some progress

app/Http/Controllers/SitemapController.php

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+<?php
+
+namespace App\Http\Controllers;
+
+use App\Models\Book;
+use Illuminate\Http\Response;
+use Illuminate\Support\Facades\URL;
+
+class SitemapController extends Controller
+{
+    /**
+     * Generate the XML sitemap.
+     */
+    public function index(): Response
+    {
+        $urls = [];
+
+        // Static and index pages
+        $urls[] = [URL::to('/'), now()];
+        $urls[] = [URL::to('/about'), null];
+        $urls[] = [URL::to('/privacy'), null];
+        $urls[] = [URL::to('/terms'), null];
+        $urls[] = [URL::to('/contact'), null];
+        $urls[] = [URL::to('/books'), now()];
+        $urls[] = [URL::to('/categories'), now()];
+
+        // Individual book pages
+        Book::select(['slug', 'updated_at'])->orderBy('updated_at', 'desc')->chunk(500, function ($books) use (&$urls) {
+            foreach ($books as $book) {
+                $urls[] = [URL::to('/books/' . $book->slug), optional($book->updated_at)];
+            }
+        });
+
+        $xml = $this->buildXml($urls);
+
+        return response($xml, 200)->header('Content-Type', 'application/xml');
+    }
+
+    /**
+     * Build a basic XML sitemap string.
+     *
+     * @param array<int, array{0:string,1:\DateTimeInterface|null}> $urls
+     */
+    protected function buildXml(array $urls): string
+    {
+        $xmlHeader = '<?xml version="1.0" encoding="UTF-8"?>';
+        $urlsetOpen = '<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">';
+        $urlsetClose = '</urlset>';
+
+        $body = '';
+        foreach ($urls as [$loc, $lastmod]) {
+            $body .= "\n  <url>\n";
+            $body .= '    <loc>' . e($loc) . "</loc>\n";
+            if ($lastmod) {
+                $body .= '    <lastmod>' . $lastmod->format('c') . "</lastmod>\n";
+            }
+            $body .= "  </url>";
+        }
+
+        return $xmlHeader . "\n" . $urlsetOpen . $body . "\n" . $urlsetClose . "\n";
+    }
+}