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README.md +7 -5
index.html +620 -19
prompts.txt +1 -0

README.md CHANGED Viewed

@@ -1,10 +1,12 @@
 ---
-title: Ai Model Collaboration Cookbook
-emoji: 💻
-colorFrom: gray
-colorTo: purple
 sdk: static
 pinned: false
 ---
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference

 ---
+title: ai-model-collaboration-cookbook
+emoji: 🐳
+colorFrom: purple
+colorTo: gray
 sdk: static
 pinned: false
+tags:
+  - deepsite
 ---
+Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference

index.html CHANGED Viewed

@@ -1,19 +1,620 @@
-<!doctype html>
-<html>
-	<head>
-		<meta charset="utf-8" />
-		<meta name="viewport" content="width=device-width" />
-		<title>My static Space</title>
-		<link rel="stylesheet" href="style.css" />
-	</head>
-	<body>
-		<div class="card">
-			<h1>Welcome to your static Space!</h1>
-			<p>You can modify this app directly by editing <i>index.html</i> in the Files and versions tab.</p>
-			<p>
-				Also don't forget to check the
-				<a href="https://huggingface.co/docs/hub/spaces" target="_blank">Spaces documentation</a>.
-			</p>
-		</div>
-	</body>
-</html>

+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8">
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
+    <title>AI Model Collaboration Cookbook for Math Research</title>
+    <script src="https://cdn.tailwindcss.com"></script>
+    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.0/css/all.min.css">
+    <style>
+        .gradient-bg {
+            background: linear-gradient(135deg, #4f46e5 0%, #7c3aed 50%, #9333ea 100%);
+        }
+        .model-card {
+            transition: all 0.3s ease;
+            border-left: 4px solid transparent;
+        }
+        .model-card:hover {
+            transform: translateY(-5px);
+            box-shadow: 0 20px 25px -5px rgba(0, 0, 0, 0.1), 0 10px 10px -5px rgba(0, 0, 0, 0.04);
+        }
+        .gpt-card {
+            border-left-color: #10a37f;
+        }
+        .gemini-card {
+            border-left-color: #4285f4;
+        }
+        .grok-card {
+            border-left-color: #000000;
+        }
+        .claude-card {
+            border-left-color: #d4a017;
+        }
+        .workflow-step {
+            position: relative;
+            padding-left: 3rem;
+        }
+        .workflow-step:before {
+            content: "";
+            position: absolute;
+            left: 1.25rem;
+            top: 0;
+            height: 100%;
+            width: 2px;
+            background-color: #e5e7eb;
+        }
+        .workflow-step:last-child:before {
+            height: 50%;
+        }
+        .workflow-step:first-child:before {
+            top: 50%;
+            height: 50%;
+        }
+        .workflow-step-number {
+            position: absolute;
+            left: 0.75rem;
+            top: 50%;
+            transform: translateY(-50%);
+            width: 2.5rem;
+            height: 2.5rem;
+            border-radius: 50%;
+            display: flex;
+            align-items: center;
+            justify-content: center;
+            font-weight: bold;
+            z-index: 10;
+        }
+        .code-block {
+            font-family: 'Courier New', Courier, monospace;
+            background-color: #1e293b;
+            color: #f8fafc;
+            border-radius: 0.375rem;
+            overflow-x: auto;
+        }
+        .json-key {
+            color: #7dd3fc;
+        }
+        .json-value {
+            color: #86efac;
+        }
+        .json-string {
+            color: #fca5a5;
+        }
+        .tab-content {
+            display: none;
+        }
+        .tab-content.active {
+            display: block;
+        }
+        .tab-button.active {
+            border-bottom: 3px solid #4f46e5;
+            color: #4f46e5;
+            font-weight: 600;
+        }
+    </style>
+</head>
+<body class="bg-gray-50 min-h-screen">
+    <!-- Header -->
+    <header class="gradient-bg text-white">
+        <div class="container mx-auto px-4 py-12">
+            <div class="flex flex-col md:flex-row justify-between items-center">
+                <div class="mb-8 md:mb-0">
+                    <h1 class="text-4xl font-bold mb-2">AI Model Collaboration Cookbook</h1>
+                    <h2 class="text-2xl font-light opacity-90">for Mathematical Research Development</h2>
+                </div>
+                <div class="bg-white/10 backdrop-blur-sm rounded-lg p-6 shadow-lg">
+                    <p class="text-lg mb-2">Multi-AI workflow for:</p>
+                    <ul class="list-disc pl-5 space-y-1">
+                        <li>Idea generation</li>
+                        <li>Error detection</li>
+                        <li>Alternative approaches</li>
+                        <li>Paper formalization</li>
+                    </ul>
+                </div>
+            </div>
+        </div>
+    </header>
+    <!-- Main Content -->
+    <main class="container mx-auto px-4 py-12">
+        <!-- Introduction -->
+        <section class="mb-16">
+            <div class="bg-white rounded-xl shadow-md overflow-hidden mb-8">
+                <div class="p-8">
+                    <h2 class="text-3xl font-bold text-gray-800 mb-4">Sophisticated AI Collaboration</h2>
+                    <p class="text-gray-600 mb-6">
+                        This cookbook provides a practical workflow utilizing multiple AI models in a collaborative process to develop, refine, and formalize mathematical research ideas.
