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<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>๐Ÿ‘ป GhostPack: Veo 3-Level Video Sorcery ๐Ÿ˜ˆ</title>
    <!-- Bootstrap CSS -->
    <link href="https://cdn.jsdelivr.net/npm/[email protected]/dist/css/bootstrap.min.css" rel="stylesheet" integrity="sha384-QWTKZyjpPEjISv5WaRU9OFeRpok6YctnYmDr5pNlyT2bRjXh0JMhjY6hW+ALEwIH" crossorigin="anonymous">
    <!-- Animate.css -->
    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/animate.css/4.1.1/animate.min.css"/>
    <!-- Custom CSS -->
    <link rel="stylesheet" href="style.css">
    <!-- Favicon -->
    <link rel="icon" href="https://huggingface.co/spaces/ghostai1/GhostPack/resolve/main/ghostpack_logo.png">
</head>
<body>
    <!-- Navbar -->
    <nav class="navbar navbar-expand-lg navbar-dark fixed-top">
        <div class="container">
            <a class="navbar-brand" href="#">๐Ÿ‘ป GhostPack</a>
            <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation">
                <span class="navbar-toggler-icon"></span>
            </button>
            <div class="collapse navbar-collapse" id="navbarNav">
                <ul class="navbar-nav ms-auto">
                    <li class="nav-item"><a class="nav-link" href="#home">Home</a></li>
                    <li class="nav-item"><a class="nav-link" href="#features">Features</a></li>
                    <li class="nav-item"><a class="nav-link" href="#optimizations">Math Sorcery</a></li>
                    <li class="nav-item"><a class="nav-link" href="#demo">Demo</a></li>
                    <li class="nav-item"><a class="nav-link" href="#future">Future</a></li>
                    <li class="nav-item"><a class="nav-link" href="#installation">Installation</a></li>
                    <li class="nav-item"><a class="nav-link" href="#usage">Usage</a></li>
                    <li class="nav-item"><a class="nav-link" href="#files">Last Files</a></li>
                    <li class="nav-item"><a class="nav-link" href="#screenshots">Screenshots</a></li>
                </ul>
            </div>
        </div>
    </nav>

    <!-- Hero Section -->
    <section id="home" class="hero-section text-center text-white">
        <div class="container">
            <h1 class="display-3 animate__animated animate__zoomIn">๐Ÿ‘ป GhostPack</h1>
            <p class="lead animate__animated animate__fadeIn animate__delay-1s">Veo 3-Level Video Sorcery Haunts Laptops with 8GB RAM! ๐Ÿ˜ˆ๐Ÿš€</p>
            <p class="animate__animated animate__fadeIn animate__delay-2s">Unleash photorealistic videos with ghostai1โ€™s math wizardry on GPUs โ‰ฅ6GB VRAM.</p>
            <div class="preview-window animate__animated animate__fadeIn animate__delay-3s">
                <img src="https://huggingface.co/spaces/ghostai1/GhostPack/resolve/main/preview_mockup.png" alt="GhostPack Preview" class="img-fluid rounded">
                <p class="mt-2">Preview: ghostgradio.py in action</p>
            </div>
            <a href="#installation" class="btn btn-ghost btn-lg animate__animated animate__pulse animate__delay-4s">Summon Now ๐Ÿ› ๏ธ</a>
            <a href="https://github.com/ghostai1/GhostPack" class="btn btn-outline-ghost btn-lg animate__animated animate__pulse animate__delay-4s" target="_blank">GitHub ๐ŸŒŸ</a>
        </div>
    </section>

