diff --git a/backlog/ggeom-pred-pow-two-sub-one.md b/backlog/ggeom-pred-pow-two-sub-one.md
new file mode 100644
index 000000000..55e2645c8
--- /dev/null
+++ b/backlog/ggeom-pred-pow-two-sub-one.md
@@ -0,0 +1,7 @@
+# ggeom-pred-pow-two-sub-one
+
+n minus one divides n to the 2 minus one.
+
+- **Source:** self-seeded polynomial-divisibility identity family.
+- **Reference:** n minus one divides n to the 2 minus one. Provable by exhibiting the cofactor and `ring`.
+- **Difficulty:** 1
diff --git a/goals/ggeom-pred-pow-two-sub-one.aisp b/goals/ggeom-pred-pow-two-sub-one.aisp
new file mode 100644
index 000000000..14e9d95c7
--- /dev/null
+++ b/goals/ggeom-pred-pow-two-sub-one.aisp
@@ -0,0 +1,20 @@
+𝔸5.1.goal.ggeom-pred-pow-two-sub-one@2026-06-17
+γ≔unsorry.goal
+⟦Ω:Goal⟧{
+  id≜ggeom-pred-pow-two-sub-one
+  phase≜prove
+  status≜proved
+  difficulty≜1
+}
+⟦Σ:Source⟧{
+  src≜backlog/ggeom-pred-pow-two-sub-one.md
+}
+⟦Γ:Deps⟧{
+  deps≜⟨⟩
+}
+⟦Λ:Artifact⟧{
+  lean≜goals/ggeom-pred-pow-two-sub-one.lean
+  sha≜973e100a0f74cbc72307737d03e67d9ddf99ebba347ec27ddea9410a1eb85c1f
+  aff≜0
+}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
diff --git a/goals/ggeom-pred-pow-two-sub-one.lean b/goals/ggeom-pred-pow-two-sub-one.lean
new file mode 100644
index 000000000..989448692
--- /dev/null
+++ b/goals/ggeom-pred-pow-two-sub-one.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem ggeom_pred_pow_two_sub_one (n : ℤ) : (n - 1) ∣ (n^2 - 1) := by
+  sorry
diff --git a/library/Unsorry/GgeomPredPowTwoSubOne.lean b/library/Unsorry/GgeomPredPowTwoSubOne.lean
new file mode 100644
index 000000000..fa5077cc3
--- /dev/null
+++ b/library/Unsorry/GgeomPredPowTwoSubOne.lean
@@ -0,0 +1,4 @@
+import Mathlib
+
+theorem ggeom_pred_pow_two_sub_one (n : ℤ) : (n - 1) ∣ (n^2 - 1) := by
+  exact ⟨n + 1, by ring⟩
diff --git a/library/index/973e100a0f74cbc72307737d03e67d9ddf99ebba347ec27ddea9410a1eb85c1f.aisp b/library/index/973e100a0f74cbc72307737d03e67d9ddf99ebba347ec27ddea9410a1eb85c1f.aisp
new file mode 100644
index 000000000..6828cfb62
--- /dev/null
+++ b/library/index/973e100a0f74cbc72307737d03e67d9ddf99ebba347ec27ddea9410a1eb85c1f.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.lemma.973e100a0f74@2026-06-17
+γ≔unsorry.lemma.index
+⟦Ω:Lemma⟧{sha≜973e100a0f74cbc72307737d03e67d9ddf99ebba347ec27ddea9410a1eb85c1f; goal≜ggeom-pred-pow-two-sub-one; name≜ggeom_pred_pow_two_sub_one}
+⟦Σ:Source⟧{src≜goals/ggeom-pred-pow-two-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-two-sub-one.mac-158f.20260617t181757355528z-d3cfbeb8.aisp b/proof-runs/ggeom-pred-pow-two-sub-one.mac-158f.20260617t181757355528z-d3cfbeb8.aisp
new file mode 100644
index 000000000..56dd01ce4
--- /dev/null
+++ b/proof-runs/ggeom-pred-pow-two-sub-one.mac-158f.20260617t181757355528z-d3cfbeb8.aisp
@@ -0,0 +1,8 @@
+𝔸5.1.run.ggeom-pred-pow-two-sub-one.mac-158f.20260617t181757355528z-d3cfbeb8@2026-06-17
+γ≔unsorry.proof.run
+⟦Ω:Run⟧{id≜20260617t181757355528z-d3cfbeb8; goal≜ggeom-pred-pow-two-sub-one; agent≜mac-158f; outcome≜proved}
+⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
+⟦Γ:Goal⟧{goal≜ggeom-pred-pow-two-sub-one}
+⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:17:57Z}
+⟦Σ:Artifact⟧{sha≜973e100a0f74cbc72307737d03e67d9ddf99ebba347ec27ddea9410a1eb85c1f}
+⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