+                        Each AI model plays a distinct role in the research development pipeline.
+                    </p>
+                    <div class="grid grid-cols-1 md:grid-cols-2 lg:grid-cols-4 gap-6">
+                        <div class="model-card gpt-card bg-white rounded-lg shadow p-6">
+                            <div class="flex items-center mb-4">
+                                <div class="w-12 h-12 rounded-full bg-green-100 flex items-center justify-center mr-4">
+                                    <i class="fas fa-brain text-green-600 text-xl"></i>
+                                </div>
+                                <h3 class="text-xl font-semibold text-gray-800">GPT-4</h3>
+                            </div>
+                            <p class="text-gray-600">Generates initial research ideas and responds to feedback</p>
+                        </div>
+                        <div class="model-card gemini-card bg-white rounded-lg shadow p-6">
+                            <div class="flex items-center mb-4">
+                                <div class="w-12 h-12 rounded-full bg-blue-100 flex items-center justify-center mr-4">
+                                    <i class="fas fa-search text-blue-600 text-xl"></i>
+                                </div>
+                                <h3 class="text-xl font-semibold text-gray-800">Gemini</h3>
+                            </div>
+                            <p class="text-gray-600">Identifies errors and conceptual problems in the research</p>
+                        </div>
+                        <div class="model-card grok-card bg-white rounded-lg shadow p-6">
+                            <div class="flex items-center mb-4">
+                                <div class="w-12 h-12 rounded-full bg-gray-100 flex items-center justify-center mr-4">
+                                    <i class="fas fa-lightbulb text-gray-800 text-xl"></i>
+                                </div>
+                                <h3 class="text-xl font-semibold text-gray-800">Grok-3</h3>
+                            </div>
+                            <p class="text-gray-600">Provides fresh perspectives and alternative approaches</p>
+                        </div>
+                        <div class="model-card claude-card bg-white rounded-lg shadow p-6">
+                            <div class="flex items-center mb-4">
+                                <div class="w-12 h-12 rounded-full bg-yellow-100 flex items-center justify-center mr-4">
+                                    <i class="fas fa-file-alt text-yellow-600 text-xl"></i>
+                                </div>
+                                <h3 class="text-xl font-semibold text-gray-800">Claude</h3>
+                            </div>
+                            <p class="text-gray-600">Formalizes the research into academic papers with LaTeX</p>
+                        </div>
+                    </div>
+                </div>
+            </div>
+        </section>
+        <!-- Workflow Visualization -->
+        <section class="mb-16">
+            <div class="bg-white rounded-xl shadow-md overflow-hidden">
+                <div class="p-8">
+                    <h2 class="text-3xl font-bold text-gray-800 mb-6">Iterative Development Flow</h2>
+                    <div class="space-y-8">
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">1</div>
+                            <div class="bg-indigo-50 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-indigo-800 mb-2">Initial Research Ideas (GPT)</h3>
+                                <p class="text-gray-700">Generate potential research directions and preliminary concepts</p>
+                            </div>
+                        </div>
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">2</div>
+                            <div class="bg-blue-50 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-blue-800 mb-2">First Evaluation (Gemini)</h3>
+                                <p class="text-gray-700">Identify errors and provide constructive feedback</p>
+                            </div>
+                        </div>
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">3</div>
+                            <div class="bg-indigo-50 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-indigo-800 mb-2">Refinement (GPT)</h3>
+                                <p class="text-gray-700">Process feedback and revise the research approach</p>
+                            </div>
+                        </div>
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">4</div>
+                            <div class="bg-blue-50 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-blue-800 mb-2">Second Evaluation (Gemini)</h3>
+                                <p class="text-gray-700">Find additional problems and validate improvements</p>
+                            </div>
+                        </div>
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">5</div>
+                            <div class="bg-purple-50 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-purple-800 mb-2">Iterative Convergence</h3>
+                                <p class="text-gray-700">Repeat refinement and evaluation until reaching consensus</p>
+                            </div>
+                        </div>
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">6</div>
+                            <div class="bg-gray-100 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-gray-800 mb-2">Fresh Perspective (Grok-3)</h3>
+                                <p class="text-gray-700">Identify fundamental issues and suggest alternative directions</p>
+                            </div>
+                        </div>
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">7</div>
+                            <div class="bg-yellow-50 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-yellow-800 mb-2">Final Consensus</h3>