    <!-- Features Section -->
    <section id="features" class="py-5 bg-dark text-white">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">โœจ Spectral Features</h2>
            <div class="row row-cols-1 row-cols-md-3 g-4">
                <div class="col">
                    <div class="card bg-ghost-card h-100" data-bs-toggle="tooltip" title="Matches Veo 3โ€™s photorealism">
                        <div class="card-body">
                            <h3 class="card-title">๐Ÿ“น Veo 3-Level AI</h3>
                            <p class="card-text">Hyper-realistic videos via next-frame prediction, running on 8GB RAM laptops.</p>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-card h-100" data-bs-toggle="tooltip" title="Blazing fast with teacache">
                        <div class="card-body">
                            <h3 class="card-title">โšก๏ธ Phantom Speed</h3>
                            <p class="card-text">Teacache cuts ~40% off generation time (~12โ€“15s/frame on RTX 3060).</p>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-card h-100" data-bs-toggle="tooltip" title="Optimized for budget hardware">
                        <div class="card-body">
                            <h3 class="card-title">๐Ÿ› ๏ธ Laptop Domination</h3>
                            <p class="card-text">13B models run on GPUs with โ‰ฅ6GB VRAM, tuned for RTX 3060 and beyond.</p>
                        </div>
                    </div>
                </div>
            </div>
        </div>
    </section>

    <!-- Optimizations Section -->
    <section id="optimizations" class="py-5 bg-light">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">๐Ÿง™โ€โ™‚๏ธ Ghostai1โ€™s Math Sorcery</h2>
            <p class="lead text-center text-dark mb-4">GhostPackโ€™s SDK is a spectral masterpiece, conjured with ghostai1โ€™s math optimizations to haunt any laptop with 8GB RAM.</p>
            
            <!-- Tabs for Optimization Categories -->
            <ul class="nav nav-tabs justify-content-center mb-4" id="optTab" role="tablist">
                <li class="nav-item" role="presentation">
                    <button class="nav-link active" id="speed-tab" data-bs-toggle="tab" data-bs-target="#speed" type="button" role="tab" aria-controls="speed" aria-selected="true">โšก๏ธ Speed</button>
                </li>
                <li class="nav-item" role="presentation">
                    <button class="nav-link" id="memory-tab" data-bs-toggle="tab" data-bs-target="#memory" type="button" role="tab" aria-controls="memory" aria-selected="false">๐Ÿ”ฎ Memory</button>
                </li>
                <li class="nav-item" role="presentation">
                    <button class="nav-link" id="compute-tab" data-bs-toggle="tab" data-bs-target="#compute" type="button" role="tab" aria-controls="compute" aria-selected="false">๐Ÿงฌ Compute</button>
                </li>
            </ul>

            <div class="tab-content" id="optTabContent">
                <!-- Speed Tab -->
                <div class="tab-pane fade show active" id="speed" role="tabpanel" aria-labelledby="speed-tab">
                    <div class="row row-cols-1 row-cols-md-3 g-4 mb-4">
                        <div class="col">
                            <div class="card bg-ghost-card text-white h-100" data-bs-toggle="modal" data-bs-target="#teacacheModal">
                                <div class="card-body text-center">
                                    <h3 class="card-title">๐Ÿ”ฎ Teacache</h3>
                                    <p class="card-text">Caches diffusion states, slashing ~40% off frame time.</p>
                                    <p><strong>Boost: 40%</strong><br>Stat: ~12s/frame on RTX 3060<br>Math: \( T_{\text{total}} \approx 0.6 \cdot T_{\text{base}} \)</p>
                                </div>
                            </div>
                        </div>
                        <div class="col">
                            <div class="card bg-ghost-card text-white h-100" data-bs-toggle="modal" data-bs-target="#sageModal">
                                <div class="card-body text-center">
                                    <h3 class="card-title">๐Ÿง™โ€โ™‚๏ธ Sage-Attention</h3>
                                    <p class="card-text">Streamlines attention layers for ~5โ€“10% speed-up.</p>
                                    <p><strong>Boost: 5โ€“10%</strong><br>Stat: ~1โ€“2s/frame saved<br>Math: \( T_{\text{attn}} \approx 0.9 \cdot T_{\text{base_attn}} \)</p>
                                </div>
                            </div>
                        </div>
                        <div class="col">
                            <div class="card bg-ghost-card text-white h-100" data-bs-toggle="modal" data-bs-target="#cudaModal">
                                <div class="card-body text-center">
                                    <h3 class="card-title">โšก CUDA Tweaks</h3>
                                    <p class="card-text">Optimized allocation for ~10โ€“15% latency cut.</p>
                                    <p><strong>Boost: 10โ€“15%</strong><br>Stat: ~10โ€“15% faster<br>Math: \( L_{\text{CUDA}} \approx 0.85 \cdot L_{\text{base}} \)</p>
                                </div>
                            </div>
                        </div>
                    </div>
                </div>

