diff --git a/src/render-html.ts b/src/render-html.ts
index 067f6e97..e2f7bcfb 100644
--- a/src/render-html.ts
+++ b/src/render-html.ts
@@ -30,11 +30,51 @@ export interface RenderOptions {
 }
 
 export function renderHtml(ast: Document, opts: RenderOptions = {}): string {
-  const blocks = ast.children
-    .filter((n) => n.type !== 'abbreviation-def')
-    .map((n) => renderBlock(n, opts, 0))
-    .filter((s) => s !== '')
-  return blocks.join('\n')
+  const out: string[] = []
+  // Section-wrapping pass (grammar PART 9 §13): every top-level heading
+  // opens a <section id="{slug}"> that holds the heading and the content
+  // up to the next same-or-shallower heading. The id lives on the
+  // <section>, not on the <h*>. Sections nest by heading level.
+  const sectionStack: number[] = [] // open section heading-levels, outer→inner
+
+  const closeTo = (level: number): void => {
+    while (sectionStack.length && sectionStack[sectionStack.length - 1]! >= level) {
+      sectionStack.pop()
+      out.push(`${indent(sectionStack.length)}</section>`)
+    }
+  }
+
+  for (const node of ast.children) {
+    if (node.type === 'abbreviation-def') continue
+    if (node.type === 'heading') {
+      closeTo(node.level)
+      const depth = sectionStack.length
+      // The id moves to <section>; any other heading attrs (classes,
+      // key-values) stay on the <h*>.
+      const id = node.attrs?.id
+      const sectionId = id ? ` id="${escapeAttr(id)}"` : ''
+      out.push(`${indent(depth)}<section${sectionId}>`)
+      sectionStack.push(node.level)
+      const headingAttrs = stripId(node.attrs)
+      const inner = renderInlines(node.children, opts)
+      out.push(
+        `${indent(depth + 1)}<h${node.level}${renderAttrs(headingAttrs)}>${inner}</h${node.level}>`,
+      )
+      continue
+    }
+    const rendered = renderBlock(node, opts, sectionStack.length)
+    if (rendered !== '') out.push(rendered)
+  }
+  closeTo(1) // close any sections still open at end of document
+  return out.join('\n')
+}
+
+/** Copy attrs without the `id` (the id moves to the enclosing <section>). */
+function stripId(attrs?: Attrs): Attrs | undefined {
+  if (!attrs) return undefined
+  if (attrs.id === undefined) return attrs
+  const { id: _omit, ...rest } = attrs
+  return rest
 }
 
 function indent(level: number): string {
diff --git a/test/corpus.test.ts b/test/corpus.test.ts
index 34885bbd..008ce78d 100644
--- a/test/corpus.test.ts
+++ b/test/corpus.test.ts
@@ -77,11 +77,23 @@ const IMPLEMENTED = new Set([
 ])
 
 /**
- * Sub-examples in IMPLEMENTED categories that are known to fail because
- * a specific construct is not yet supported. Move out of this set as
- * implementation lands.
+ * Sub-examples in IMPLEMENTED categories that are temporarily skipped.
+ *
+ * These heading fixtures still show the pre-§13 bare `<h* id="…">` shape.
+ * The renderer now emits the `<section id="…"><h*>…</h*></section>`
+ * wrapping (grammar PART 9 §13), so the impl is AHEAD of the vendored
+ * spec corpus. Re-add each entry once the carve repo re-vendors carve-lib
+ * and rewrites these fixtures to the section-wrapped shape, then bumps the
+ * spec submodule here. Same coordination pattern as the ASCII-slug change.
  */
-const KNOWN_GAPS = new Set<string>([])
+const KNOWN_GAPS = new Set<string>([
+  '02-headings',
+  '02-headings-2',
+  '02-headings-3',
+  '02-headings-4',
+  '17-attributes',
+  '19-heading-ids',
+])
 
 const baseSlug = (name: string) => name.replace(/-\d+$/, '')
 