+                                <p class="text-gray-700">Synthesize insights from all models into coherent research</p>
+                            </div>
+                        </div>
+                        <div class="workflow-step">
+                            <div class="workflow-step-number gradient-bg text-white">8</div>
+                            <div class="bg-amber-50 rounded-lg p-6">
+                                <h3 class="text-xl font-semibold text-amber-800 mb-2">Academic Formalization (Claude)</h3>
+                                <p class="text-gray-700">Outline and draft comprehensive LaTeX paper</p>
+                            </div>
+                        </div>
+                    </div>
+                </div>
+            </div>
+        </section>
+        <!-- API Details Section -->
+        <section class="mb-16">
+            <h2 class="text-3xl font-bold text-gray-800 mb-8">API Implementation Details</h2>
+            <div class="bg-white rounded-xl shadow-md overflow-hidden">
+                <!-- Tabs -->
+                <div class="border-b border-gray-200">
+                    <nav class="flex -mb-px">
+                        <button onclick="openTab(event, 'gpt-tab')" class="tab-button active py-4 px-6 text-center border-b-2 font-medium text-sm">
+                            <i class="fas fa-brain mr-2"></i>GPT-4
+                        </button>
+                        <button onclick="openTab(event, 'gemini-tab')" class="tab-button py-4 px-6 text-center border-b-2 font-medium text-sm">
+                            <i class="fas fa-search mr-2"></i>Gemini
+                        </button>
+                        <button onclick="openTab(event, 'grok-tab')" class="tab-button py-4 px-6 text-center border-b-2 font-medium text-sm">
+                            <i class="fas fa-lightbulb mr-2"></i>Grok-3
+                        </button>
+                        <button onclick="openTab(event, 'claude-tab')" class="tab-button py-4 px-6 text-center border-b-2 font-medium text-sm">
+                            <i class="fas fa-file-alt mr-2"></i>Claude
+                        </button>
+                    </nav>
+                </div>
+                <!-- Tab Contents -->
+                <div class="p-8">
+                    <!-- GPT Tab -->
+                    <div id="gpt-tab" class="tab-content active">
+                        <h3 class="text-2xl font-semibold text-gray-800 mb-4">GPT-3.5/4 (OpenAI)</h3>
+                        <p class="text-gray-600 mb-6">
+                            GPT models from OpenAI initiate the research process by generating initial ideas and responding to feedback.
+                        </p>
+                        <div class="mb-8">
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample cURL Command</h4>
+                            <div class="code-block p-4 mb-4">
+                                <pre><code>curl https://api.openai.com/v1/chat/completions \
+  -H "Content-Type: application/json" \
+  -H "Authorization: Bearer YOUR_OPENAI_API_KEY" \
+  -d '{
+    "model": "gpt-4",
+    "messages": [
+      {
+        "role": "system",
+        "content": "You are a helpful mathematics research assistant."
+      },
+      {
+        "role": "user",
+        "content": "I'm exploring new approaches to mathematical optimization in topological spaces. Can you suggest 7 potentially novel research directions?"
+      }
+    ],
+    "temperature": 0.7
+  }'</code></pre>
+                            </div>
+                        </div>
+                        <div>
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample Response</h4>
+                            <div class="code-block p-4">
+                                <pre><code>{
+  <span class="json-key">"id"</span>: <span class="json-string">"chatcmpl-123ABC"</span>,
+  <span class="json-key">"object"</span>: <span class="json-string">"chat.completion"</span>,
+  <span class="json-key">"created"</span>: <span class="json-value">1714675020</span>,
+  <span class="json-key">"model"</span>: <span class="json-string">"gpt-4"</span>,
+  <span class="json-key">"choices"</span>: [
+    {
+      <span class="json-key">"index"</span>: <span class="json-value">0</span>,
+      <span class="json-key">"message"</span>: {
+        <span class="json-key">"role"</span>: <span class="json-string">"assistant"</span>,
+        <span class="json-key">"content"</span>: <span class="json-string">"Here are 7 potentially novel research directions for mathematical optimization in topological spaces:\n\n1. Persistent Homology for Optimization Landscapes: Applying persistent homology to characterize the topological structure of non-convex optimization landscapes...\n\n2. Sheaf-Theoretic Approaches to Distributed Optimization: Developing frameworks where optimization variables are sections of sheaves...\n\n[...additional ideas...]"</span>
+      },
+      <span class="json-key">"finish_reason"</span>: <span class="json-string">"stop"</span>
+    }
+  ],
+  <span class="json-key">"usage"</span>: {
+    <span class="json-key">"prompt_tokens"</span>: <span class="json-value">65</span>,
+    <span class="json-key">"completion_tokens"</span>: <span class="json-value">420</span>,
+    <span class="json-key">"total_tokens"</span>: <span class="json-value">485</span>
+  }
+}</code></pre>
+                            </div>
+                        </div>
+                    </div>
+                    <!-- Gemini Tab -->
+                    <div id="gemini-tab" class="tab-content">
+                        <h3 class="text-2xl font-semibold text-gray-800 mb-4">Gemini API (Google)</h3>
+                        <p class="text-gray-600 mb-6">
+                            Gemini serves as a critical evaluation step, identifying errors and problems in the developing research.