                <!-- Memory Tab -->
                <div class="tab-pane fade" id="memory" role="tabpanel" aria-labelledby="memory-tab">
                    <div class="row row-cols-1 row-cols-md-2 g-4 mb-4">
                        <div class="col">
                            <div class="card bg-ghost-card text-white h-100" data-bs-toggle="modal" data-bs-target="#contextModal">
                                <div class="card-body text-center">
                                    <h3 class="card-title">๐Ÿงฌ Context Packing</h3>
                                    <p class="card-text">Compresses contexts, saving ~50% VRAM.</p>
                                    <p><strong>Boost: 50%</strong><br>Stat: ~2โ€“3GB saved<br>Math: \( M_{\text{VRAM}} \propto O(1) \)</p>
                                </div>
                            </div>
                        </div>
                        <div class="col">
                            <div class="card bg-ghost-card text-white h-100" data-bs-toggle="modal" data-bs-target="#tcmallocModal">
                                <div class="card-body text-center">
                                    <h3 class="card-title">๐Ÿ’พ tcmalloc</h3>
                                    <p class="card-text">Cuts memory overhead by ~5โ€“20%.</p>
                                    <p><strong>Boost: 5โ€“20%</strong><br>Stat: ~15% CPU relief<br>Math: \( O_{\text{mem}} \approx 0.8 \cdot O_{\text{glibc}} \)</p>
                                </div>
                            </div>
                        </div>
                    </div>
                </div>

                <!-- Compute Tab -->
                <div class="tab-pane fade" id="compute" role="tabpanel" aria-labelledby="compute-tab">
                    <div class="row row-cols-1 row-cols-md-1 g-4 mb-4">
                        <div class="col">
                            <div class="card bg-ghost-card text-white h-100" data-bs-toggle="modal" data-bs-target="#batchingModal">
                                <div class="card-body text-center">
                                    <h3 class="card-title">โšก Dynamic Batching</h3>
                                    <p class="card-text">Adapts batches for ~30โ€“50% throughput gain.</p>
                                    <p><strong>Boost: 30โ€“50%</strong><br>Stat: ~1.5x FPS<br>Math: \( \text{Throughput} \propto B \cdot \text{FPS}_{\text{base}} \)</p>
                                </div>
                            </div>
                        </div>
                    </div>
                </div>
            </div>

            <!-- Optimization Breakdown -->
            <div class="row mt-4">
                <div class="col-md-12">
                    <h3 class="mb-3 text-white">Optimization Breakdown</h3>
                    <ul class="text-white">
                        <li><strong>๐Ÿ”ฎ Compressed Context Packing</strong>: Collapses frame contexts into a fixed-size matrix, slashing VRAM by ~50% (\( M_{\text{VRAM}} \propto O(1) \)), enabling 60s videos on 6GB VRAM GPUs.</li>
                        <li><strong>๐Ÿงฌ Dynamic Batching</strong>: Adapts batches (2โ€“4 frames), boosting throughput by ~30โ€“50% (\( \text{Throughput} \propto B \)), ideal for RTX 3050.</li>
                        <li><strong>โšก๏ธ Teacache Efficiency</strong>: Caches diffusion states, cutting ~40% off compute time (\( T_{\text{total}} \approx 0.6T_{\text{base}} \)), hitting ~10โ€“15s/frame on RTX 3060.</li>
                        <li><strong>๐Ÿง™โ€โ™‚๏ธ Sage-Attention</strong>: Streamlines attention layers, saving ~5โ€“10% time (\( T_{\text{attn}} \approx 0.9T_{\text{base_attn}} \)).</li>
                        <li><strong>๐Ÿ’พ tcmalloc</strong>: Reduces memory overhead by ~5โ€“20% (\( O_{\text{mem}} \approx 0.8O_{\text{glibc}} \)), easing CPU load by ~15%.</li>
                        <li><strong>โšก CUDA Tweaks</strong>: Cuts latency by ~10โ€“15% (\( L_{\text{CUDA}} \approx 0.85L_{\text{base}} \)) with optimized allocation.</li>
                    </ul>
                </div>
            </div>

