From 21034fbf80a8c22eae621d465dc4bd9ca607e125 Mon Sep 17 00:00:00 2001
From: OceanLi <122793010+ohdearquant@users.noreply.github.com>
Date: Wed, 17 Jun 2026 14:23:36 -0400
Subject: [PATCH] prove(gself-pow-five-add-pow-three):
 gself_pow_five_add_pow_three by mac-158f

---
 backlog/gself-pow-five-add-pow-three.md       |  7 +++++++
 goals/gself-pow-five-add-pow-three.aisp       | 20 +++++++++++++++++++
 goals/gself-pow-five-add-pow-three.lean       |  4 ++++
 library/Unsorry/GselfPowFiveAddPowThree.lean  |  4 ++++
 ...a6691347136d692f98a9bc7c7da270c9878cc.aisp |  8 ++++++++
 ...-158f.20260617t182336488221z-f64233f2.aisp |  8 ++++++++
 6 files changed, 51 insertions(+)
 create mode 100644 backlog/gself-pow-five-add-pow-three.md
 create mode 100644 goals/gself-pow-five-add-pow-three.aisp
 create mode 100644 goals/gself-pow-five-add-pow-three.lean
 create mode 100644 library/Unsorry/GselfPowFiveAddPowThree.lean
 create mode 100644 library/index/296a2a8aaed2d7c8087d40dc447a6691347136d692f98a9bc7c7da270c9878cc.aisp
 create mode 100644 proof-runs/gself-pow-five-add-pow-three.mac-158f.20260617t182336488221z-f64233f2.aisp

diff --git a/backlog/gself-pow-five-add-pow-three.md b/backlog/gself-pow-five-add-pow-three.md
new file mode 100644
index 000000000..cb6dd4d5f
--- /dev/null
+++ b/backlog/gself-pow-five-add-pow-three.md
@@ -0,0 +1,7 @@
+# gself-pow-five-add-pow-three
+
+n to the 1 divides n to the 5 plus n to the 3.
+
+- **Source:** self-seeded polynomial-divisibility identity family.
+- **Reference:** n to the 1 divides n to the 5 plus n to the 3. Provable by exhibiting the cofactor and `ring`.
+- **Difficulty:** 1
diff --git a/goals/gself-pow-five-add-pow-three.aisp b/goals/gself-pow-five-add-pow-three.aisp
new file mode 100644
index 000000000..c6e3a057f
--- /dev/null
+++ b/goals/gself-pow-five-add-pow-three.aisp
@@ -0,0 +1,20 @@
+𝔸5.1.goal.gself-pow-five-add-pow-three@2026-06-17
+γ≔unsorry.goal
+⟦Ω:Goal⟧{
+  id≜gself-pow-five-add-pow-three
+  phase≜prove
+  status≜proved
+  difficulty≜1
+}
+⟦Σ:Source⟧{
+  src≜backlog/gself-pow-five-add-pow-three.md
+}
+⟦Γ:Deps⟧{
+  deps≜⟨⟩
+}
+⟦Λ:Artifact⟧{
+  lean≜goals/gself-pow-five-add-pow-three.lean
+  sha≜296a2a8aaed2d7c8087d40dc447a6691347136d692f98a9bc7c7da270c9878cc
+  aff≜0
+}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/goals/gself-pow-five-add-pow-three.lean b/goals/gself-pow-five-add-pow-three.lean
new file mode 100644
index 000000000..966801181
--- /dev/null
+++ b/goals/gself-pow-five-add-pow-three.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_five_add_pow_three (n : ℤ) : (n) ∣ (n^5 + n^3) := by
+  sorry
diff --git a/library/Unsorry/GselfPowFiveAddPowThree.lean b/library/Unsorry/GselfPowFiveAddPowThree.lean
new file mode 100644
index 000000000..b6b5d2d15
--- /dev/null
+++ b/library/Unsorry/GselfPowFiveAddPowThree.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_five_add_pow_three (n : ℤ) : (n) ∣ (n^5 + n^3) := by
+  exact ⟨n^4 + n^2, by ring⟩
diff --git a/library/index/296a2a8aaed2d7c8087d40dc447a6691347136d692f98a9bc7c7da270c9878cc.aisp b/library/index/296a2a8aaed2d7c8087d40dc447a6691347136d692f98a9bc7c7da270c9878cc.aisp
new file mode 100644
index 000000000..cb14e53ff
--- /dev/null
+++ b/library/index/296a2a8aaed2d7c8087d40dc447a6691347136d692f98a9bc7c7da270c9878cc.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.lemma.296a2a8aaed2@2026-06-17
+γ≔unsorry.lemma.index
+⟦Ω:Lemma⟧{sha≜296a2a8aaed2d7c8087d40dc447a6691347136d692f98a9bc7c7da270c9878cc; goal≜gself-pow-five-add-pow-three; name≜gself_pow_five_add_pow_three}
+⟦Σ:Source⟧{src≜goals/gself-pow-five-add-pow-three.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-five-add-pow-three.mac-158f.20260617t182336488221z-f64233f2.aisp b/proof-runs/gself-pow-five-add-pow-three.mac-158f.20260617t182336488221z-f64233f2.aisp
new file mode 100644
index 000000000..8e8c43441
--- /dev/null
+++ b/proof-runs/gself-pow-five-add-pow-three.mac-158f.20260617t182336488221z-f64233f2.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.run.gself-pow-five-add-pow-three.mac-158f.20260617t182336488221z-f64233f2@2026-06-17
+γ≔unsorry.proof.run
+⟦Ω:Run⟧{id≜20260617t182336488221z-f64233f2; goal≜gself-pow-five-add-pow-three; agent≜mac-158f; outcome≜proved}
+⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
+⟦Γ:Goal⟧{goal≜gself-pow-five-add-pow-three}
+⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:23:36Z}
+⟦Σ:Artifact⟧{sha≜296a2a8aaed2d7c8087d40dc447a6691347136d692f98a9bc7c7da270c9878cc}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