flutter App
+<p align="center">
+  <img
+    src="https://raw.githubusercontent.com/vishnu32510/fact_pulse/main/assets/icon/icon.png"
+    alt="Fact Dynamics logo"
+    width="80"
+    height="80"
+    style="border-radius: 14px;"
+  />
+</p>
+
+**Hackathon Submission** - Built for Perplexity Hackathon in Information Tools & Deep Research categories.
+
+Fact Dynamics is a cross-platform Flutter app that provides real-time fact-checking for spoken content and images. Perfect for live debates, presentations, and on-the-fly information verification.
+
+
+## Features
+
+* Real-time speech transcription and fact-checking during live conversations
+* Image text extraction and claim verification with source citations
+* Claim rating system (TRUE, FALSE, MISLEADING, UNVERIFIABLE) with explanations
+* Source Citations** - Provides authoritative URLs backing each verdict
+
+* Debate mode with continuous speech recognition and streaming feedback
+* User authentication via Firebase (Google, Email) with persistent chat history
+* Cross-platform support for iOS, Android, and Web
+
+## Prerequisites
+
+* Flutter SDK 3.0.0 or newer
+* Dart SDK 2.17.0 or newer
+* Firebase CLI for authentication and database setup
+* Perplexity API key for Sonar integration
+* Device with microphone access for speech recognition
+
+## Installation (Follow Detailed guideline on the Repository)
+
+```bash
+git clone https://github.com/vishnu32510/fact_pulse.git
+cd fact_pulse
+flutter pub get
+```
+
+## Usage
+
+**Real-time Speech Fact-Checking:**
+- Streams 5-second audio chunks through Flutter's `speech_to_text`
+- Sends transcribed snippets to Sonar API with structured prompts
+- Returns JSON with claims, ratings (TRUE/FALSE/MISLEADING/UNVERIFIABLE), explanations, and sources
+
+**Image Analysis:**
+- Uploads images/URLs to Sonar API for text extraction
+- Verifies extracted claims against authoritative sources
+- Provides comprehensive analysis with source attribution
+
+## Screenshots
+
+<table>
+  <tr>
+    <td>
+      <img
+        src="https://raw.githubusercontent.com/vishnu32510/fact_pulse/main/assets/screenshots/2.%20Dashboard.png"
+        alt="Dashboard"
+        width="200"
+      />
+    </td>
+    <td>
+      <img
+        src="https://raw.githubusercontent.com/vishnu32510/fact_pulse/main/assets/screenshots/4.%20Fact%20Checks(Speech,%20Debate,%20Image).png"
+        alt="Fact checking interface"
+        width="200"
+      />
+    </td>
+  </tr>
+</table>
+
+## Code Explanation
+
+* Frontend: Flutter with BLoC pattern for state management targeting iOS, Android, and Web
+* Backend: Firebase (Firestore, Authentication) for user data and chat history persistence  
+* Speech Processing: speech_to_text package for real-time audio transcription
+* API Integration: Custom Dart client calling Perplexity Sonar API with structured prompts
+* Image Processing: Built-in image picker with base64 encoding for multimodal analysis
+* Data Architecture: Firestore collections per user with subcollections for debates, speeches, and images
+
+## Open Source SDKs
+
+Built two reusable packages for the Flutter community:
+- **[perplexity_dart](https://pub.dev/packages/perplexity_dart)** - Core Dart SDK for Perplexity API
+- **[perplexity_flutter](https://pub.dev/packages/perplexity_flutter)** - Flutter widgets and BLoC integration
+
+
+## Links
+
+- **[GitHub Repository](https://github.com/vishnu32510/fact_pulse)** - Full source code
+- **[Live Demo](https://fact-pulse.web.app/)** - Try the web version
+- **[Demo Video](https://youtu.be/92IoX19Djtc)** - Watch it in action
+- **[Devpost Submission](https://devpost.com/software/fact-dynamics)** - Hackathon entry