            <!-- VRAM Requirements Table -->
            <div class="row mt-4">
                <div class="col-md-12">
                    <h3 class="text-center text-white mb-3">VRAM Requirements ๐Ÿ–ฅ๏ธ</h3>
                    <div class="table-responsive">
                        <table class="table table-dark table-bordered">
                            <thead>
                                <tr>
                                    <th>GPU</th>
                                    <th>VRAM</th>
                                    <th>Performance</th>
                                    <th>Notes</th>
                                </tr>
                            </thead>
                            <tbody>
                                <tr>
                                    <td>GTX 1650</td>
                                    <td>6GB</td>
                                    <td>~18โ€“25s/frame</td>
                                    <td>Minimum, teacache recommended.</td>
                                </tr>
                                <tr>
                                    <td>RTX 3050</td>
                                    <td>8GB</td>
                                    <td>~15โ€“20s/frame</td>
                                    <td>Balanced, batch size 2.</td>
                                </tr>
                                <tr>
                                    <td>RTX 3060</td>
                                    <td>12GB</td>
                                    <td>~10โ€“15s/frame</td>
                                    <td>Optimal, batch size 2โ€“4.</td>
                                </tr>
                                <tr>
                                    <td>RTX 4090</td>
                                    <td>24GB</td>
                                    <td>~1.5โ€“2.5s/frame</td>
                                    <td>High-end, max batch size.</td>
                                </tr>
                            </tbody>
                        </table>
                    </div>
                </div>
            </div>
        </div>
    </section>

    <!-- Demo Video Showcase -->
    <section id="demo" class="py-5 bg-dark text-white">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">๐ŸŽฅ Demo Video Showcase</h2>
            <p class="lead text-center mb-4">Witness GhostPackโ€™s spectral video generation in action!</p>
            <div class="row">
                <div class="col-md-8 mx-auto">
                    <div class="card bg-ghost-card">
                        <div class="card-body text-center">
                            <video src="https://huggingface.co/spaces/ghostai1/GhostPack/resolve/main/demo_video.mp4" controls loop class="img-fluid rounded" style="max-height: 400px;"></video>
                            <p class="mt-3">Sample output from ghostgradio.py, showcasing a neon-lit spectral figure.</p>
                        </div>
                    </div>
                </div>
            </div>
        </div>
    </section>

    <!-- Future Features Section -->
    <section id="future" class="py-5 bg-light text-dark">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">๐ŸŒŒ Future Spectral Phantoms</h2>
            <p class="lead text-center mb-4">GhostPack is brewing epic upgrades:</p>
            <div class="row row-cols-1 row-cols-md-2 g-4">
                <div class="col">
                    <div class="card bg-ghost-light h-100">
                        <div class="card-body">
                            <h3 class="card-title">๐Ÿ—ฃ๏ธ Voice Generation</h3>
                            <p class="card-text">AI-driven voice synthesis to narrate videos with ghostly tones, coming to ghostgradio.py.</p>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-light h-100">
                        <div class="card-body">
                            <h3 class="card-title">๐Ÿ–ผ๏ธ AI Images</h3>
                            <p class="card-text">Generate spectral starting frames with AI-crafted images for cinematic pipelines.</p>
                        </div>
                    </div>
                </div>
            </div>
        </div>
    </section>