+                        </p>
+                        <div class="mb-8">
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample cURL Command</h4>
+                            <div class="code-block p-4 mb-4">
+                                <pre><code>curl -X POST \
+  https://generativelanguage.googleapis.com/v1beta/models/gemini-pro:generateContent \
+  -H "Content-Type: application/json" \
+  -H "Authorization: Bearer YOUR_GEMINI_API_KEY" \
+  -d '{
+    "contents": [
+      {
+        "parts": [
+          {
+            "text": "Review the following mathematical approach for errors and conceptual problems:\n\nTopological Optimization Through Sheaf Cohomology\n\nWe propose a novel optimization framework for non-convex functions on manifolds using sheaf cohomology. The key insight is that optimization trajectories can be represented as sections of sheaves..."
+          }
+        ]
+      }
+    ],
+    "generationConfig": {
+      "temperature": 0.2,
+      "topK": 40,
+      "topP": 0.95,
+      "maxOutputTokens": 8192
+    }
+  }'</code></pre>
+                            </div>
+                        </div>
+                        <div>
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample Response</h4>
+                            <div class="code-block p-4">
+                                <pre><code>{
+  <span class="json-key">"candidates"</span>: [
+    {
+      <span class="json-key">"content"</span>: {
+        <span class="json-key">"parts"</span>: [
+          {
+            <span class="json-key">"text"</span>: <span class="json-string">"I've reviewed your mathematical approach and identified several issues:\n\n1. Conceptual Error: The proposed sheaf cohomology framework assumes that optimization trajectories form global sections, but this isn't generally true for non-convex functions on arbitrary manifolds.\n\n2. Mathematical Inconsistency: Your definition of the obstruction cocycle doesn't account for singularities in the gradient field...\n\n[...additional feedback...]"</span>
+          }
+        ],
+        <span class="json-key">"role"</span>: <span class="json-string">"model"</span>
+      },
+      <span class="json-key">"finishReason"</span>: <span class="json-string">"STOP"</span>,
+      <span class="json-key">"index"</span>: <span class="json-value">0</span>
+    }
+  ],
+  <span class="json-key">"promptFeedback"</span>: {
+    <span class="json-key">"safetyRatings"</span>: [
+      {
+        <span class="json-key">"category"</span>: <span class="json-string">"HARM_CATEGORY_DANGEROUS_CONTENT"</span>,
+        <span class="json-key">"probability"</span>: <span class="json-string">"NEGLIGIBLE"</span>
+      }
+    ]
+  }
+}</code></pre>
+                            </div>
+                        </div>
+                    </div>
+                    <!-- Grok Tab -->
+                    <div id="grok-tab" class="tab-content">
+                        <h3 class="text-2xl font-semibold text-gray-800 mb-4">Grok-3 API (xAI)</h3>
+                        <p class="text-gray-600 mb-6">
+                            Grok-3 provides a fresh perspective on the research, identifying fundamental errors and suggesting alternative approaches.
+                        </p>
+                        <div class="mb-8">
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample cURL Command</h4>
+                            <div class="code-block p-4 mb-4">
+                                <pre><code>curl -X POST \
+  https://api.grok.x/v1/chat/completions \
+  -H "Content-Type: application/json" \
+  -H "Authorization: Bearer YOUR_GROK_API_KEY" \
+  -H "Cookie: x-anonuserid=YOUR_ANON_USER_ID; x-challenge=YOUR_CHALLENGE; x-signature=YOUR_SIGNATURE; sso=YOUR_SSO; sso-rw=YOUR_SSO_RW" \
+  -d '{
+    "messages": [
+      {
+        "role": "system",
+        "content": "You are a critical mathematical researcher who can identify fundamental issues in approaches."
