What does this research mean for the field?

Recent analytical breakthroughs resolving the Erdős Reciprocal Sums Conjecture for 3-AP free sets can be comprehensively exposited, and foundational components such as dyadic slice sum reductions can be formally verified using the Lean 4 interactive theorem prover. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To resolve the Erdős Reciprocal Sums Conjecture for sets of integers lacking arithmetic progressions and provide a formal, machine-checked verification of these analytical bounds.

August 29, 2026Open Access

Erdős Reciprocal Sums Conjecture for Sets without Arithmetic Progressions

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CNCharles EDOU NZE

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Implication

Theoretical analysis demonstrates finite reciprocal sum bounds in progression-free integer sets, confirming convergence through machine-checked verification.

Key Points

To resolve the Erdős Reciprocal Sums Conjecture for sets of integers lacking arithmetic progressions and provide a formal, machine-checked verification of these analytical bounds.
Derived an analytical dyadic slicing framework bounding reciprocal sums via sub-logarithmic density decay rates.
Synthesized higher-order Fourier analysis, almost-periodicity, and density increment strategies on Bohr sets from Bloom-Sisask and Kelley-Meka methodologies.
Formalized progression-free predicates, dyadic slice reductions, and reciprocal bounds using the Lean 4 interactive theorem prover with zero axioms or sorry placeholders.
Linked reciprocal sum convergence directly to density decay rates, validating the definitive finite bound for three-term arithmetic progressions.
Computed numerical evaluations and explicit reciprocal sums for greedy Stanley sequences and high-density Behrend sets.
Achieved machine-checked verification of core reductions and finite progression-free reciprocal evaluations in Mathlib with zero linter warnings.

Cite This Study

Charles EDOU NZE (2026) studied this question.

synapsesocial.com/papers/6a92997e8e5d7d1fc0c1182b https://doi.org/10.5281/zenodo.22133102

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Implication

Theoretical analysis demonstrates finite reciprocal sum bounds in progression-free integer sets, confirming convergence through machine-checked verification.

Erdős Reciprocal Sums Conjecture for Sets without Arithmetic Progressions

Discussion

Member takes

Implication

Key Points

Cite This Study

Erdős Reciprocal Sums Conjecture for Sets without Arithmetic Progressions

Discussion

Member takes

Implication

Key Points

Cite This Study

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