    <!-- Installation Section -->
    <section id="installation" class="py-5 bg-dark text-white">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">๐Ÿ› ๏ธ Unleash GhostPack</h2>
            <p class="lead text-center mb-4">Summon from GitHub. Requires >30GB disk space.</p>
            <div class="row row-cols-1 row-cols-md-3 g-4">
                <div class="col">
                    <div class="card bg-ghost-card h-100">
                        <div class="card-body">
                            <h3 class="card-title">๐Ÿง Ubuntu</h3>
                            <pre><code class="code-block">git clone https://github.com/ghostai1/GhostPack
cd GhostPack
chmod +x install_ubuntu.sh
./install_ubuntu.sh</code></pre>
                            <p>NVIDIA GPU, 8GB RAM, Python 3.10, CUDA 12.6.</p>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-card h-100">
                        <div class="card-body">
                            <h3 class="card-title">๐ŸชŸ Windows</h3>
                            <pre><code class="code-block">git clone https://github.com/ghostai1/GhostPack
cd GhostPack
install.bat</code></pre>
                            <p>Auto-downloads models (>30GB).</p>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-card h-100">
                        <div class="card-body">
                            <h3 class="card-title">๐ŸŽ macOS</h3>
                            <pre><code class="code-block">git clone https://github.com/ghostai1/GhostPack
cd GhostPack
chmod +x install_macos.sh
./install_macos.sh</code></pre>
                            <p>M1/M2 support (slower).</p>
                        </div>
                    </div>
                </div>
            </div>
        </div>
    </section>

    <!-- Usage Section -->
    <section id="usage" class="py-5 bg-light text-dark">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">๐Ÿ“น Weave Ghostly Videos</h2>
            <ol>
                <li><strong>Launch Phantom GUI</strong>:
                    <div class="card bg-ghost-light">
                        <div class="card-body">
                            <pre><code class="code-block">source ~/ghostpack_venv/venv/bin/activate
cd ~/ghostpack_venv
python ghostgradio.py --port 5666 --server 0.0.0.0</code></pre>
                        </div>
                    </div>
                </li>
                <li><strong>Craft Spells</strong>:
                    <ul>
                        <li>Upload an image.</li>
                        <li>Prompt: โ€œA spectral figure glides through a neon-lit city.โ€</li>
                        <li>Enable teacache (โšก๏ธ speed).</li>
                        <li>Set 15fps, 5s video (~75 frames).</li>
                    </ul>
                </li>
                <li><strong>Summon Spirits</strong>: Run <code>nvidia-smi</code> (~80โ€“100% GPU).</li>
            </ol>
        </div>
    </section>

    <!-- Screenshots Section -->
    <section id="screenshots" class="py-5 bg-dark text-white">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">๐Ÿ“ธ Screenshots</h2>
            <p class="lead text-center mb-4">Check out GhostPackโ€™s spectral magic in action!</p>
            <div class="row row-cols-1 row-cols-md-3 g-4">
                <div class="col">
                    <div class="card bg-ghost-card h-100">
                        <div class="card-body text-center">
                            <img src="https://cdn-uploads.huggingface.co/production/uploads/6421b1c68adc8881b974a89d/7R4MeWxnB3D2-Lw0vxxUL.png" class="img-fluid rounded" style="max-height: 300px;">
                            <p class="mt-2">Main</p>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-card h-100">
                        <div class="card-body text-center">
                            <img src="https://cdn-uploads.huggingface.co/production/uploads/6421b1c68adc8881b974a89d/9qNVRX2eM2iCY8xQKcOwW.png

