From 80d43c2ad32b28a20ef8a5c834d0cc7db685f56b Mon Sep 17 00:00:00 2001
From: OceanLi <122793010+ohdearquant@users.noreply.github.com>
Date: Wed, 17 Jun 2026 14:22:27 -0400
Subject: [PATCH] prove(gself-pow-four-add-pow-one): gself_pow_four_add_pow_one
 by mac-158f

---
 backlog/gself-pow-four-add-pow-one.md         |  7 +++++++
 goals/gself-pow-four-add-pow-one.aisp         | 20 +++++++++++++++++++
 goals/gself-pow-four-add-pow-one.lean         |  4 ++++
 library/Unsorry/GselfPowFourAddPowOne.lean    |  4 ++++
 ...65dc16d9a1cb0f48325a1b72a396ba2190ad8.aisp |  8 ++++++++
 ...-158f.20260617t182227515714z-aff4cf82.aisp |  8 ++++++++
 6 files changed, 51 insertions(+)
 create mode 100644 backlog/gself-pow-four-add-pow-one.md
 create mode 100644 goals/gself-pow-four-add-pow-one.aisp
 create mode 100644 goals/gself-pow-four-add-pow-one.lean
 create mode 100644 library/Unsorry/GselfPowFourAddPowOne.lean
 create mode 100644 library/index/a065c0ad0f716052f575f4dabdf65dc16d9a1cb0f48325a1b72a396ba2190ad8.aisp
 create mode 100644 proof-runs/gself-pow-four-add-pow-one.mac-158f.20260617t182227515714z-aff4cf82.aisp

diff --git a/backlog/gself-pow-four-add-pow-one.md b/backlog/gself-pow-four-add-pow-one.md
new file mode 100644
index 000000000..143d026f8
--- /dev/null
+++ b/backlog/gself-pow-four-add-pow-one.md
@@ -0,0 +1,7 @@
+# gself-pow-four-add-pow-one
+
+n to the 1 divides n to the 4 plus n to the 1.
+
+- **Source:** self-seeded polynomial-divisibility identity family.
+- **Reference:** n to the 1 divides n to the 4 plus n to the 1. Provable by exhibiting the cofactor and `ring`.
+- **Difficulty:** 1
diff --git a/goals/gself-pow-four-add-pow-one.aisp b/goals/gself-pow-four-add-pow-one.aisp
new file mode 100644
index 000000000..a07e20cac
--- /dev/null
+++ b/goals/gself-pow-four-add-pow-one.aisp
@@ -0,0 +1,20 @@
+𝔸5.1.goal.gself-pow-four-add-pow-one@2026-06-17
+γ≔unsorry.goal
+⟦Ω:Goal⟧{
+  id≜gself-pow-four-add-pow-one
+  phase≜prove
+  status≜proved
+  difficulty≜1
+}
+⟦Σ:Source⟧{
+  src≜backlog/gself-pow-four-add-pow-one.md
+}
+⟦Γ:Deps⟧{
+  deps≜⟨⟩
+}
+⟦Λ:Artifact⟧{
+  lean≜goals/gself-pow-four-add-pow-one.lean
+  sha≜a065c0ad0f716052f575f4dabdf65dc16d9a1cb0f48325a1b72a396ba2190ad8
+  aff≜0
+}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/goals/gself-pow-four-add-pow-one.lean b/goals/gself-pow-four-add-pow-one.lean
new file mode 100644
index 000000000..c6721979e
--- /dev/null
+++ b/goals/gself-pow-four-add-pow-one.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_four_add_pow_one (n : ℤ) : (n) ∣ (n^4 + n) := by
+  sorry
diff --git a/library/Unsorry/GselfPowFourAddPowOne.lean b/library/Unsorry/GselfPowFourAddPowOne.lean
new file mode 100644
index 000000000..f88e0ffc2
--- /dev/null
+++ b/library/Unsorry/GselfPowFourAddPowOne.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem gself_pow_four_add_pow_one (n : ℤ) : (n) ∣ (n^4 + n) := by
+  exact ⟨n^3 + 1, by ring⟩
diff --git a/library/index/a065c0ad0f716052f575f4dabdf65dc16d9a1cb0f48325a1b72a396ba2190ad8.aisp b/library/index/a065c0ad0f716052f575f4dabdf65dc16d9a1cb0f48325a1b72a396ba2190ad8.aisp
new file mode 100644
index 000000000..0a1120bd4
--- /dev/null
+++ b/library/index/a065c0ad0f716052f575f4dabdf65dc16d9a1cb0f48325a1b72a396ba2190ad8.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.lemma.a065c0ad0f71@2026-06-17
+γ≔unsorry.lemma.index
+⟦Ω:Lemma⟧{sha≜a065c0ad0f716052f575f4dabdf65dc16d9a1cb0f48325a1b72a396ba2190ad8; goal≜gself-pow-four-add-pow-one; name≜gself_pow_four_add_pow_one}
+⟦Σ:Source⟧{src≜goals/gself-pow-four-add-pow-one.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-one.mac-158f.20260617t182227515714z-aff4cf82.aisp b/proof-runs/gself-pow-four-add-pow-one.mac-158f.20260617t182227515714z-aff4cf82.aisp
new file mode 100644
index 000000000..9c83891e8
--- /dev/null
+++ b/proof-runs/gself-pow-four-add-pow-one.mac-158f.20260617t182227515714z-aff4cf82.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.run.gself-pow-four-add-pow-one.mac-158f.20260617t182227515714z-aff4cf82@2026-06-17
+γ≔unsorry.proof.run
+⟦Ω:Run⟧{id≜20260617t182227515714z-aff4cf82; goal≜gself-pow-four-add-pow-one; agent≜mac-158f; outcome≜proved}
+⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
+⟦Γ:Goal⟧{goal≜gself-pow-four-add-pow-one}
+⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:22:27Z}
+⟦Σ:Artifact⟧{sha≜a065c0ad0f716052f575f4dabdf65dc16d9a1cb0f48325a1b72a396ba2190ad8}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