diff --git a/cves/2016/CVE-2016-0856.md b/cves/2016/CVE-2016-0856.md
index 6ee07b491c8..712f7337703 100644
--- a/cves/2016/CVE-2016-0856.md
+++ b/cves/2016/CVE-2016-0856.md
@@ -14,5 +14,3 @@ No PoCs from references.
 
 #### Github
 - https://github.com/readloud/PoC
-- https://github.com/hamzamalik3461/CVE-2026-20841
-- https://github.com/404godd/CVE-2026-20841-PoC
diff --git a/index/github.txt b/index/github.txt
index a7b094e352c..04134fa043f 100644
--- a/index/github.txt
+++ b/index/github.txt
@@ -26828,5 +26828,3 @@ CVE-2021-36260 - https://github.com/kwekre/poc
 CVE-2021-44228 - https://github.com/kwekre/poc
 CVE-2024-55591 - https://github.com/uLl0a/cve-2024-55591-poc
 CVE-2026-82221 - https://github.com/gabrielftanaka/CVE-2026-82221
-CVE-2016-0856 - https://github.com/404godd/CVE-2026-20841-PoC
-CVE-2016-0856 - https://github.com/hamzamalik3461/CVE-2026-20841
diff --git a/scripts/update_cves.py b/scripts/update_cves.py
index c457bff1309..4060703f55d 100755
--- a/scripts/update_cves.py
+++ b/scripts/update_cves.py
@@ -341,9 +341,9 @@ def qualifying_repo_cves(
     description = str(repo.get("description") or "")
     topics = " ".join(topic_names(repo))
     readme = readme_text(repo)
+    all_name_cves = extract_cves(full_name) | extract_cves(normalise_identity(full_name))
     all_identity_cves = (
-        extract_cves(full_name)
-        | extract_cves(normalise_identity(full_name))
+        all_name_cves
         | extract_cves(description)
         | extract_cves(topics)
     )
@@ -384,15 +384,20 @@ def qualifying_repo_cves(
             accepted.add(cve_id)
     for cve_id in description_cves | topic_cves:
         has_context = readme_has_poc_context(readme, cve_id, full_name)
+        has_cve_artifact = root_has_cve_artifact(repo, cve_id)
+        if all_name_cves and cve_id not in all_name_cves and not has_cve_artifact:
+            continue
         if (
             (not identity_is_non_poc or cve_id in name_cves)
             and (metadata_has_poc or has_context)
-            and (has_context or root_has_poc_artifact(repo, cve_id) or has_code)
+            and (has_context or has_cve_artifact or has_code)
         ):
             accepted.add(cve_id)
     for cve_id in readme_cves:
         has_artifact = root_has_poc_artifact(repo, cve_id)
         has_cve_artifact = root_has_cve_artifact(repo, cve_id)
+        if all_name_cves and cve_id not in all_name_cves and not has_cve_artifact:
+            continue
         if all_identity_cves and cve_id not in all_identity_cves and not has_cve_artifact:
             continue
         if identity_cves and cve_id not in identity_cves and not has_artifact:
diff --git a/tests/test_update_cves.py b/tests/test_update_cves.py
index f45eaab6b41..92a88dfed49 100644
--- a/tests/test_update_cves.py
+++ b/tests/test_update_cves.py
@@ -82,6 +82,12 @@ class RepositoryClassificationTests(unittest.TestCase):
             "Proof of concept for CVE-2026-20841",
             "The approach resembles the CVE-2016-0856 exploit.",
         )
+        repo["repositoryTopics"] = {
+            "nodes": [
+                {"topic": {"name": "cve-2016-0856"}},
+                {"topic": {"name": "cve-2026-20841"}},
+            ]
+        }
         repo["root"] = {"entries": [{"name": "PoC.md"}]}
         self.assertEqual(update_cves.qualifying_repo_cves(repo, 2016, []), set())
         self.assertEqual(