diff --git a/src/resources/filters/crossref/theorems.lua b/src/resources/filters/crossref/theorems.lua
index 68a7704caf9..de1fbb989b5 100644
--- a/src/resources/filters/crossref/theorems.lua
+++ b/src/resources/filters/crossref/theorems.lua
@@ -37,98 +37,6 @@ function crossref_theorems()
       proof.order = add_crossref(label, type, title)
       return proof
     end,
-    Div = function(el)
-      local type = refType(el.attr.identifier)
-      local theoremType = theorem_types[type]
-      if theoremType then
-        internal_error()
-      else
-        -- see if this is a proof, remark, or solution
-        local proof = proof_type(el)
-        if proof ~= nil then
-
-          -- ensure requisite latex is injected
-          crossref.using_theorems = true
-
-          if proof.env ~= "proof" then
-            el.attr.classes:insert("proof")
-          end
-
-          -- capture then remove name
-          -- 
-          -- we have string_to_quarto_ast_inlines but we don't need it here
-          -- because this filter happened after shortcode processing, and this
-          -- is a regular div we're processing
-          local name = markdownToInlines(el.attr.attributes["name"])
-          if not name or #name == 0 then
-            name = resolveHeadingCaption(el)
-          end
-          el.attr.attributes["name"] = nil 
-
-          -- output
-          if _quarto.format.isLatexOutput() then
-            local preamble = pandoc.List()
-            preamble:insert(pandoc.RawInline("latex", "\\begin{" .. proof.env .. "}"))
-            if name ~= nil then
-              preamble:insert(pandoc.RawInline("latex", "["))
-              tappend(preamble, name)
-              preamble:insert(pandoc.RawInline("latex", "]"))
-            end
-            preamble:insert(pandoc.RawInline("latex", "\n"))
-            -- https://github.com/quarto-dev/quarto-cli/issues/6077
-            if el.content[1].t == "Para" then
-              preamble:extend(el.content[1].content)
-              el.content[1].content = preamble
-            else
-              if (el.content[1].t ~= "Para") then
-                -- required trick to get correct alignement when non Para content first
-                preamble:insert(pandoc.RawInline('latex', "\\leavevmode"))
-              end
-              el.content:insert(1, pandoc.Plain(preamble))
-            end
-            local end_env = "\\end{" .. proof.env .. "}"
-            -- https://github.com/quarto-dev/quarto-cli/issues/6077
-            if el.content[#el.content].t == "Para" then
-              el.content[#el.content].content:insert(pandoc.RawInline("latex", "\n" .. end_env))
-            elseif el.content[#el.content].t == "RawBlock" and el.content[#el.content].format == "latex" then
-              -- this is required for no empty line between end_env and previous latex block
-              el.content[#el.content].text = el.content[#el.content].text .. "\n" .. end_env
-            else
-              el.content:insert(pandoc.RawBlock("latex", end_env))
-            end
-          elseif _quarto.format.isJatsOutput() then
-            el = jatsTheorem(el,  nil, name )
-          else
-            local span = pandoc.Span(
-              { pandoc.Emph(pandoc.Str(envTitle(proof.env, proof.title)))},
-              pandoc.Attr("", { "proof-title" })
-            )
-            if name ~= nil then
-              span.content:insert(pandoc.Str(" ("))
-              tappend(span.content, name)
-              span.content:insert(pandoc.Str(")"))
-            end
-            tappend(span.content, { pandoc.Str(". ")})
-
-            -- if the first block is a paragraph, then prepend the title span
-            if #el.content > 0 and 
-               el.content[1].t == "Para" and
-               el.content[1].content ~= nil and 
-               #el.content[1].content > 0 then
-              el.content[1].content:insert(1, span)
-            else
-              -- else insert a new paragraph
-              el.content:insert(1, pandoc.Para{span})
-            end
-          end
-
-        end
-
-      end
-     
-      return el
-    
-    end
   }
 
 end
diff --git a/src/resources/filters/layout/pandoc3_figure.lua b/src/resources/filters/layout/pandoc3_figure.lua
index 42b66e54f28..2ebb335fb96 100644
--- a/src/resources/filters/layout/pandoc3_figure.lua
