diff --git a/backlog/ggeom-pred-pow-six-sub-one.md b/backlog/ggeom-pred-pow-six-sub-one.md
new file mode 100644
index 000000000..d0cbdab35
--- /dev/null
+++ b/backlog/ggeom-pred-pow-six-sub-one.md
@@ -0,0 +1,7 @@
+# ggeom-pred-pow-six-sub-one
+
+n minus one divides n to the 6 minus one.
+
+- **Source:** self-seeded polynomial-divisibility identity family.
+- **Reference:** n minus one divides n to the 6 minus one. Provable by exhibiting the cofactor and `ring`.
+- **Difficulty:** 1
diff --git a/goals/ggeom-pred-pow-six-sub-one.aisp b/goals/ggeom-pred-pow-six-sub-one.aisp
new file mode 100644
index 000000000..fe1812199
--- /dev/null
+++ b/goals/ggeom-pred-pow-six-sub-one.aisp
@@ -0,0 +1,20 @@
+𝔸5.1.goal.ggeom-pred-pow-six-sub-one@2026-06-17
+γ≔unsorry.goal
+⟦Ω:Goal⟧{
+  id≜ggeom-pred-pow-six-sub-one
+  phase≜prove
+  status≜proved
+  difficulty≜1
+}
+⟦Σ:Source⟧{
+  src≜backlog/ggeom-pred-pow-six-sub-one.md
+}
+⟦Γ:Deps⟧{
+  deps≜⟨⟩
+}
+⟦Λ:Artifact⟧{
+  lean≜goals/ggeom-pred-pow-six-sub-one.lean
+  sha≜40e9fe30cf4d1c490bb14bfecdb006c526e580ceb7c5b06a50637f03179af96a
+  aff≜0
+}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/goals/ggeom-pred-pow-six-sub-one.lean b/goals/ggeom-pred-pow-six-sub-one.lean
new file mode 100644
index 000000000..5ccab80a4
--- /dev/null
+++ b/goals/ggeom-pred-pow-six-sub-one.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem ggeom_pred_pow_six_sub_one (n : ℤ) : (n - 1) ∣ (n^6 - 1) := by
+  sorry
diff --git a/library/Unsorry/GgeomPredPowSixSubOne.lean b/library/Unsorry/GgeomPredPowSixSubOne.lean
new file mode 100644
index 000000000..cd09ce805
--- /dev/null
+++ b/library/Unsorry/GgeomPredPowSixSubOne.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem ggeom_pred_pow_six_sub_one (n : ℤ) : (n - 1) ∣ (n^6 - 1) := by
+  exact ⟨n^5 + n^4 + n^3 + n^2 + n + 1, by ring⟩
diff --git a/library/index/40e9fe30cf4d1c490bb14bfecdb006c526e580ceb7c5b06a50637f03179af96a.aisp b/library/index/40e9fe30cf4d1c490bb14bfecdb006c526e580ceb7c5b06a50637f03179af96a.aisp
new file mode 100644
index 000000000..fc0b7ffef
--- /dev/null
+++ b/library/index/40e9fe30cf4d1c490bb14bfecdb006c526e580ceb7c5b06a50637f03179af96a.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.lemma.40e9fe30cf4d@2026-06-17
+γ≔unsorry.lemma.index
+⟦Ω:Lemma⟧{sha≜40e9fe30cf4d1c490bb14bfecdb006c526e580ceb7c5b06a50637f03179af96a; goal≜ggeom-pred-pow-six-sub-one; name≜ggeom_pred_pow_six_sub_one}
+⟦Σ:Source⟧{src≜goals/ggeom-pred-pow-six-sub-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/ggeom-pred-pow-six-sub-one.mac-158f.20260617t181902893624z-2f6d006e.aisp b/proof-runs/ggeom-pred-pow-six-sub-one.mac-158f.20260617t181902893624z-2f6d006e.aisp
new file mode 100644
index 000000000..b85f7cd50
--- /dev/null
+++ b/proof-runs/ggeom-pred-pow-six-sub-one.mac-158f.20260617t181902893624z-2f6d006e.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.run.ggeom-pred-pow-six-sub-one.mac-158f.20260617t181902893624z-2f6d006e@2026-06-17
+γ≔unsorry.proof.run
+⟦Ω:Run⟧{id≜20260617t181902893624z-2f6d006e; goal≜ggeom-pred-pow-six-sub-one; agent≜mac-158f; outcome≜proved}
+⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
+⟦Γ:Goal⟧{goal≜ggeom-pred-pow-six-sub-one}
+⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:19:02Z}
+⟦Σ:Artifact⟧{sha≜40e9fe30cf4d1c490bb14bfecdb006c526e580ceb7c5b06a50637f03179af96a}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