diff --git a/layouts/_default/_markup/render-heading.html b/layouts/_default/_markup/render-heading.html
new file mode 100644
index 0000000..4b2ed19
--- /dev/null
+++ b/layouts/_default/_markup/render-heading.html
@@ -0,0 +1,9 @@
+{{- /*
+  Heading render hook.
+  Emits <hN id="…">…<a href="#…" class="anchor" aria-label="…">¶</a></hN>.
+*/ -}}
+{{- $label := i18n "AnchorLabel" | default "Anchor" -}}
+<h{{ .Level }} id="{{ .Anchor | safeURL }}">
+  {{- .Text | safeHTML -}}
+  <a href="#{{ .Anchor | safeURL }}" class="anchor" aria-label="{{ $label }}">&para;</a>
+</h{{ .Level }}>
diff --git a/layouts/_default/_markup/render-image.html b/layouts/_default/_markup/render-image.html
new file mode 100644
index 0000000..5de3bfb
--- /dev/null
+++ b/layouts/_default/_markup/render-image.html
@@ -0,0 +1,44 @@
+{{- /*
+  Image render hook.
+  Emits <img> with loading="lazy" decoding="async". When the source resolves
+  to a Page Resource, derives a responsive srcset via images.Process/Resize
+  and sets intrinsic width/height to reduce CLS.
+*/ -}}
+{{- $src := .Destination -}}
+{{- $alt := .Text -}}
+{{- $title := .Title -}}
+{{- $isExternal := or (strings.HasPrefix $src "http:") (strings.HasPrefix $src "https:") (strings.HasPrefix $src "//") -}}
+{{- $resource := false -}}
+{{- if and (not $isExternal) .Page -}}
+  {{- with .Page.Resources.GetMatch $src -}}
+    {{- if eq .ResourceType "image" -}}
+      {{- $resource = . -}}
+    {{- end -}}
+  {{- end -}}
+{{- end -}}
+{{- if $resource -}}
+  {{- $orig := $resource -}}
+  {{- $w := $orig.Width -}}
+  {{- $h := $orig.Height -}}
+  {{- $widths := slice 480 768 1200 1600 -}}
+  {{- $srcset := slice -}}
+  {{- range $widths -}}
+    {{- if le . $w -}}
+      {{- $img := $orig.Resize (printf "%dx" .) -}}
+      {{- $srcset = $srcset | append (printf "%s %dw" $img.RelPermalink .) -}}
+    {{- end -}}
+  {{- end -}}
+  {{- $srcset = $srcset | append (printf "%s %dw" $orig.RelPermalink $w) -}}
+  <img src="{{ $orig.RelPermalink }}"
+    {{- with $alt }} alt="{{ . }}"{{ end }}
+    {{- with $title }} title="{{ . }}"{{ end }}
+    width="{{ $w }}" height="{{ $h }}"
+    srcset="{{ delimit $srcset ", " }}"
+    sizes="(max-width: 768px) 100vw, 768px"
+    loading="lazy" decoding="async">
+{{- else -}}
+  <img src="{{ $src | safeURL }}"
+    {{- with $alt }} alt="{{ . }}"{{ end }}
+    {{- with $title }} title="{{ . }}"{{ end }}
+    loading="lazy" decoding="async">
+{{- end -}}
diff --git a/layouts/_default/_markup/render-inline.html b/layouts/_default/_markup/render-inline.html
index bf904a2..98c6f6e 100644
--- a/layouts/_default/_markup/render-inline.html
+++ b/layouts/_default/_markup/render-inline.html
@@ -1,8 +1,7 @@
+{{- /*
+  Inline render hook.
+  Trust assumption: inline content is authored markdown (LaTeX math source);
+  safeHTML preserves $...$ delimiters for client-side KaTeX processing.