+++ b/src/resources/filters/layout/pandoc3_figure.lua
@@ -11,14 +11,8 @@ function render_pandoc3_figure()
   local function html_handle_linked_image(figure)
     local div = pandoc.Div({})
     div.identifier = "fig-yesiamafigure" -- this is a bad hack to make discoverLinkedFigureDiv work
-    local link = nil
-    if figure.content[1].t == "Plain" then
-      local plain = figure.content[1]
-      if plain.content[1].t == "Link" then
-        link = plain.content[1]
-      end
-    end
-    if link == nil then
+    local link = quarto.utils.match("[1]/Plain/[1]/Link")(figure)
+    if not link then
       return nil
     end
     div.content:insert(pandoc.Para({link}))
@@ -197,6 +191,9 @@ function render_pandoc3_figure()
             end
           end
         end
+        if #figure.content == 0 then
+          return nil
+        end
         return make_typst_figure({
           content = figure.content[1],
           caption = figure.caption.long[1],
diff --git a/src/resources/filters/quarto-post/latexdiv.lua b/src/resources/filters/quarto-post/latexdiv.lua
index 4d0a0d0c384..ca74cb94f0e 100644
--- a/src/resources/filters/quarto-post/latexdiv.lua
+++ b/src/resources/filters/quarto-post/latexdiv.lua
@@ -34,7 +34,7 @@ function latexDiv()
       
       -- if the first and last div blocks are paragraphs then we can
       -- bring the environment begin/end closer to the content
-      if divEl.content[1].t == "Para" and divEl.content[#divEl.content].t == "Para" then
+      if quarto.utils.match("[1]/Para")(divEl) and divEl.content[#divEl.content].t == "Para" then
         table.insert(divEl.content[1].content, 1, pandoc.RawInline('tex', beginEnv .. "\n"))
         table.insert(divEl.content[#divEl.content].content, pandoc.RawInline('tex', "\n" .. endEnv))
       else
diff --git a/src/resources/filters/quarto-pre/parsefiguredivs.lua b/src/resources/filters/quarto-pre/parsefiguredivs.lua
index 6215af8f2e0..466f0475f5c 100644
--- a/src/resources/filters/quarto-pre/parsefiguredivs.lua
+++ b/src/resources/filters/quarto-pre/parsefiguredivs.lua
@@ -305,11 +305,9 @@ function parse_floatreftargets()
     local identifier = div.identifier
     local attr = pandoc.Attr(identifier, div.classes, div.attributes)
     assert(content)
-    if (#content == 1 and content[1].t == "Para" and
-        content[1].content[1].t == "Image") then
-      -- if the div contains a single image, then we simply use the image as
-      -- the content
-      content = content[1].content[1]
+    local single_image = quarto.utils.match("[1]/Para/[1]/Image")(content)
+    if #content == 1 and single_image then
+      content = single_image
 
       -- don't merge classes because they often have CSS consequences 
       -- but merge attributes because they're needed to correctly resolve
@@ -486,7 +484,7 @@ function parse_floatreftargets()
       if category == nil then
         return nil
       end
-      if #fig.content ~= 1 and fig.content[1].t ~= "Plain" then
+      if #fig.content ~= 1 or fig.content[1].t ~= "Plain" then
         -- we don't know how to parse this pandoc 3 figure
         -- just return as is
         return nil
diff --git a/tests/docs/smoke-all/crossrefs/float/empty-figure-content-filter.lua b/tests/docs/smoke-all/crossrefs/float/empty-figure-content-filter.lua
new file mode 100644
index 00000000000..ab15f03d174
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/float/empty-figure-content-filter.lua
@@ -0,0 +1,7 @@
+-- Test helper: empties Figure content to trigger unguarded .content[1].t access
+function Figure(fig)
+  if fig.identifier == "fig-emptied" then
+    fig.content = pandoc.Blocks({})
+    return fig
+  end
+end
diff --git a/tests/docs/smoke-all/crossrefs/float/empty-figure-content.qmd b/tests/docs/smoke-all/crossrefs/float/empty-figure-content.qmd
new file mode 100644
index 00000000000..0fe211a47bc
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/float/empty-figure-content.qmd
@@ -0,0 +1,25 @@
+---
+title: Empty Figure content guard
+format: pdf
+keep-tex: true
+filters:
+  - at: pre-ast
+    path: empty-figure-content-filter.lua
+_quarto:
+  tests:
+    pdf:
+      noErrors: default
+      ensureLatexFileRegexMatches:
+        -
+          - '\\begin\{figure\}'
+---
+
+## Normal figure
+
+![A caption](img/surus.jpg){#fig-normal}
+
+See @fig-normal.