" alt="Screenshot 2" class="img-fluid rounded" style="max-height: 300px;">
                            <p class="mt-2">Advanced Settings</p>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-card h-100">
                        <div class="card-body text-center">
                            <img src="https://cdn-uploads.huggingface.co/production/uploads/6421b1c68adc8881b974a89d/--fIS9ITg4-VqN22ySoa2.png" alt="Screenshot 3" class="img-fluid rounded" style="max-height: 300px;">
                            <p class="mt-2">Logs</p>
                        </div>
                    </div>
                </div>
            </div>
            <p class="text-center mt-4 text-white">Upload your screenshots to Hugging Face to replace placeholders!</p>
        </div>
    </section>

    <!-- Last Files Section -->
    <section id="files" class="py-5 bg-light text-dark">
        <div class="container">
            <h2 class="text-center mb-5 animate__animated animate__fadeIn">๐Ÿ“‚ Latest Conjurations</h2>
            <p class="lead text-center mb-4">Explore the latest files and logs from the GhostPack repo.</p>
            <div class="row row-cols-1 row-cols-md-2 g-4">
                <div class="col">
                    <div class="card bg-ghost-light h-100">
                        <div class="card-body text-center">
                            <h3 class="card-title">๐Ÿ“œ Latest File</h3>
                            <p class="card-text">Check out <code>ghostgradio.py</code>, the heart of GhostPackโ€™s GUI.</p>
                            <a href="https://github.com/ghostai1/GhostPack/blob/main/ghostgradio.py" class="btn btn-ghost" target="_blank">View File</a>
                        </div>
                    </div>
                </div>
                <div class="col">
                    <div class="card bg-ghost-light h-100">
                        <div class="card-body text-center">
                            <h3 class="card-title">๐Ÿ“‹ Logs</h3>
                            <p class="card-text">Dive into render logs for debugging and insights.</p>
                            <a href="https://github.com/ghostai1/GhostPack/tree/main/outputs" class="btn btn-ghost" target="_blank">View Logs</a>
                        </div>
                    </div>
                </div>
            </div>
            <div class="text-center mt-4">
                <a href="https://github.com/ghostai1/GhostPack" class="btn btn-outline-ghost me-3" target="_blank">Refresh Repo ๐Ÿ”„</a>
                <a href="https://github.com/ghostai1/GhostPack/tree/main/outputs" class="btn btn-ghost" target="_blank">Refresh Logs ๐Ÿ“ฅ</a>
            </div>
        </div>
    </section>

    <!-- Footer -->
    <footer class="bg-ghost-black text-white text-center py-4">
        <p>๐Ÿ‘ป GhostPack by ghostai1 | <a href="https://github.com/ghostai1/GhostPack" target="_blank">GitHub</a> | <a href="https://huggingface.co/spaces/ghostai1/GhostPack" target="_blank">Hugging Face</a> | Apache-2.0 License</p>
        <p>Forged in ๐Ÿ˜ˆ hellfire with โšก๏ธ to haunt video generation forever!</p>
    </footer>

