What does this research mean for the field?

The mathematical proofs resolving the Cameron-Erdős Conjecture on sum-free sets, including structural cardinality thresholds and parity dichotomies, are fully formalized and machine-verified using the Lean 4 interactive theorem prover. Novelty: ClaimNovelty.CONFIRMATORY. Consensus alignment: ConsensusAlignment.SUPPORTS_CONSENSUS.

What question did this study set out to answer?

To resolve the asymptotic enumeration of sum-free subsets in the Cameron-Erdős conjecture and construct a machine-checked formal proof.

August 29, 2026Open Access

Cameron-Erdős Conjecture on Sum-Free Sets

View Full Paper

Ask AI

Bookmark

Authors

CNCharles EDOU NZE

Discussion

Member takes

Implication

Theoretical analysis demonstrates asymptotic bounds for sum-free subsets in integer intervals, highlighting the formal verification of the Cameron-Erdős conjecture.

Key Points

To resolve the asymptotic enumeration of sum-free subsets in the Cameron-Erdős conjecture and construct a machine-checked formal proof.
Divided sum-free subsets into odd-dominant and even-dominant classes to apply distinct structural bounds.
Employed the hypergraph container method on 3-uniform hypergraphs of Schur triples to bound even-dominant subsets.
Formalized algebraic invariants and certificates in the Lean 4 interactive theorem prover using Mathlib.
Proved that the maximum cardinality of any sum-free subset of {1, …, N} is exactly μ(N) = ⌈N/2⌉.
Bounded odd-dominant subsets to |Sodd(N)| = O(2^(N/2)) and even-dominant subsets to |Seven(N)| = o(2^(N/2)), confirming s(N) = Θ(2^(N/2)).
Achieved complete machine-checked formal verification in Lean 4 with 0 axioms, 0 linter warnings, and 0 sorry placeholders.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a9299db8e5d7d1fc0c12256 https://doi.org/10.5281/zenodo.22131949

View Full Paper

Ask AI

Bookmark

Implication

Theoretical analysis demonstrates asymptotic bounds for sum-free subsets in integer intervals, highlighting the formal verification of the Cameron-Erdős conjecture.

Cameron-Erdős Conjecture on Sum-Free Sets

Discussion

Member takes

Implication

Key Points

Cite This Study

Cameron-Erdős Conjecture on Sum-Free Sets

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider