feat: add cross-validated-search example for hallucination-free responses

This example demonstrates how to use cross-validated-search with Ollama
to prevent hallucinations by verifying facts against multiple sources.

Features:
- Confidence scoring (Verified/Likely True/Uncertain/Likely False)
- Cross-validation across multiple search engines
- No API key required - completely free
- Seamless integration with Ollama's chat API

The example shows how to:
1. Perform cross-validated web searches
2. Format results with confidence indicators
3. Pass verified context to LLM for accurate responses

examples/cross-validated-search.py

@@ -0,0 +1,141 @@
+# /// script
+# requires-python = ">=3.11"
+# dependencies = [
+#     "cross-validated-search",
+#     "ollama",
+#     "rich",
+# ]
+# ///
+"""
+Cross-Validated Search Example for Ollama
+
+This example demonstrates how to use cross-validated-search to prevent
+hallucinations in LLM responses by verifying facts against multiple sources.
+
+cross-validated-search provides:
+- Confidence scoring (Verified/Likely True/Uncertain/Likely False)
+- Cross-validation across multiple search engines
+- No API key required - completely free
+
+Install: pip install cross-validated-search
+"""
+
+from rich import print
+from rich.table import Table
+from rich.panel import Panel
+
+from ollama import chat
+from cross_validated_search import CrossValidatedSearcher
+
+
+def search_with_confidence(query: str) -> dict:
+  """
+  Perform a cross-validated web search and return results with confidence scores.
+  """
+  searcher = CrossValidatedSearcher()
+  results = searcher.search(query, search_type='text', max_results=5)
+
+  return {
+    'query': query,
+    'answer': results.answer,
+    'confidence': results.confidence,
+    'sources': [
+      {
+        'engine': r.engine,
+        'title': r.title,
+        'url': r.url,
+        'snippet': r.snippet[:100] + '...' if len(r.snippet) > 100 else r.snippet,
+      }
+      for r in results.sources
+    ],
+  }
+
+
+def format_context_for_llm(search_results: dict) -> str:
+  """
+  Format search results as context for the LLM.
+  """
+  context_parts = [f"Query: {search_results['query']}"]
+
+  # Add confidence indicator
+  confidence_emoji = {
+    'verified': '✅',
+    'likely_true': '🟢',
+    'uncertain': '🟡',
+    'likely_false': '🔴',
+  }
+  emoji = confidence_emoji.get(search_results['confidence'], '❓')
+  context_parts.append(f"Confidence: {emoji} {search_results['confidence']}")
+
+  # Add sources
+  context_parts.append("\nSources:")
+  for i, source in enumerate(search_results['sources'][:3], 1):
+    context_parts.append(f"{i}. [{source['engine']}] {source['title']}")
+    context_parts.append(f"   {source['url']}")
+
+  # Add answer summary
+  if search_results['answer']:
+    context_parts.append(f"\nSummary: {search_results['answer']}")
+
+  return '\n'.join(context_parts)
+
+
+def main():
+  print(Panel.fit(
+    "[bold blue]Cross-Validated Search + Ollama[/bold blue]\n"
+    "Prevent hallucinations with confidence-scored search results",
+    title="🥚 cross-validated-search",
+  ))
+
+  # Example queries to test
+  queries = [
+    "What is the latest version of Python?",
+    "When was the first iPhone released?",
+    "What is the population of Tokyo?",
+  ]
+
+  for query in queries:
+    print(f"\n[bold cyan]Searching:[/bold cyan] {query}")
+
+    # Step 1: Perform cross-validated search
+    search_results = search_with_confidence(query)
+
+    # Step 2: Display search results with confidence
+    table = Table(title=f"Results for: {query}")
+    table.add_column("Engine", style="cyan")
+    table.add_column("Title", style="green")
+    table.add_column("Confidence", style="bold")
+
+    for source in search_results['sources'][:3]:
+      table.add_row(source['engine'], source['title'][:40], search_results['confidence'])
+
+    print(table)
+
+    # Step 3: Format context for LLM
+    context = format_context_for_llm(search_results)
+
+    # Step 4: Query LLM with verified context
+    print(f"\n[bold yellow]Asking LLM with verified context...[/bold yellow]")
+
+    response = chat(
+      model='llama3.2',
+      messages=[
+        {
+          'role': 'system',
+          'content': 'You are a helpful assistant. Always cite your sources and indicate confidence levels when answering factual questions. If the confidence is low, acknowledge uncertainty.',
+        },
+        {
+          'role': 'user',
+          'content': f"Based on these verified search results, please answer:\n\n{context}\n\nPlease provide a concise answer and cite the sources.",
+        },
+      ],
+    )
+
+    print(f"\n[bold green]LLM Response:[/bold green]")
+    print(response.message.content)
+
+    print("\n" + "=" * 60)
+
+
+if __name__ == '__main__':
+  main()