diff --git a/density-chain.md b/density-chain.md
index ecd80bd..9ace8d0 100644
--- a/density-chain.md
+++ b/density-chain.md
@@ -5,7 +5,7 @@ venue: "arXiv preprint (cs.AI); v1 2025-12-31"
 source: "https://arxiv.org/abs/2512.24601 (pinned: arXiv:2512.24601v3, 2026-05-11 — the latest version as of verification)"
 license: "CC BY 4.0 (per the arXiv record)"
 date_summarized: 2026-07-18
-verified_against_source: 2026-07-18
+verified_against_source: 2026-07-20
 tier_budget_words: 150
 tags: [recursive-language-models, long-context, inference-time-scaling, repl, agents, mit-csail]
 entity_ledger:
@@ -159,9 +159,9 @@ what we spend our days building.
 - Canonical source: https://arxiv.org/abs/2512.24601
 - Version studied: arXiv:2512.24601v3 (submitted 2026-05-11; v3 is the
   latest as of verification; v1 2025-12-31, v2 2026-01-28)
-- Verified against source: 2026-07-18, studied from the arXiv v3 PDF fetched
-  fresh from arXiv; section, table, figure, and algorithm numbering follows
-  that PDF
+- Verified against source: 2026-07-20 (re-verification; prior verification
+  2026-07-18), studied from the arXiv v3 PDF fetched fresh from arXiv;
+  section, table, figure, and algorithm numbering follows that PDF
 - Source license: CC BY 4.0, per the arXiv record
 - Authors' code: https://github.com/alexzhang13/rlm [Abstract]
 - Revisions or errata noticed since v3: none
diff --git a/index.json b/index.json
index 863ade7..39eaaf6 100644
--- a/index.json
+++ b/index.json
@@ -1,6 +1,6 @@
 {
   "schema_version": 1,
-  "updated": "2026-07-18",
+  "updated": "2026-07-20",
   "repo": "https://github.com/OpenCnid/recursive-language-models",
   "notes": [
     {
@@ -20,7 +20,7 @@
       "pinned_date": "2026-05-11",
       "source_license": "CC BY 4.0",
       "date_summarized": "2026-07-18",
-      "verified_against_source": "2026-07-18",
+      "verified_against_source": "2026-07-20",
       "tier_budget_words": 150,
       "tags": [
         "recursive-language-models",