+      },
+      {
+        "role": "user",
+        "content": "Here is a detailed report on a mathematical research approach. Please identify any fundamental errors and suggest alternative directions if needed:\n\nConsensus Approach: Topological Optimization Through Sheaf Cohomology with Persistence Diagram Analysis...[detailed mathematical content]"
+      }
+    ],
+    "model": "grok-3",
+    "temperature": 0.7
+  }'</code></pre>
+                            </div>
+                        </div>
+                        <div>
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample Response</h4>
+                            <div class="code-block p-4">
+                                <pre><code>{
+  <span class="json-key">"id"</span>: <span class="json-string">"chatcmpl-XYZ789"</span>,
+  <span class="json-key">"object"</span>: <span class="json-string">"chat.completion"</span>,
+  <span class="json-key">"created"</span>: <span class="json-value">1714675100</span>,
+  <span class="json-key">"model"</span>: <span class="json-string">"grok-3"</span>,
+  <span class="json-key">"choices"</span>: [
+    {
+      <span class="json-key">"index"</span>: <span class="json-value">0</span>,
+      <span class="json-key">"message"</span>: {
+        <span class="json-key">"role"</span>: <span class="json-string">"assistant"</span>,
+        <span class="json-key">"content"</span>: <span class="json-string">"I've identified a fundamental flaw in your approach that completely undermines the central thesis:\n\nThe primary error lies in the assumption that sheaf cohomology obstructions can be systematically minimized using gradient descent. This overlooks a critical issue: the obstruction classes themselves form a discrete invariant, not a continuous one amenable to gradient-based optimization.\n\nInstead, I suggest pivoting to a completely different direction: consider using discrete Morse theory combined with stratified spaces. This approach would allow you to...\n\n[...detailed alternative approach...]"</span>
+      },
+      <span class="json-key">"finish_reason"</span>: <span class="json-string">"stop"</span>
+    }
+  ]
+}</code></pre>
+                            </div>
+                        </div>
+                    </div>
+                    <!-- Claude Tab -->
+                    <div id="claude-tab" class="tab-content">
+                        <h3 class="text-2xl font-semibold text-gray-800 mb-4">Claude API (Anthropic)</h3>
+                        <p class="text-gray-600 mb-6">
+                            Claude finalizes the process by outlining and drafting a formal academic paper with extensive LaTeX code.
+                        </p>
+                        <div class="mb-8">
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample cURL Command</h4>
+                            <div class="code-block p-4 mb-4">
+                                <pre><code>curl -X POST \
+  https://api.anthropic.com/v1/messages \
+  -H "Content-Type: application/json" \
+  -H "x-api-key: YOUR_CLAUDE_API_KEY" \
+  -H "anthropic-version: 2023-06-01" \
+  -d '{
+    "model": "claude-3-sonnet",
+    "max_tokens": 4000,
+    "messages": [
+      {
+        "role": "user",
+        "content": "Based on the following consensus research report, please outline a formal academic paper following standard mathematics journal conventions. After I approve the outline, I will ask you to generate LaTeX for each section according to my style/notation conventions.\n\nConsensus Report: Discrete Morse Theory Approaches to Non-Convex Optimization on Stratified Spaces...[detailed research content]"
+      }
+    ]
+  }'</code></pre>
+                            </div>
+                        </div>
+                        <div>
+                            <h4 class="text-lg font-medium text-gray-700 mb-3">Sample Response</h4>
+                            <div class="code-block p-4">
+                                <pre><code>{
+  <span class="json-key">"id"</span>: <span class="json-string">"msg_01ABCxyz"</span>,
+  <span class="json-key">"type"</span>: <span class="json-string">"message"</span>,
+  <span class="json-key">"role"</span>: <span class="json-string">"assistant"</span>,
+  <span class="json-key">"content"</span>: [
+    {
+      <span class="json-key">"type"</span>: <span class="json-string">"text"</span>,
+      <span class="json-key">"text"</span>: <span class="json-string">"# Proposed Paper Outline: \"Discrete Morse Theory for Non-Convex Optimization on Stratified Spaces\"\n\n## 1. Introduction\n- Motivation from optimization challenges on manifolds\n- Limitations of current approaches\n- Brief overview of stratified spaces and discrete Morse theory\n- Statement of main contributions\n\n## 2. Preliminaries\n- 2.1 Stratified Spaces\n- 2.2 Discrete Morse Theory\n- 2.3 Optimization on Manifolds\n\n## 3. Discrete Morse Optimization Framework\n- 3.1 Discretization of the Domain\n- 3.2 Morse Function Construction\n- 3.3 Critical Point Analysis\n\n[...additional sections...]\n\n## 7. Conclusion and Future Work\n\nDoes this outline meet your expectations? Once approved, I can proceed with generating LaTeX for each section according to your style conventions."</span>
+    }
+  ],
+  <span class="json-key">"model"</span>: <span class="json-string">"claude-3-sonnet"</span>,
+  <span class="json-key">"stop_reason"</span>: <span class="json-string">"end_turn"</span>
+}</code></pre>
+                            </div>
+                        </div>
+                    </div>
+                </div>
+            </div>
+        </section>
+        <!-- Implementation Notes -->
+        <section class="mb-16">
+            <div class="bg-white rounded-xl shadow-md overflow-hidden">
+                <div class="p-8">
+                    <h2 class="text-3xl font-bold text-gray-800 mb-6">Implementation Notes</h2>
+                    <div class="grid grid-cols-1 md:grid-cols-2 gap-6">
+                        <div class="bg-indigo-50 rounded-lg p-6">
+                            <h3 class="text-xl font-semibold text-indigo-800 mb-3 flex items-center">
+                                <i class="fas fa-key mr-2"></i> Authentication
+                            </h3>
+                            <ul class="list-disc pl-5 space-y-2 text-gray-700">
+                                <li><span class="font-medium">OpenAI:</span> Bearer token authentication</li>
+                                <li><span class="font-medium">Gemini:</span> API key authentication via Bearer token</li>
+                                <li><span class="font-medium">Grok-3:</span> Cookie-based authentication (unofficial API)</li>
+                                <li><span class="font-medium">Claude:</span> API key via x-api-key header</li>
+                            </ul>
+                        </div>
+                        <div class="bg-blue-50 rounded-lg p-6">
+                            <h3 class="text-xl font-semibold text-blue-800 mb-3 flex items-center">
+                                <i class="fas fa-exclamation-triangle mr-2"></i> Error Handling
+                            </h3>
+                            <p class="text-gray-700">
+                                Implement robust error handling for each API call, as reliability may vary across services.