+*/ -}}
 {{- $text := .Text | strings.TrimSpace -}}
-{{- if and (hasPrefix $text "$") (hasSuffix $text "$") (not (hasPrefix $text "$$")) -}}
-  {{/* Inline math - output directly without wrapping */}}
-  {{ $text | safeHTML }}
-{{- else -}}
-  {{/* Regular inline text */}}
-  {{ $text | safeHTML }}
-{{- end -}}
+{{ $text | safeHTML }}
diff --git a/layouts/_default/_markup/render-link.html b/layouts/_default/_markup/render-link.html
index d09802f..39b3abc 100644
--- a/layouts/_default/_markup/render-link.html
+++ b/layouts/_default/_markup/render-link.html
@@ -1,15 +1,16 @@
+{{- /*
+  Link render hook.
+  Hugo's render-link context provides resolved URLs; no manual BaseURL prepend needed.
+*/ -}}
 {{- $url := .Destination -}}
 {{- $isExternal := or (strings.HasPrefix $url "http:") (strings.HasPrefix $url "https:") -}}
-{{- $fullUrl := $url -}}
-{{- if and (not $isExternal) (strings.HasPrefix $url "/") -}}
-  {{- $fullUrl = printf "%s%s" (.Page.Site.BaseURL | strings.TrimSuffix "/") $url -}}
-{{- end -}}
-
-<a href="{{ $fullUrl | safeURL }}"
+{{- $isInternalAbsolute := and (not $isExternal) (strings.HasPrefix $url "/") -}}
+<a href="{{ $url | safeURL }}"
   {{- with .Title }} title="{{ . }}"{{ end -}}
   {{- if $isExternal }} rel="external" target="_blank"{{ end -}}
-  {{- if and (not $isExternal) (strings.HasPrefix $url "/") }} data-internal-link="{{ $url }}" class="internal-link"{{ end -}}
->
-  {{- with .Text }}{{ . }}{{ end -}}
-</a>
-{{- /* chomp trailing newline */ -}}
+  {{- if $isInternalAbsolute }} data-internal-link="{{ $url }}" class="internal-link"{{ end -}}
+>{{- with .Text }}{{ . | safeHTML }}{{ end -}}</a>
+{{- /*
+  Note: .Text is rendered inline content (may contain emphasis tags etc.);
+  safeHTML preserves those tags.
+*/ -}}
diff --git a/layouts/_default/_markup/render-paragraph.html b/layouts/_default/_markup/render-paragraph.html
index 95d8e0e..fda6721 100644
--- a/layouts/_default/_markup/render-paragraph.html
+++ b/layouts/_default/_markup/render-paragraph.html
@@ -1,11 +1,14 @@
-{{- $content := .Inner | strings.TrimSpace -}}
+{{- /*
+  Paragraph render hook.
+  Trust assumption: math branches emit raw markdown ($$...$$ / $...$) so
+  client-side KaTeX can process it; safeHTML is intentional there.
+  Default branch lets Hugo's auto-escaping handle authored content.