    <!-- Modals -->
    <div class="modal fade" id="teacacheModal" tabindex="-1" aria-labelledby="teacacheModalLabel" aria-hidden="true">
        <div class="modal-dialog modal-lg">
            <div class="modal-content bg-ghost-card text-white">
                <div class="modal-header">
                    <h5 class="modal-title" id="teacacheModalLabel">๐Ÿ”ฎ Teacache</h5>
                    <button type="button" class="btn-close btn-close-white" data-bs-dismiss="modal" aria-label="Close"></button>
                </div>
                <div class="modal-body">
                    <p>Teacache caches diffusion states, reducing compute by ~30โ€“40% and slashing frame time by ~40% (~12s/frame on RTX 3060).</p>
                    <p><strong>Math</strong>: \( T_{\text{total}} \approx 0.6 \cdot T_{\text{base}} \).</p>
                </div>
            </div>
        </div>
    </div>
    <div class="modal fade" id="contextModal" tabindex="-1" aria-labelledby="contextModalLabel" aria-hidden="true">
        <div class="modal-dialog modal-lg">
            <div class="modal-content bg-ghost-card text-white">
                <div class="modal-header">
                    <h5 class="modal-title" id="contextModalLabel">๐Ÿงฌ Context Packing</h5>
                    <button type="button" class="btn-close btn-close-white" data-bs-dismiss="modal" aria-label="Close"></button>
                </div>
                <div class="modal-body">
                    <p>Compresses frame contexts to a fixed-size matrix, saving ~50% VRAM (~2โ€“3GB for 60s videos).</p>
                    <p><strong>Math</strong>: \( M_{\text{VRAM}} \propto O(1) \).</p>
                </div>
            </div>
        </div>
    </div>
    <div class="modal fade" id="batchingModal" tabindex="-1" aria-labelledby="batchingModalLabel" aria-hidden="true">
        <div class="modal-dialog modal-lg">
            <div class="modal-content bg-ghost-card text-white">
                <div class="modal-header">
                    <h5 class="modal-title" id="batchingModalLabel">โšก Dynamic Batching</h5>
                    <button type="button" class="btn-close btn-close-white" data-bs-dismiss="modal" aria-label="Close"></button>
                </div>
                <div class="modal-body">
                    <p>Adapts batch sizes (2โ€“4 frames), boosting throughput by ~30โ€“50% (~1.5x FPS).</p>
                    <p><strong>Math</strong>: \( \text{Throughput} \propto B \cdot \text{FPS}_{\text{base}} \).</p>
                </div>
            </div>
        </div>
    </div>
    <div class="modal fade" id="sageModal" tabindex="-1" aria-labelledby="sageModalLabel" aria-hidden="true">
        <div class="modal-dialog modal-lg">
            <div class="modal-content bg-ghost-card text-white">
                <div class="modal-header">
                    <h5 class="modal-title" id="sageModalLabel">๐Ÿง™โ€โ™‚๏ธ Sage-Attention</h5>
                    <button type="button" class="btn-close btn-close-white" data-bs-dismiss="modal" aria-label="Close"></button>
                </div>
                <div class="modal-body">
                    <p>Optimizes attention layers, saving ~5โ€“10% time (~1โ€“2s/frame).</p>
                    <p><strong>Math</strong>: \( T_{\text{attn}} \approx 0.9 \cdot T_{\text{base_attn}} \).</p>
                </div>
            </div>
        </div>
    </div>
    <div class="modal fade" id="tcmallocModal" tabindex="-1" aria-labelledby="tcmallocModalLabel" aria-hidden="true">
        <div class="modal-dialog modal-lg">
            <div class="modal-content bg-ghost-card text-white">
                <div class="modal-header">
                    <h5 class="modal-title" id="tcmallocModalLabel">๐Ÿ’พ tcmalloc</h5>
                    <button type="button" class="btn-close btn-close-white" data-bs-dismiss="modal" aria-label="Close"></button>
                </div>
                <div class="modal-body">
                    <p>Reduces memory overhead by ~5โ€“20%, easing CPU load by ~15%.</p>
                    <p><strong>Math</strong>: \( O_{\text{mem}} \approx 0.8 \cdot O_{\text{glibc}} \).</p>
                </div>
            </div>
        </div>
    </div>
    <div class="modal fade" id="cudaModal" tabindex="-1" aria-labelledby="cudaModalLabel" aria-hidden="true">
        <div class="modal-dialog modal-lg">
            <div class="modal-content bg-ghost-card text-white">
                <div class="modal-header">
                    <h5 class="modal-title" id="cudaModalLabel">โšก CUDA Tweaks</h5>
                    <button type="button" class="btn-close btn-close-white" data-bs-dismiss="modal" aria-label="Close"></button>
                </div>
                <div class="modal-body">
                    <p>Optimizes CUDA allocation, reducing latency by ~10โ€“15%.</p>
                    <p><strong>Math</strong>: \( L_{\text{CUDA}} \approx 0.85 \cdot L_{\text{base}} \).</p>
                </div>
            </div>
        </div>
    </div>

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