+
+## Figure with content stripped by filter
+
+![Emptied caption](img/surus.jpg){#fig-emptied}
diff --git a/tests/docs/smoke-all/crossrefs/float/empty-pandoc3-figure-filter.lua b/tests/docs/smoke-all/crossrefs/float/empty-pandoc3-figure-filter.lua
new file mode 100644
index 00000000000..18155d7b19b
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/float/empty-pandoc3-figure-filter.lua
@@ -0,0 +1,8 @@
+-- Test helper: empties non-crossref Figure content to trigger
+-- unguarded .content[1].t access in pandoc3_figure.lua
+function Figure(fig)
+  if fig.identifier == "" then
+    fig.content = pandoc.Blocks({})
+    return fig
+  end
+end
diff --git a/tests/docs/smoke-all/crossrefs/float/empty-pandoc3-figure.qmd b/tests/docs/smoke-all/crossrefs/float/empty-pandoc3-figure.qmd
new file mode 100644
index 00000000000..5742c805c32
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/float/empty-pandoc3-figure.qmd
@@ -0,0 +1,15 @@
+---
+title: Empty Pandoc 3 Figure content guard
+format: html
+filters:
+  - at: pre-ast
+    path: empty-pandoc3-figure-filter.lua
+_quarto:
+  tests:
+    html:
+      noErrors: default
+---
+
+## Figure without cross-ref identifier
+
+![A plain figure caption](img/surus.jpg)
diff --git a/tests/docs/smoke-all/crossrefs/float/empty-para-inlines-filter.lua b/tests/docs/smoke-all/crossrefs/float/empty-para-inlines-filter.lua
new file mode 100644
index 00000000000..49886f1a437
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/float/empty-para-inlines-filter.lua
@@ -0,0 +1,10 @@
+-- Test helper: creates a fig-div with a single empty Para (no inlines)
+-- and a fig-cap attribute for caption, triggering unguarded
+-- content[1].content[1].t access in parsefiguredivs.lua:309
+function Div(div)
+  if div.identifier == "fig-empty-para" then
+    div.content = pandoc.Blocks({pandoc.Para({})})
+    div.attributes["fig-cap"] = "External caption"
+    return div
+  end
+end
diff --git a/tests/docs/smoke-all/crossrefs/float/empty-para-inlines.qmd b/tests/docs/smoke-all/crossrefs/float/empty-para-inlines.qmd
new file mode 100644
index 00000000000..0dea796941f
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/float/empty-para-inlines.qmd
@@ -0,0 +1,21 @@
+---
+title: Empty Para inlines guard
+format: html
+filters:
+  - at: pre-ast
+    path: empty-para-inlines-filter.lua
+_quarto:
+  tests:
+    html:
+      noErrors: default
+---
+
+## Figure div with content replaced by empty Para
+
+::: {#fig-empty-para}
+![Normal image](img/surus.jpg)
+
+Normal caption
+:::
+
+See @fig-empty-para.
diff --git a/tests/docs/smoke-all/crossrefs/theorem/proof-rendering-html.qmd b/tests/docs/smoke-all/crossrefs/theorem/proof-rendering-html.qmd
new file mode 100644
index 00000000000..89d9286abf0
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/theorem/proof-rendering-html.qmd
@@ -0,0 +1,35 @@
+---
+title: Proof rendering (HTML)
+format: html
+_quarto:
+  tests:
+    html:
+      noErrors: default
+      ensureHtmlElements:
+        -
+          - 'div.proof'
+          - '.proof-title'
+---
+
+## Proof with content
+
+::: {.proof}
+This is a proof with content.
+:::
+
+## Named proof
+
+::: {.proof name="Of the main theorem"}
+Named proof body.
+:::
+
+## Empty proof
+
+::: {.proof}
+:::
+
+## Remark
+
+::: {.remark}
+This is a remark.
+:::
diff --git a/tests/docs/smoke-all/crossrefs/theorem/proof-rendering.qmd b/tests/docs/smoke-all/crossrefs/theorem/proof-rendering.qmd
new file mode 100644
index 00000000000..ec401f26fb4
--- /dev/null
+++ b/tests/docs/smoke-all/crossrefs/theorem/proof-rendering.qmd
@@ -0,0 +1,39 @@
+---
+title: Proof rendering
+format: pdf
+keep-tex: true
+_quarto:
+  tests:
+    pdf:
+      noErrors: default
+      ensureLatexFileRegexMatches:
+        -
+          - '\\begin\{proof\}'
+          - '\\end\{proof\}'
+          - '\\begin\{proof\}\[Of the main theorem\]'
+          - '\\begin\{remark\}'
+          - '\\end\{remark\}'
+---
+
+## Proof with content
+
+::: {.proof}
+This is a proof with content.
+:::
+
+## Named proof
+
+::: {.proof name="Of the main theorem"}
+Named proof body.
+:::
+
+## Empty proof
+
+::: {.proof}
+:::
+
+## Remark
+
+::: {.remark}
+This is a remark.
+:::
diff --git a/tests/docs/smoke-all/latex/empty-latex-div.qmd b/tests/docs/smoke-all/latex/empty-latex-div.qmd
new file mode 100644
index 00000000000..fc97fed664a
--- /dev/null
+++ b/tests/docs/smoke-all/latex/empty-latex-div.qmd
@@ -0,0 +1,26 @@
+---
+title: Empty LaTeX div
+format: pdf
+keep-tex: true
+_quarto:
+  tests:
+    pdf:
+      noErrors: default
+      ensureLatexFileRegexMatches:
+        -
+          - '\\begin\{center\}'
+          - '\\end\{center\}'
+          - '\\begin\{flushright\}'
+          - '\\end\{flushright\}'
+---
+
+## Non-empty LaTeX div
+
+::: {.center latex="true"}
+Some centered content.
+:::
+
+## Empty LaTeX div
+
+::: {.flushright latex="true"}
+:::