+                                Monitor response status codes and implement retry mechanisms with exponential backoff.
+                            </p>
+                        </div>
+                        <div class="bg-purple-50 rounded-lg p-6">
+                            <h3 class="text-xl font-semibold text-purple-800 mb-3 flex items-center">
+                                <i class="fas fa-tachometer-alt mr-2"></i> Rate Limiting
+                            </h3>
+                            <p class="text-gray-700">
+                                All services implement rate limits. Monitor response headers like <code class="bg-purple-100 px-1 rounded">x-ratelimit-remaining-requests</code>
+                                to avoid exceeding limits and implement appropriate throttling.
+                            </p>
+                        </div>
+                        <div class="bg-green-50 rounded-lg p-6">
+                            <h3 class="text-xl font-semibold text-green-800 mb-3 flex items-center">
+                                <i class="fas fa-code mr-2"></i> Context Management
+                            </h3>
+                            <p class="text-gray-700">
+                                For complex mathematical research, models may need longer context windows.
+                                Select appropriate model versions that support longer contexts and implement context window management strategies.
+                            </p>
+                        </div>
+                    </div>
+                </div>
+            </div>
+        </section>
+        <!-- Conclusion -->
+        <section>
+            <div class="bg-white rounded-xl shadow-md overflow-hidden">
+                <div class="p-8">
+                    <h2 class="text-3xl font-bold text-gray-800 mb-4">Conclusion</h2>
+                    <div class="prose max-w-none text-gray-700">
+                        <p>
+                            This multi-model approach leverages the unique strengths of each AI system to create a robust research development pipeline.
+                            By validating ideas across different models, researchers can identify and address conceptual flaws more effectively than with any single model.
+                            The workflow represents an emerging pattern of AI collaboration that might become standard practice for complex intellectual work.
+                        </p>
+                        <p>
+                            Developers implementing this workflow should monitor the evolution of these APIs, as capabilities and endpoints may change as the underlying models are updated.
+                            The collaborative nature of this approach helps mitigate individual model weaknesses while amplifying their collective strengths.
+                        </p>
+                        <div class="mt-6 p-4 bg-yellow-50 border-l-4 border-yellow-400">
+                            <div class="flex">
+                                <div class="flex-shrink-0">
+                                    <i class="fas fa-lightbulb text-yellow-500"></i>
+                                </div>
+                                <div class="ml-3">
+                                    <p class="text-sm text-yellow-700">
+                                        <strong>Pro Tip:</strong> Consider implementing a caching layer for API responses to reduce costs and improve performance during iterative development.
+                                    </p>
+                                </div>
+                            </div>
+                        </div>
+                    </div>
+                </div>
+            </div>
+        </section>
+    </main>
+    <!-- Footer -->
+    <footer class="gradient-bg text-white py-12">
+        <div class="container mx-auto px-4">
+            <div class="flex flex-col md:flex-row justify-between items-center">
+                <div class="mb-6 md:mb-0">
+                    <h3 class="text-2xl font-bold mb-2">AI Model Collaboration Cookbook</h3>
+                    <p class="opacity-90">For Mathematical Research Development</p>
+                </div>
+                <div class="flex space-x-6">
+                    <a href="#" class="hover:opacity-75 transition-opacity">
+                        <i class="fab fa-github text-2xl"></i>
+                    </a>
+                    <a href="#" class="hover:opacity-75 transition-opacity">
+                        <i class="fab fa-twitter text-2xl"></i>
+                    </a>
+                    <a href="#" class="hover:opacity-75 transition-opacity">
+                        <i class="fab fa-linkedin text-2xl"></i>
+                    </a>
+                </div>
+            </div>
+            <div class="border-t border-white/20 mt-8 pt-8 text-center md:text-left">
+                <p class="text-sm opacity-80">© 2023 AI Research Collaboration Framework. All rights reserved.</p>
+            </div>
+        </div>
+    </footer>
+    <script>
+        function openTab(evt, tabName) {
+            // Hide all tab contents
+            const tabContents = document.getElementsByClassName("tab-content");
