docs(site): surface arXiv paper across hero and footer

- Hero gains a third 'Read the paper' CTA with arXiv chip
- Footer Protocol column gets an arXiv link
- Footer version string corrected v0.2 -> v0.3.1

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

Author: WaylandYang

docs/site/src/components/HeroSection.vue

@@ -39,6 +39,17 @@
         <a href="https://github.com/device-context-protocol" class="btn btn-secondary">
           View on GitHub
         </a>
+        <a
+          href="https://arxiv.org/abs/2605.26159"
+          class="btn btn-secondary"
+          target="_blank"
+          rel="noopener"
+        >
+          Read the paper
+          <span class="ml-1 px-1.5 py-0.5 rounded text-[10.5px] font-mono font-semibold bg-[#b31b1b] text-white align-middle">
+            arXiv
+          </span>
+        </a>
       </div>
     </div>
   </header>

docs/site/src/components/SiteFooter.vue

@@ -7,6 +7,7 @@ const cols = [
       { label: 'Architecture',  href: '#architecture' },
       { label: 'Comparison',    href: '#compare' },
       { label: 'Rationale',     href: 'https://github.com/device-context-protocol/dcp/blob/main/docs/RATIONALE.md' },
+      { label: 'Paper (arXiv:2605.26159)', href: 'https://arxiv.org/abs/2605.26159' },
     ],
   },
   {
@@ -63,7 +64,7 @@ const cols = [
 
       <div class="pt-7 border-t border-slate-800 flex flex-wrap justify-between items-center gap-4 text-slate-500 text-[13px]">
         <span>© 2026 DCP authors · MIT licensed · Not affiliated with Anthropic, Inc.</span>
-        <span class="font-mono text-[11px]">v0.2 · spec draft</span>
+        <span class="font-mono text-[11px]">v0.3.1 · spec draft</span>
       </div>
     </div>
   </footer>