Kernel-prove the weak Giuga prime-divisor criterion

[DomTheDeveloper]

Green result

The exact historical proof of the weak Giuga prime-divisor criterion now compiles against the current catalog definitions:

IsWeakGiuga n ↔ ∀ p ∈ n.primeFactors, p ∣ (n / p - 1)

for composite n.

Verification

Focused run 30213363291 passed:

• exact historical source-blob verification;
• current catalog-module build;
• exact theorem extraction without reformatting;
• no-hole/no-trust scan;
• complete Lean compilation;
• exact theorem axiom audit.

Axiom footprint:

[propext, Classical.choice, Quot.sound]

No sorryAx or compiler-trust dependency appears. The build has only deprecation/unused-simp warnings inherited from the historical proof.

Status

Green proof recovery. The canonical admitted declaration still needs a focused restoration and style cleanup before promotion to _PRs/ready/. This audit-only PR should not merge.

[github-actions]

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