+*/ -}}
+{{- $content := .Text | strings.TrimSpace -}}
 {{- if and (hasPrefix $content "$$") (hasSuffix $content "$$") -}}
-  {{/* Block math - output directly without <p> wrapper */}}
   {{ $content | safeHTML }}
 {{- else if and (hasPrefix $content "$") (hasSuffix $content "$") (not (strings.Contains $content "\n")) (not (strings.Contains $content " ")) -}}
-  {{/* Single inline math expression - output directly without <p> wrapper */}}
   {{ $content | safeHTML }}
 {{- else -}}
-  {{/* All other content including paragraphs with inline math - wrap in <p> and let KaTeX process */}}
   <p>{{ $content }}</p>
 {{- end -}}
diff --git a/layouts/partials/recent-posts-grid.html b/layouts/partials/recent-posts-grid.html
index 72d98d2..b601f9f 100644
--- a/layouts/partials/recent-posts-grid.html
+++ b/layouts/partials/recent-posts-grid.html
@@ -1,29 +1,29 @@
 <div class="recent-posts-grid">
-  {{ $recentPosts := first 6 (where site.RegularPages "Type" "posts") }}
-  {{ range $recentPosts }}
-    <div class="recent-post-card">  <!-- Changed from post-card -->
+  {{- $sections := site.Params.mainSections | default (slice "posts") -}}
+  {{- $recentPosts := first 6 (where site.RegularPages "Section" "in" $sections) -}}
+  {{- range $recentPosts }}
+    <div class="recent-post-card">
       <h3 class="post-title"><a href="{{ .Permalink | relURL }}" class="post-link">{{ .Title }}</a></h3>
       <div class="post-meta">
-        <div class="post-date">{{ .Date.Format "Jan 2, 2006" }}</div>
-        {{ if .Params.tags }}
+        <div class="post-date">{{ time.Format "Jan 2, 2006" .Date }}</div>
+        {{- if .Params.tags }}
         <div class="post-tags">
-          {{ $tagCount := len .Params.tags }}
-          {{ $maxTags := 2 }}
-          {{ $allTags := .Params.tags }}
-          
-          {{ range $index, $tag := .Params.tags }}
-            {{ if lt $index $maxTags }}
-              <span class="tag">{{ . }}</span>
-            {{ else if eq $index $maxTags }}
-              {{ $remainingTags := after $maxTags $allTags }}
+          {{- $tagCount := len .Params.tags -}}
+          {{- $maxTags := 2 -}}
+          {{- $allTags := .Params.tags -}}
+          {{- range $index, $tag := .Params.tags }}
+            {{- if lt $index $maxTags }}
+              <span class="tag">{{ $tag }}</span>
+            {{- else if eq $index $maxTags }}
+              {{- $remainingTags := after $maxTags $allTags -}}
               <span class="tag tag-more" data-tooltip="{{ delimit $remainingTags ", " }}">+{{ sub $tagCount $maxTags }}</span>
-              {{ break }}
-            {{ end }}
-          {{ end }}
+              {{- break -}}
+            {{- end -}}
+          {{- end }}
         </div>
-        {{ end }}
+        {{- end }}
       </div>
       <div class="post-summary">{{ .Summary | plainify | truncate 200 }}</div>
     </div>
-  {{ end }}
+  {{- end }}
 </div>
diff --git a/layouts/shortcodes/cite.html b/layouts/shortcodes/cite.html
index acf9e96..27fb2f8 100644
--- a/layouts/shortcodes/cite.html
+++ b/layouts/shortcodes/cite.html
@@ -1,21 +1,24 @@
+{{- /*
+  Citation shortcode.
+  Usage: {{< cite "key" "references.bib" "apa" "false" >}}
+  Stores citation state on .Page.Store (Hugo 0.85+).
+*/ -}}
 {{- $citationKey := .Get 0 | default "" -}}
 {{- $bibFile := .Get 1 | default "references.bib" -}}
-{{- $existingNum := .Page.Scratch.Get (printf "citation-%s-num" $citationKey) -}}
+{{- $existingNum := .Page.Store.Get (printf "citation-%s-num" $citationKey) -}}
 {{- if $existingNum -}}
-  {{- $citationId := printf "citation-%s" $citationKey -}}
   {{- $existingCitation := index (.Page.Store.Get "citations") $citationKey -}}
   <sup class="citation-ref" data-citation-key="{{ $citationKey }}" title="{{ $existingCitation }}">{{ $existingNum }}</sup>
