From ebd0799bf5694f1673a5b7d745a62f7d2391e640 Mon Sep 17 00:00:00 2001
From: OceanLi <122793010+ohdearquant@users.noreply.github.com>
Date: Wed, 17 Jun 2026 14:23:23 -0400
Subject: [PATCH] prove(gself-pow-five-add-pow-two): gself_pow_five_add_pow_two
 by mac-158f

---
 backlog/gself-pow-five-add-pow-two.md         |  7 +++++++
 goals/gself-pow-five-add-pow-two.aisp         | 20 +++++++++++++++++++
 goals/gself-pow-five-add-pow-two.lean         |  4 ++++
 library/Unsorry/GselfPowFiveAddPowTwo.lean    |  4 ++++
 ...4104f39794a4ad52bb0db129f39378aa160dc.aisp |  8 ++++++++
 ...-158f.20260617t182322671511z-bace0765.aisp |  8 ++++++++
 6 files changed, 51 insertions(+)
 create mode 100644 backlog/gself-pow-five-add-pow-two.md
 create mode 100644 goals/gself-pow-five-add-pow-two.aisp
 create mode 100644 goals/gself-pow-five-add-pow-two.lean
 create mode 100644 library/Unsorry/GselfPowFiveAddPowTwo.lean
 create mode 100644 library/index/a0259896d4bdbee5725dc19b30e4104f39794a4ad52bb0db129f39378aa160dc.aisp
 create mode 100644 proof-runs/gself-pow-five-add-pow-two.mac-158f.20260617t182322671511z-bace0765.aisp

diff --git a/backlog/gself-pow-five-add-pow-two.md b/backlog/gself-pow-five-add-pow-two.md
new file mode 100644
index 000000000..11da3e6bf
--- /dev/null
+++ b/backlog/gself-pow-five-add-pow-two.md
@@ -0,0 +1,7 @@
+# gself-pow-five-add-pow-two
+
+n to the 1 divides n to the 5 plus n to the 2.
+
+- **Source:** self-seeded polynomial-divisibility identity family.
+- **Reference:** n to the 1 divides n to the 5 plus n to the 2. Provable by exhibiting the cofactor and `ring`.
+- **Difficulty:** 1
diff --git a/goals/gself-pow-five-add-pow-two.aisp b/goals/gself-pow-five-add-pow-two.aisp
new file mode 100644
index 000000000..0503cc4ae
--- /dev/null
+++ b/goals/gself-pow-five-add-pow-two.aisp
@@ -0,0 +1,20 @@
+𝔸5.1.goal.gself-pow-five-add-pow-two@2026-06-17
+γ≔unsorry.goal
+⟦Ω:Goal⟧{
+  id≜gself-pow-five-add-pow-two
+  phase≜prove
+  status≜proved
+  difficulty≜1
+}
+⟦Σ:Source⟧{
+  src≜backlog/gself-pow-five-add-pow-two.md
+}
+⟦Γ:Deps⟧{
+  deps≜⟨⟩
+}
+⟦Λ:Artifact⟧{
+  lean≜goals/gself-pow-five-add-pow-two.lean
+  sha≜a0259896d4bdbee5725dc19b30e4104f39794a4ad52bb0db129f39378aa160dc
+  aff≜0
+}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/goals/gself-pow-five-add-pow-two.lean b/goals/gself-pow-five-add-pow-two.lean
new file mode 100644
index 000000000..48a626003
--- /dev/null
+++ b/goals/gself-pow-five-add-pow-two.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_five_add_pow_two (n : ℤ) : (n) ∣ (n^5 + n^2) := by
+  sorry
diff --git a/library/Unsorry/GselfPowFiveAddPowTwo.lean b/library/Unsorry/GselfPowFiveAddPowTwo.lean
new file mode 100644
index 000000000..31d8d852e
--- /dev/null
+++ b/library/Unsorry/GselfPowFiveAddPowTwo.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_five_add_pow_two (n : ℤ) : (n) ∣ (n^5 + n^2) := by
+  exact ⟨n^4 + n, by ring⟩
diff --git a/library/index/a0259896d4bdbee5725dc19b30e4104f39794a4ad52bb0db129f39378aa160dc.aisp b/library/index/a0259896d4bdbee5725dc19b30e4104f39794a4ad52bb0db129f39378aa160dc.aisp
new file mode 100644
index 000000000..961bf1fca
--- /dev/null
+++ b/library/index/a0259896d4bdbee5725dc19b30e4104f39794a4ad52bb0db129f39378aa160dc.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.lemma.a0259896d4bd@2026-06-17
+γ≔unsorry.lemma.index
+⟦Ω:Lemma⟧{sha≜a0259896d4bdbee5725dc19b30e4104f39794a4ad52bb0db129f39378aa160dc; goal≜gself-pow-five-add-pow-two; name≜gself_pow_five_add_pow_two}
+⟦Σ:Source⟧{src≜goals/gself-pow-five-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-five-add-pow-two.mac-158f.20260617t182322671511z-bace0765.aisp b/proof-runs/gself-pow-five-add-pow-two.mac-158f.20260617t182322671511z-bace0765.aisp
new file mode 100644
index 000000000..017437c4f
--- /dev/null
+++ b/proof-runs/gself-pow-five-add-pow-two.mac-158f.20260617t182322671511z-bace0765.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.run.gself-pow-five-add-pow-two.mac-158f.20260617t182322671511z-bace0765@2026-06-17
+γ≔unsorry.proof.run
+⟦Ω:Run⟧{id≜20260617t182322671511z-bace0765; goal≜gself-pow-five-add-pow-two; agent≜mac-158f; outcome≜proved}
+⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
+⟦Γ:Goal⟧{goal≜gself-pow-five-add-pow-two}
+⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:23:22Z}
+⟦Σ:Artifact⟧{sha≜a0259896d4bdbee5725dc19b30e4104f39794a4ad52bb0db129f39378aa160dc}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