diff --git a/test/heading-ids.test.ts b/test/heading-ids.test.ts
index c2d554e2..6e8c3d8d 100644
--- a/test/heading-ids.test.ts
+++ b/test/heading-ids.test.ts
@@ -107,7 +107,9 @@ describe('resolveHeadingIds', () => {
   })
   it('resolves </#id> to a link with cloned target text', () => {
     const html = carveToHtml('# Getting Started\n\nSee </#getting-started>.')
-    expect(html).toContain('<h1 id="getting-started">Getting Started</h1>')
+    // The id lives on the <section>, not the <h1> (PART 9 §13).
+    expect(html).toContain('<section id="getting-started">')
+    expect(html).toContain('<h1>Getting Started</h1>')
     expect(html).toContain('<a href="#getting-started">Getting Started</a>')
   })
   it('renders an unresolved </#id> as literal text', () => {
diff --git a/test/implicit-heading-refs.test.ts b/test/implicit-heading-refs.test.ts
index 30acd69c..8be3fb4a 100644
--- a/test/implicit-heading-refs.test.ts
+++ b/test/implicit-heading-refs.test.ts
@@ -179,8 +179,11 @@ describe('implicit heading references ([Heading][])', () => {
     // resolves to first-occurrence -> heading 1 (`#api`). The link inside
     // heading 1 self-resolves to "#api". Matches carve-php.
     const html = h('# [API][]\n\n# API\n\n[API][]')
-    expect(html).toContain('<h1 id="api"><a href="#api">API</a></h1>')
-    expect(html).toContain('<h1 id="api-2">API</h1>')
+    // ids live on <section>, headings carry no id (PART 9 §13).
+    expect(html).toContain('<section id="api">')
+    expect(html).toContain('<h1><a href="#api">API</a></h1>')
+    expect(html).toContain('<section id="api-2">')
+    expect(html).toContain('<h1>API</h1>')
     expect(html).toContain('<p><a href="#api">API</a></p>')
   })
 })
diff --git a/test/section-wrapper.test.ts b/test/section-wrapper.test.ts
new file mode 100644
index 00000000..22d77e78
--- /dev/null
+++ b/test/section-wrapper.test.ts
@@ -0,0 +1,101 @@
+import { describe, it, expect } from 'vitest'
+import { carveToHtml } from '../src/index.js'
+
+const h = (s: string) => carveToHtml(s)
+
+/**
+ * Heading section wrapping (grammar PART 9 §13): every top-level heading
+ * emits <section id="{slug}"> around itself and the content up to the
+ * next same-or-shallower heading. The id lives on the <section>, not the
+ * <h*>. Sections nest by heading level. Matches djot.
+ */
+describe('heading <section> wrapping', () => {
+  it('wraps a single heading and its body', () => {
+    expect(h('# Intro\n\nText.')).toBe(
+      '<section id="intro">\n  <h1>Intro</h1>\n  <p>Text.</p>\n</section>',
+    )
+  })
+
+  it('nests a deeper heading inside the shallower section', () => {
+    expect(h('# A\n\n## B')).toBe(
+      '<section id="a">\n  <h1>A</h1>\n  <section id="b">\n    <h2>B</h2>\n  </section>\n</section>',
+    )
+  })
+
+  it('produces sibling sections for same-level headings', () => {
+    expect(h('# A\n\n# B')).toBe(
+      '<section id="a">\n  <h1>A</h1>\n</section>\n<section id="b">\n  <h1>B</h1>\n</section>',
+    )
+  })
+
+  it('closes a deeper section when a shallower heading follows', () => {
+    const html = h('# A\n\n## B\n\n# C')
+    expect(html).toBe(
+      [
+        '<section id="a">',
+        '  <h1>A</h1>',
+        '  <section id="b">',
+        '    <h2>B</h2>',
+        '  </section>',
+        '</section>',
+        '<section id="c">',
+        '  <h1>C</h1>',
+        '</section>',
+      ].join('\n'),
+    )
+  })
+
+  it('nests by level number across a skipped level', () => {
+    expect(h('# H1\n\n### H3')).toBe(
+      '<section id="h1">\n  <h1>H1</h1>\n  <section id="h3">\n    <h3>H3</h3>\n  </section>\n</section>',
+    )
+  })
+
+  it('puts an explicit {#id} on the section, other attrs on the heading', () => {
+    expect(h('# Title {.large #intro}\n\nP.')).toBe(
+      '<section id="intro">\n  <h1 class="large">Title</h1>\n  <p>P.</p>\n</section>',
+    )
+  })
+
+  it('emits no <section> for a document without headings', () => {
+    expect(h('Just a paragraph.')).toBe('<p>Just a paragraph.</p>')
+  })
+
+  it('emits no <section> for an empty document', () => {
+    expect(h('')).toBe('')
+  })
+
+  it('closes all open sections at end of document', () => {
+    const html = h('# A\n\n## B\n\n### C')
+    // Three nested opens; closes are innermost-first and indented to
+    // each section's own depth.
+    expect(html).toBe(
+      [
+        '<section id="a">',
+        '  <h1>A</h1>',
+        '  <section id="b">',
+        '    <h2>B</h2>',
+        '    <section id="c">',
+        '      <h3>C</h3>',
+        '    </section>',
+        '  </section>',
+        '</section>',
+      ].join('\n'),
+    )
+  })
+
+  it('keeps the fragment target resolvable via crossref', () => {
+    const html = h('# Getting Started\n\nSee </#getting-started>.')
+    expect(html).toContain('<section id="getting-started">')
+    expect(html).toContain('<h1>Getting Started</h1>')
+    expect(html).toContain('<a href="#getting-started">Getting Started</a>')
+  })
+
+  it('does not wrap a heading nested inside a blockquote', () => {
+    // resolveHeadingIds only assigns ids to top-level headings, so nested
+    // headings carry no id and stay bare <h*> with no <section>.
+    const html = h('> # Sub\n')
+    expect(html).not.toContain('<section')
+    expect(html).toContain('<h1>Sub</h1>')
+  })
+})