 {{- else -}}
-  {{- /* New citation - increment counter and store */ -}}
-  {{- $num := .Page.Scratch.Get "citeCounter" | default 0 -}}
+  {{- $num := .Page.Store.Get "citeCounter" | default 0 -}}
   {{- $num = add $num 1 -}}
-  {{- .Page.Scratch.Set "citeCounter" $num -}}
-  {{- .Page.Scratch.Set (printf "citation-%s-num" $citationKey) $num -}}
+  {{- .Page.Store.Set "citeCounter" $num -}}
+  {{- .Page.Store.Set (printf "citation-%s-num" $citationKey) $num -}}
   {{- $style := .Get 2 | default "apa" -}}
   {{- $showNotes := .Get 3 | default "false" -}}
   {{- $citationId := printf "citation-%s" $citationKey -}}
-  {{- printf `<sup class="citation-ref" data-citation-key="%s">%d</sup><span class="citation-marker" data-citation-key="%s" data-bib-file="%s" data-citation-style="%s" data-show-notes="%s" data-citation-id="%s"></span><span class="sidenote sidenote-hidden citation-sidenote" id="%s" lang="%s" data-citation-key="%s" data-bib-file="%s" data-citation-style="%s" data-show-notes="%s"><sup class="citation-sup">%d.</sup><span class="citation citation-inline" data-citation-key="%s" data-bib-file="%s" data-citation-style="%s"></span></span>` $citationKey $num $citationKey $bibFile $style $showNotes $citationId $citationId (.Site.Language.Lang | default "en") $citationKey $bibFile $style $showNotes $num $citationKey $bibFile $style | safeHTML -}}
-  {{- /* Store citation data for reuse */ -}}
+  {{- $lang := site.Language.Lang | default "en" -}}
+<sup class="citation-ref" data-citation-key="{{ $citationKey }}">{{ $num }}</sup><span class="citation-marker" data-citation-key="{{ $citationKey }}" data-bib-file="{{ $bibFile }}" data-citation-style="{{ $style }}" data-show-notes="{{ $showNotes }}" data-citation-id="{{ $citationId }}"></span><span class="sidenote sidenote-hidden citation-sidenote" id="{{ $citationId }}" lang="{{ $lang }}" data-citation-key="{{ $citationKey }}" data-bib-file="{{ $bibFile }}" data-citation-style="{{ $style }}" data-show-notes="{{ $showNotes }}"><sup class="citation-sup">{{ $num }}.</sup><span class="citation citation-inline" data-citation-key="{{ $citationKey }}" data-bib-file="{{ $bibFile }}" data-citation-style="{{ $style }}"></span></span>
   {{- $citations := .Page.Store.Get "citations" | default dict -}}
   {{- $citations = merge $citations (dict $citationKey (dict "id" $citationId "style" $style "bibFile" $bibFile)) -}}
   {{- .Page.Store.Set "citations" $citations -}}
diff --git a/layouts/shortcodes/sidenote.html b/layouts/shortcodes/sidenote.html
index 061da42..02b138e 100644
--- a/layouts/shortcodes/sidenote.html
+++ b/layouts/shortcodes/sidenote.html
@@ -1,7 +1,13 @@
-{{- $counter := .Page.Scratch.Get "sidenoteCounter" | default 0 -}}
+{{- /*
+  Sidenote shortcode.
+  Usage: {{< sidenote >}}note text{{< /sidenote >}}
+  Tracks counter on .Page.Store (Hugo 0.85+).
+*/ -}}
+{{- $counter := .Page.Store.Get "sidenoteCounter" | default 0 -}}
 {{- $counter = add $counter 1 -}}
-{{- .Page.Scratch.Set "sidenoteCounter" $counter -}}
+{{- .Page.Store.Set "sidenoteCounter" $counter -}}
 {{- $letter := printf "%c" (add $counter 96) -}}
 {{- $content := .Inner | markdownify -}}
 {{- $cleanContent := $content | plainify -}}
-{{- printf `<sup class="sidenote-ref" title="%s">%s</sup><span class="sidenote sidenote-hidden" lang="%s"><sup class="sidenote-sup">%s.</sup>%s</span>` $cleanContent $letter (.Site.Language.Lang | default "en") $letter $content | safeHTML -}}
+{{- $lang := site.Language.Lang | default "en" -}}
+<sup class="sidenote-ref" title="{{ $cleanContent }}">{{ $letter }}</sup><span class="sidenote sidenote-hidden" lang="{{ $lang }}"><sup class="sidenote-sup">{{ $letter }}.</sup>{{ $content }}</span>