What does this research mean for the field?

The Erdős-Ginzburg-Ziv Theorem, along with its foundational proofs for prime and composite moduli and its lattice generalizations, can be exhaustively synthesized and 100% machine-verified using the Lean 4 interactive theorem prover. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Provide a comprehensive theoretical synthesis and machine-checked formal verification of the Erdős-Ginzburg-Ziv theorem and its algebraic extensions in additive number theory.

August 29, 2026Open Access

Erdős-Ginzburg-Ziv Theorem on Zero-Sum Sequences

View Full Paper

Ask AI

Bookmark

Provide a comprehensive theoretical synthesis and machine-checked formal verification of the Erdős-Ginzburg-Ziv theorem and its algebraic extensions in additive number theory.
Derived proofs for prime moduli using Chevalley-Warning symmetric power systems over finite fields and Cauchy-Davenport additive expansion.
Established composite modulus cases via block partitioning and hierarchical averaging induction, alongside review of two-dimensional lattice generalizations.
Machine-certified the base cases, sharpness thresholds, and submultiset sum predicates using the Lean 4 interactive theorem prover and Mathlib.
Proved the exact minimality of the 2n - 1 length threshold using the extremal multiset containing n - 1 zeros and n - 1 ones.
Demonstrated that validity for factors a and b unconditionally guarantees validity for composite products n = ab through non-elliptical induction.
Completed formalization in Lean 4 with zero unproven sorry placeholders, zero custom axioms, and zero linter warnings.

Discussion

No takes yet. Share an insight, caveat, or question.

Implication

Mathematical analysis demonstrates zero-sum sequence existence and complete Lean 4 formalization in integer multisets, highlighting algebraic connections across additive combinatorics.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a92994d8e5d7d1fc0c11280 https://doi.org/10.5281/zenodo.22132951

View Full Paper

Ask AI

Bookmark

Implication

Mathematical analysis demonstrates zero-sum sequence existence and complete Lean 4 formalization in integer multisets, highlighting algebraic connections across additive combinatorics.

Erdős-Ginzburg-Ziv Theorem on Zero-Sum Sequences

Key Points

Discussion

Implication

Cite This Study

Erdős-Ginzburg-Ziv Theorem on Zero-Sum Sequences

Key Points

Discussion

Implication

Cite This Study

Also Consider

Also Consider