+            for (let i = 0; i < tabContents.length; i++) {
+                tabContents[i].classList.remove("active");
+            }
+            // Remove active class from all tab buttons
+            const tabButtons = document.getElementsByClassName("tab-button");
+            for (let i = 0; i < tabButtons.length; i++) {
+                tabButtons[i].classList.remove("active");
+            }
+            // Show the current tab and add active class to the button
+            document.getElementById(tabName).classList.add("active");
+            evt.currentTarget.classList.add("active");
+        }
+    </script>
+<p style="border-radius: 8px; text-align: center; font-size: 12px; color: #fff; margin-top: 16px;position: fixed; left: 8px; bottom: 8px; z-index: 10; background: rgba(0, 0, 0, 0.8); padding: 4px 8px;">Made with <img src="https://enzostvs-deepsite.hf.space/logo.svg" alt="DeepSite Logo" style="width: 16px; height: 16px; vertical-align: middle;display:inline-block;margin-right:3px;filter:brightness(0) invert(1);"><a href="https://enzostvs-deepsite.hf.space" style="color: #fff;text-decoration: underline;" target="_blank" >DeepSite</a> - 🧬 <a href="https://enzostvs-deepsite.hf.space?remix=LukasBe/ai-model-collaboration-cookbook" style="color: #fff;text-decoration: underline;" target="_blank" >Remix</a></p></body>
+</html>

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	@@ -0,0 +1 @@

+ Implement the following workflow in great looking practical UI: # AI Model Collaboration Cookbook for Math Research Development A sophisticated workflow utilizing multiple AI models in a collaborative process to develop, refine, and formalize a mathematical research idea. This cookbook provides developers with practical API call examples for each AI service mentioned in the workflow. ## GPT-3.5/4 (OpenAI) GPT models from OpenAI initiate the research process by generating initial ideas and responding to feedback. ### Sample cURL Command ```bash curl https://api.openai.com/v1/chat/completions \ -H "Content-Type: application/json" \ -H "Authorization: Bearer YOUR_OPENAI_API_KEY" \ -d '{ "model": "gpt-4o", "messages": [ { "role": "system", "content": "You are a helpful mathematics research assistant." }, { "role": "user", "content": "I'm exploring new approaches to mathematical optimization in topological spaces. Can you suggest 7 potentially novel research directions?" } ], "temperature": 0.7 }' ``` ### Sample Response ```json { "id": "chatcmpl-123ABC", "object": "chat.completion", "created": 1714675020, "model": "gpt-4o", "choices": [ { "index": 0, "message": { "role": "assistant", "content": "Here are 7 potentially novel research directions for mathematical optimization in topological spaces:\n\n1. Persistent Homology for Optimization Landscapes: Applying persistent homology to characterize the topological structure of non-convex optimization landscapes...\n\n2. Sheaf-Theoretic Approaches to Distributed Optimization: Developing frameworks where optimization variables are sections of sheaves...\n\n[...additional ideas...]" }, "finish_reason": "stop" } ], "usage": { "prompt_tokens": 65, "completion_tokens": 420, "total_tokens": 485 } } ``` ## Gemini API (Google) Gemini serves as a critical evaluation step, identifying errors and problems in the developing research. ### Sample cURL Command ```bash curl -X POST \ https://generativelanguage.googleapis.com/v1beta/models/gemini-pro:generateContent \ -H "Content-Type: application/json" \ -H "Authorization: Bearer YOUR_GEMINI_API_KEY" \ -d '{ "contents": [ { "parts": [ { "text": "Review the following mathematical approach for errors and conceptual problems:\n\nTopological Optimization Through Sheaf Cohomology\n\nWe propose a novel optimization framework for non-convex functions on manifolds using sheaf cohomology. The key insight is that optimization trajectories can be represented as sections of sheaves..." } ] } ], "generationConfig": { "temperature": 0.2, "topK": 40, "topP": 0.95, "maxOutputTokens": 8192 } }' ``` ### Sample Response ```json { "candidates": [ { "content": { "parts": [ { "text": "I've reviewed your mathematical approach and identified several issues:\n\n1. Conceptual Error: The proposed sheaf cohomology framework assumes that optimization trajectories form global sections, but this isn't generally true for non-convex functions on arbitrary manifolds.\n\n2. Mathematical Inconsistency: Your definition of the obstruction cocycle doesn't account for singularities in the gradient field...\n\n[...additional feedback...]" } ], "role": "model" }, "finishReason": "STOP", "index": 0 } ], "promptFeedback": { "safetyRatings": [ { "category": "HARM_CATEGORY_DANGEROUS_CONTENT", "probability": "NEGLIGIBLE" } ] } } ``` ## Grok-3 API (xAI) Grok-3 provides a fresh perspective on the research, identifying fundamental errors and suggesting alternative approaches. ### Sample cURL Command ```bash curl -X POST \ https://api.grok.x/v1/chat/completions \ -H "Content-Type: application/json" \ -H "Authorization: Bearer YOUR_GROK_API_KEY" \ -H "Cookie: x-anonuserid=YOUR_ANON_USER_ID; x-challenge=YOUR_CHALLENGE; x-signature=YOUR_SIGNATURE; sso=YOUR_SSO; sso-rw=YOUR_SSO_RW" \ -d '{ "messages": [ { "role": "system", "content": "You are a critical mathematical researcher who can identify fundamental issues in approaches." }, { "role": "user", "content": "Here is a detailed report on a mathematical research approach. Please identify any fundamental errors and suggest alternative directions if needed:\n\nConsensus Approach: Topological Optimization Through Sheaf Cohomology with Persistence Diagram Analysis...