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prove(gself-pow-six-add-pow-four): gself_pow_six_add_pow_four by mac-158f #2239

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43a1cd6
prove(gself-pow-six-add-pow-four): gself_pow_six_add_pow_four by mac-…
ohdearquant Jun 17, 2026
771a6c6
Merge branch 'main' into queued/prove/gself-pow-six-add-pow-four/mac-…
perttu Jun 18, 2026
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7 changes: 7 additions & 0 deletions backlog/gself-pow-six-add-pow-four.md
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# gself-pow-six-add-pow-four

n to the 1 divides n to the 6 plus n to the 4.

- **Source:** self-seeded polynomial-divisibility identity family.
- **Reference:** n to the 1 divides n to the 6 plus n to the 4. Provable by exhibiting the cofactor and `ring`.
- **Difficulty:** 1
20 changes: 20 additions & 0 deletions goals/gself-pow-six-add-pow-four.aisp
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𝔸5.1.goal.gself-pow-six-add-pow-four@2026-06-17
γ≔unsorry.goal
⟦Ω:Goal⟧{
id≜gself-pow-six-add-pow-four
phase≜prove
status≜proved
difficulty≜1
}
⟦Σ:Source⟧{
src≜backlog/gself-pow-six-add-pow-four.md
}
⟦Γ:Deps⟧{
deps≜⟨⟩
}
⟦Λ:Artifact⟧{
lean≜goals/gself-pow-six-add-pow-four.lean
sha≜fabd9af2348551dd0d3d368701ad8a88fc6589529147a2da5439692d152ff44a
aff≜0
}
⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
4 changes: 4 additions & 0 deletions goals/gself-pow-six-add-pow-four.lean
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import Mathlib

theorem gself_pow_six_add_pow_four (n : ℤ) : (n) ∣ (n^6 + n^4) := by
sorry
4 changes: 4 additions & 0 deletions library/Unsorry/GselfPowSixAddPowFour.lean
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import Mathlib

theorem gself_pow_six_add_pow_four (n : ℤ) : (n) ∣ (n^6 + n^4) := by
exact ⟨n^5 + n^3, by ring⟩
8 changes: 8 additions & 0 deletions library/index/fabd9af2348551dd0d3d368701ad8a88fc6589529147a2da5439692d152ff44a.aisp
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𝔸5.1.lemma.fabd9af23485@2026-06-17
γ≔unsorry.lemma.index
⟦Ω:Lemma⟧{sha≜fabd9af2348551dd0d3d368701ad8a88fc6589529147a2da5439692d152ff44a; goal≜gself-pow-six-add-pow-four; name≜gself_pow_six_add_pow_four}
⟦Σ:Source⟧{src≜goals/gself-pow-six-add-pow-four.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≜◊⁺⟩
8 changes: 8 additions & 0 deletions proof-runs/gself-pow-six-add-pow-four.mac-158f.20260617t182449370855z-70e27665.aisp
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𝔸5.1.run.gself-pow-six-add-pow-four.mac-158f.20260617t182449370855z-70e27665@2026-06-17
γ≔unsorry.proof.run
⟦Ω:Run⟧{id≜20260617t182449370855z-70e27665; goal≜gself-pow-six-add-pow-four; agent≜mac-158f; outcome≜proved}
⟦Π:Provenance⟧{solver≜ohdearquant; provider≜claude; model≜template-ring-cofactor}
⟦Γ:Goal⟧{goal≜gself-pow-six-add-pow-four}
⟦Λ:Metrics⟧{attempts≜1; solve_s≜0; ended≜2026-06-17T18:24:49Z}
⟦Σ:Artifact⟧{sha≜fabd9af2348551dd0d3d368701ad8a88fc6589529147a2da5439692d152ff44a}
⟦Ε⟧⟨δ≜0.60;τ≜◊⁺⟩
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