Source labels openChecked July 26, 2026

Lam--Litt conjecture: Omega Integrality Implies Algebraicity

implies 2): if the coefficients of $f$ satisfy the $\omega$ -integrality condition for some superlinear $\omega$ , then there exists $N$ such that for all $n$ , the $n$ -th coefficient of $f$ is in $\mathbb{Z}[1/N]$ .

Number theory AMS 11 AMS 14

Mathematical statement

implies 2): if the coefficients of $f$ satisfy the $\omega$ -integrality condition for some superlinear $\omega$ , then there exists $N$ such that for all $n$ , the $n$ -th coefficient of $f$ is in $\mathbb{Z}[1/N]$ .

Statement source: Litt's Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

lam_litt.variants.omega_integrality_implies_algebraicity

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem lam_litt.variants.omega_integrality_implies_algebraicity {n : ℕ} (f : PowerSeries ℚ)    (g : MvRatFunc (Fin (n + 1)) ℚ) (hODE : IsSolutionOfAlgebraicODE n f g)    (ω : Nat.Primes → ℤ) (hω : omegaSuperlinear ω ∧ omegaIntegral ω (PowerSeries.coeff · f)) :    ∃ N : ℕ, IsCoeffIntegralAdjointInvNat f N := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Litt's problem 1background arxiv/2501.13175background