agenticsnz · ohdearquant · Jun 19, 2026 · Jun 17, 2026 · Jun 18, 2026
diff --git a/backlog/gself-pow-four-add-pow-two.md b/backlog/gself-pow-four-add-pow-two.md
@@ -0,0 +1,7 @@
+# gself-pow-four-add-pow-two
+
+n to the 1 divides n to the 4 plus n to the 2.
+
+- **Source:** self-seeded polynomial-divisibility identity family.
+- **Reference:** n to the 1 divides n to the 4 plus n to the 2. Provable by exhibiting the cofactor and `ring`.
+- **Difficulty:** 1
diff --git a/goals/gself-pow-four-add-pow-two.aisp b/goals/gself-pow-four-add-pow-two.aisp
@@ -0,0 +1,20 @@
+𝔸5.1.goal.gself-pow-four-add-pow-two@2026-06-17
+γ≔unsorry.goal
+⟦Ω:Goal⟧{
+  id≜gself-pow-four-add-pow-two
+  phase≜prove
+  status≜proved
+  difficulty≜1
+}
+⟦Σ:Source⟧{
+  src≜backlog/gself-pow-four-add-pow-two.md
+}
+⟦Γ:Deps⟧{
+  deps≜⟨⟩
+}
+⟦Λ:Artifact⟧{
+  lean≜goals/gself-pow-four-add-pow-two.lean
+  sha≜606984ed3145cd857a17033830761f57fc2fb37b3a0679f01eaa63f70104cef8
+  aff≜0
+}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/goals/gself-pow-four-add-pow-two.lean b/goals/gself-pow-four-add-pow-two.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_four_add_pow_two (n : ℤ) : (n) ∣ (n^4 + n^2) := by
+  sorry
diff --git a/library/Unsorry/GselfPowFourAddPowTwo.lean b/library/Unsorry/GselfPowFourAddPowTwo.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_four_add_pow_two (n : ℤ) : (n) ∣ (n^4 + n^2) := by
+  exact ⟨n^3 + n, by ring⟩
diff --git a/library/index/606984ed3145cd857a17033830761f57fc2fb37b3a0679f01eaa63f70104cef8.aisp b/library/index/606984ed3145cd857a17033830761f57fc2fb37b3a0679f01eaa63f70104cef8.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.lemma.606984ed3145@2026-06-17
+γ≔unsorry.lemma.index
+⟦Ω:Lemma⟧{sha≜606984ed3145cd857a17033830761f57fc2fb37b3a0679f01eaa63f70104cef8; goal≜gself-pow-four-add-pow-two; name≜gself_pow_four_add_pow_two}
+⟦Σ:Source⟧{src≜goals/gself-pow-four-add-pow-two.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-four-add-pow-two.mac-158f.20260617t182241255352z-4725992c.aisp b/proof-runs/gself-pow-four-add-pow-two.mac-158f.20260617t182241255352z-4725992c.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.run.gself-pow-four-add-pow-two.mac-158f.20260617t182241255352z-4725992c@2026-06-17
+γ≔unsorry.proof.run
+⟦Ω:Run⟧{id≜20260617t182241255352z-4725992c; goal≜gself-pow-four-add-pow-two; agent≜mac-158f; outcome≜proved}
+⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
+⟦Γ:Goal⟧{goal≜gself-pow-four-add-pow-two}
+⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:22:41Z}
+⟦Σ:Artifact⟧{sha≜606984ed3145cd857a17033830761f57fc2fb37b3a0679f01eaa63f70104cef8}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