diff --git a/backlog/gself-pow-three-pow-five-add-pow-four.md b/backlog/gself-pow-three-pow-five-add-pow-four.md
new file mode 100644
index 000000000..a00d4fbb4
--- /dev/null
+++ b/backlog/gself-pow-three-pow-five-add-pow-four.md
@@ -0,0 +1,7 @@
+# gself-pow-three-pow-five-add-pow-four
+
+n to the 3 divides n to the 5 plus n to the 4.
+
+- **Source:** self-seeded polynomial-divisibility identity family.
+- **Reference:** n to the 3 divides n to the 5 plus n to the 4. Provable by exhibiting the cofactor and `ring`.
+- **Difficulty:** 1
diff --git a/goals/gself-pow-three-pow-five-add-pow-four.aisp b/goals/gself-pow-three-pow-five-add-pow-four.aisp
new file mode 100644
index 000000000..db8b30033
--- /dev/null
+++ b/goals/gself-pow-three-pow-five-add-pow-four.aisp
@@ -0,0 +1,20 @@
+𝔸5.1.goal.gself-pow-three-pow-five-add-pow-four@2026-06-17
+γ≔unsorry.goal
+⟦Ω:Goal⟧{
+  id≜gself-pow-three-pow-five-add-pow-four
+  phase≜prove
+  status≜proved
+  difficulty≜1
+}
+⟦Σ:Source⟧{
+  src≜backlog/gself-pow-three-pow-five-add-pow-four.md
+}
+⟦Γ:Deps⟧{
+  deps≜⟨⟩
+}
+⟦Λ:Artifact⟧{
+  lean≜goals/gself-pow-three-pow-five-add-pow-four.lean
+  sha≜8352041ef54bc58e3e0ec3a2bb2ad1d0a023840c06330fa7ffe1fd8c526fc318
+  aff≜0
+}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/goals/gself-pow-three-pow-five-add-pow-four.lean b/goals/gself-pow-three-pow-five-add-pow-four.lean
new file mode 100644
index 000000000..94d00f246
--- /dev/null
+++ b/goals/gself-pow-three-pow-five-add-pow-four.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_three_pow_five_add_pow_four (n : ℤ) : (n^3) ∣ (n^5 + n^4) := by
+  sorry
diff --git a/library/Unsorry/GselfPowThreePowFiveAddPowFour.lean b/library/Unsorry/GselfPowThreePowFiveAddPowFour.lean
new file mode 100644
index 000000000..125458597
--- /dev/null
+++ b/library/Unsorry/GselfPowThreePowFiveAddPowFour.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_three_pow_five_add_pow_four (n : ℤ) : (n^3) ∣ (n^5 + n^4) := by
+  exact ⟨n^2 + n, by ring⟩
diff --git a/library/index/8352041ef54bc58e3e0ec3a2bb2ad1d0a023840c06330fa7ffe1fd8c526fc318.aisp b/library/index/8352041ef54bc58e3e0ec3a2bb2ad1d0a023840c06330fa7ffe1fd8c526fc318.aisp
new file mode 100644
index 000000000..6248e2bbb
--- /dev/null
+++ b/library/index/8352041ef54bc58e3e0ec3a2bb2ad1d0a023840c06330fa7ffe1fd8c526fc318.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.lemma.8352041ef54b@2026-06-17
+γ≔unsorry.lemma.index
+⟦Ω:Lemma⟧{sha≜8352041ef54bc58e3e0ec3a2bb2ad1d0a023840c06330fa7ffe1fd8c526fc318; goal≜gself-pow-three-pow-five-add-pow-four; name≜gself_pow_three_pow_five_add_pow_four}
+⟦Σ:Source⟧{src≜goals/gself-pow-three-pow-five-add-pow-four.lean}
+⟦Γ:Tags⟧{tags≜⟨⟩}
+⟦Λ:Meta⟧{use≜0; aff≜0}
+⟦Π:Provenance⟧{solver≜ohdearquant; agent≜mac-158f; provider≜claude; model≜template-ring-cofactor; attempts≜1}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/proof-runs/gself-pow-three-pow-five-add-pow-four.mac-158f.20260617t182842151772z-33d88512.aisp b/proof-runs/gself-pow-three-pow-five-add-pow-four.mac-158f.20260617t182842151772z-33d88512.aisp
new file mode 100644
index 000000000..a4869a95c
--- /dev/null
+++ b/proof-runs/gself-pow-three-pow-five-add-pow-four.mac-158f.20260617t182842151772z-33d88512.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.run.gself-pow-three-pow-five-add-pow-four.mac-158f.20260617t182842151772z-33d88512@2026-06-17
+γ≔unsorry.proof.run
+⟦Ω:Run⟧{id≜20260617t182842151772z-33d88512; goal≜gself-pow-three-pow-five-add-pow-four; agent≜mac-158f; outcome≜proved}
+⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
+⟦Γ:Goal⟧{goal≜gself-pow-three-pow-five-add-pow-four}
+⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:28:42Z}
+⟦Σ:Artifact⟧{sha≜8352041ef54bc58e3e0ec3a2bb2ad1d0a023840c06330fa7ffe1fd8c526fc318}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