[detailed mathematical content]" } ], "model": "grok-3", "temperature": 0.7 }' ``` ### Sample Response ```json { "id": "chatcmpl-XYZ789", "object": "chat.completion", "created": 1714675100, "model": "grok-3", "choices": [ { "index": 0, "message": { "role": "assistant", "content": "I've identified a fundamental flaw in your approach that completely undermines the central thesis:\n\nThe primary error lies in the assumption that sheaf cohomology obstructions can be systematically minimized using gradient descent. This overlooks a critical issue: the obstruction classes themselves form a discrete invariant, not a continuous one amenable to gradient-based optimization.\n\nInstead, I suggest pivoting to a completely different direction: consider using discrete Morse theory combined with stratified spaces. This approach would allow you to...\n\n[...detailed alternative approach...]" }, "finish_reason": "stop" } ] } ``` ## Claude API (Anthropic) Claude finalizes the process by outlining and drafting a formal academic paper with extensive LaTeX code. ### Sample cURL Command ```bash curl -X POST \ https://api.anthropic.com/v1/messages \ -H "Content-Type: application/json" \ -H "x-api-key: YOUR_CLAUDE_API_KEY" \ -H "anthropic-version: 2023-06-01" \ -d '{ "model": "claude-3-7-sonnet", "max_tokens": 4000, "messages": [ { "role": "user", "content": "Based on the following consensus research report, please outline a formal academic paper following standard mathematics journal conventions. After I approve the outline, I will ask you to generate LaTeX for each section according to my style/notation conventions.\n\nConsensus Report: Discrete Morse Theory Approaches to Non-Convex Optimization on Stratified Spaces...[detailed research content]" } ] }' ``` ### Sample Response ```json { "id": "msg_01ABCxyz", "type": "message", "role": "assistant", "content": [ { "type": "text", "text": "# Proposed Paper Outline: \"Discrete Morse Theory for Non-Convex Optimization on Stratified Spaces\"\n\n## 1. Introduction\n- Motivation from optimization challenges on manifolds\n- Limitations of current approaches\n- Brief overview of stratified spaces and discrete Morse theory\n- Statement of main contributions\n\n## 2. Preliminaries\n- 2.1 Stratified Spaces\n- 2.2 Discrete Morse Theory\n- 2.3 Optimization on Manifolds\n\n## 3. Discrete Morse Optimization Framework\n- 3.1 Discretization of the Domain\n- 3.2 Morse Function Construction\n- 3.3 Critical Point Analysis\n\n[...additional sections...]\n\n## 7. Conclusion and Future Work\n\nDoes this outline meet your expectations? Once approved, I can proceed with generating LaTeX for each section according to your style conventions." } ], "model": "claude-3-7-sonnet", "stop_reason": "end_turn" } ``` ## Iterative Development Flow The complete workflow involves iterative refinement across these models: 1. **Initial Research Ideas (GPT)**: Generate potential research directions 2. **First Evaluation (Gemini)**: Identify errors and provide feedback 3. **Refinement (GPT)**: Process feedback and revise approach 4. **Second Evaluation (Gemini)**: Find additional problems 5. **Iterative Convergence**: Repeat steps 3-4 until reaching consensus 6. **Fresh Perspective (Grok-3)**: Identify fundamental issues and redirect if needed 7. **Final Consensus**: Synthesize insights from all models 8. **Academic Formalization (Claude)**: Outline and draft comprehensive LaTeX paper ## Implementation Notes 1. **Authentication**: Each service requires different authentication methods: - OpenAI: Bearer token authentication[^7][^8] - Gemini: API key authentication via Bearer token[^4] - Grok-3: Cookie-based authentication (unofficial API)[^5] - Claude: API key via x-api-key header 2. **Error Handling**: Implement robust error handling for each API call, as reliability may vary across services. 3. **Rate Limiting**: All services implement rate limits. Monitor the response headers like `x-ratelimit-remaining-requests` to avoid exceeding limits[^8]. 4. **Context Management**: For complex mathematical research, models may need longer context windows. Select appropriate model versions that support longer contexts. 5. **Response Processing**: Parse and extract key insights from each model response to feed into the next stage of the workflow. ## Conclusion This multi-model approach leverages the unique strengths of each AI system to create a robust research development pipeline. By validating ideas across different models, researchers can identify and address conceptual flaws more effectively than with any single model. The workflow represents an emerging pattern of AI collaboration that might become standard practice for complex intellectual work. Developers implementing this workflow should monitor the evolution of these APIs, as capabilities and endpoints may change as the underlying models are updated.