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```typescript
// AI Dev Tool: ArXiv API Integration Wrapper
// ============================================
// A production-ready API integration wrapper for ArXiv API
// with rate limiting and error handling.

import axios, { AxiosError } from 'axios';
import { z } from 'zod';

// Define the ArXiv API schema
const arxivSchema = z.object({
  title: z.string(),
  authors: z.array(z.string()),
  abstract: z.string(),
  doi: z.string().optional(),
});

// Define the ArXiv API integration wrapper class
class ArXivAPI {
  private apiKey: string;
  private axiosInstance: axios.AxiosInstance;

/**
   * Initialize the ArXiv API integration wrapper
   * @param apiKey - The ArXiv API key
   */
  constructor(apiKey: string) {
    this.apiKey = apiKey;
    this.axiosInstance = axios.create({
      baseURL: 'https://api.arxiv.org/',
      headers: {
        'Content-Type': 'application/json',
        'Authorization': `Bearer ${apiKey}`,
      },
    });
  }

/**
   * Fetch a paper by its ID
   * @param paperId - The ID of the paper to fetch

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