feat: add Martinet totally real towers eval problem#385
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Add Theorem 3.2 of Bloom-Sawin-Schildkraut-Zhelezov (arXiv:2605.28781), the existence of asymptotically-good totally real towers: totally real number fields of growing degree with bounded root discriminant. This is the sole classical input taken as an axiom in the sum_product formalization of the refutation of the sum-product conjecture over ℝ (SumProduct.exists_totallyReal_discr_le), resting on Martinet's class field theory tower construction not yet in Mathlib. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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This PR adds Theorem 3.2 of Bloom–Sawin–Schildkraut–Zhelezov, The sum-product conjecture is false for real numbers (arXiv:2605.28781), as an eval problem: there is an absolute constant
C > 0such that for infinitely many degreesdthere is a totally real number fieldKof degreedoverℚwith|Δ_K| ≤ C^d(asymptotically-good totally real towers with bounded root discriminant). This is the sole classical input taken as an axiom in the sum_product formalization (SumProduct.exists_totallyReal_discr_le); it rests on Martinet's class field theory tower construction (Golod–Shafarevich), which is not yet in Mathlib, so it is a genuine known-hard gap rather than a project-invented one.The statement is a closed existential in pure Mathlib vocabulary (no trusted helper definitions). It was checked for faithfulness against the paper's Theorem 3.2 by an independent review (matched verbatim to the arXiv text), and the module builds with only the expected
sorry.🤖 Prepared with Claude Code