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Research / Jan 2026–Aug 3, 2026

Sparse additive bases for sets of density zero (Erdős #333)

The numbered question and its assumptions are given in the linked Erdős problem statement.

Model / AI: Aletheia, GPT-5.2

self-reporteddebunked (novelty claim)
Aug 3, 2026

Sparse additive bases for sets of density zero (Erdős #333) — retracted claim

Model / AI: GPT-5.2

debunked (novelty claim)

announced as solved with GPT-5.2; Erdős had resolved it himself in a 1977 paper. Barreto retracted, saying "I've fallen for this twice now".

Source review pending. Imported from the original notes; linked claims and artifacts have not been re-audited in this restructuring.