diff --git a/sift/pyproject.toml b/sift/pyproject.toml
index 23289ad..cc2a89a 100644
--- a/sift/pyproject.toml
+++ b/sift/pyproject.toml
@@ -6,7 +6,7 @@ build-backend = "setuptools.build_meta"
 name = "sift"
 version = "0.0.0"
 description = "Sift through wikipedia dumps and extract interesting info"
-dependencies = ["mwxml >= 0.3.3, < 0.4", "wikitextparser >= 0.55.13, < 0.56"]
+dependencies = ["mwxml >= 0.3.4, < 0.4", "wikitextparser >= 0.56.2, < 0.57"]
 
 [project.scripts]
 sift = "sift:main"
diff --git a/sift/sift.py b/sift/sift.py
index 78c1f1d..18dbb88 100644
--- a/sift/sift.py
+++ b/sift/sift.py
@@ -1,28 +1,159 @@
 import json
+import re
 import sys
-from pathlib import Path
 
 import mwxml  # https://pythonhosted.org/mwxml/
 import wikitextparser as wtp  # https://github.com/5j9/wikitextparser#readme
 
+# A link can have two important properties:
+# 1. It can be inside a bigger structure (e.g. an infobox template)
+# 2. It can be inside parentheses
+#
+# The first link that is neither in parentheses nor part of any template is
+# considered the first link of the article for the purposes of the
+# Philosophy Game.
+#
+# The parentheses "(" and ")" are only recognized outside of certain
+# components like templates.
+#
+# https://en.wikipedia.org/wiki/Wikipedia:Getting_to_Philosophy
+# https://diff.wikimedia.org/2018/04/20/why-it-took-a-long-time-to-build-that-tiny-link-preview-on-wikipedia/
+# https://www.mediawiki.org/wiki/Page_Previews/API_Specification
+
 
 def eprint(*args, **kwargs):
     print(*args, file=sys.stderr, **kwargs)
 
 
-# https://pythonhosted.org/mwxml/iteration.html#mwxml.Page
-def process_page(page):
+def advance_delims(delims, to):
+    delta = 0
+
+    while delims:
+        i, opening = delims[-1]
+        if i <= to:
+            delims.pop()
+            delta += 1 if opening else -1
+        else:
+            break
+
+    return delta
+
+
+def find_spans(page):
+    # Within any of these spans, parentheses are ignored.
+    spans = []
+    spans.extend(i.span for i in page.comments)
+    spans.extend(i.span for i in page.external_links)
+    spans.extend(i.span for i in page.get_tags())  # Usually <ref>
+    spans.extend(i.span for i in page.tables)
+    spans.extend(i.span for i in page.templates)
+    spans.extend(i.span for i in page.wikilinks)
+
+    span_delims = []
+    span_delims.extend((s, True) for s, _ in spans)
+    span_delims.extend((e, False) for _, e in spans)
+    span_delims.sort()
+    return span_delims
+
+
+def find_parens(page, span_delims):
+    span_delims = list(reversed(sorted(span_delims)))
+
+    open_spans = 0
+    paren_delims = []
+
+    for m in re.finditer(r"\(|\)", page.string):
+        start, end = m.span()
+
+        open_spans += advance_delims(span_delims, start)
+        if open_spans != 0:
+            continue
+
+        opening = m.group(0) == "("
+        pos = start if opening else end
+        paren_delims.append((pos, opening))
+
+    return paren_delims
+
+
+def fix_parens(paren_delims):
+    # First, remove closing parens that close nonexistent opening parens.
+    open_parens = 0
+    paren_delims_2 = []
+    for i, opening in paren_delims:
+        if opening:
+            open_parens += 1
+            paren_delims_2.append((i, opening))
+        elif open_parens > 0:
+            open_parens -= 1
+            paren_delims_2.append((i, opening))
+        else:
+            eprint(f"(removed weird closing paren at {i})")
+
+    # Then, remove opening parens that would never be closed.
+    open_parens = 0
+    paren_delims_3 = []
+    for i, opening in reversed(paren_delims_2):
+        if not opening:
+            open_parens += 1
+            paren_delims_3.append((i, opening))
+        elif open_parens > 0:
+            open_parens -= 1
+            paren_delims_3.append((i, opening))
+        else:
+            eprint(f"(removed weird opening paren at {i})")
+    paren_delims_3.reverse()
+
+    return paren_delims_3
+
+
+def format_link(link, in_parens, in_structure):
+    title = link.title.strip()
+    start, end = link.span
+    flags = in_structure << 1 | in_parens
+    return (title, start, end - start, flags)
+
+
+def find_links(page, paren_delims):
+    paren_delims = list(reversed(sorted(paren_delims)))
+
+    open_parens = 0
+    links = []
+
+    for link in page.wikilinks:
+        start, end = link.span
+        open_parens += advance_delims(paren_delims, start)
+        in_parens = open_parens != 0
+        in_structure = link.parent() is not None
+        links.append(format_link(link, in_parens, in_structure))
+
+    return links
+
+
+def pair_parens(paren_delims):
+    starts = []
+    spans = []
+    for i, opening in paren_delims:
+        if opening:
+            starts.append(i)
+        else:
+            spans.append((starts.pop(), i))
+    return spans
+
+
+def process_xmldump_page(page):
+    # https://pythonhosted.org/mwxml/iteration.html#mwxml.Page
     if page.namespace != 0:
         return
     eprint(f"{page.id:8} - {page.title!r}")
 
     [revision] = list(page)  # Every page has exactly one revision
     text = revision.text or ""
-
-    links = []
-    for link in wtp.parse(text).wikilinks:
-        start, end = link.span
-        links.append((link.title.strip(), start, end))
+    parsed = wtp.parse(text)
+    span_delims = find_spans(parsed)
+    paren_delims = find_parens(parsed, span_delims)
+    paren_delims_fixed = fix_parens(paren_delims)
+    links = find_links(parsed, paren_delims_fixed)
 
     info = {
         "id": page.id,
@@ -40,4 +171,4 @@ def process_page(page):
 def main():
     dump = mwxml.Dump.from_file(sys.stdin)
     for page in dump.pages:
-        process_page(page)
+        process_xmldump_page(page)