What was already known
Haight and Szemerédi established existence of such a set, and Erdős asked how fast its mass could grow.
AI involvement
Ho credits GPT-5.4 Pro with materially generating and shaping the argument through dialogue. Ho directed, revised and explained the work; Tao’s later proof is separately credited.
The author explicitly describes material model generation of the core arguments within human-guided iterative work.
Importance
Gives the sharp obstruction to growth for the integer-ratio question.
Limitations
Ho reports vetting the main construction, and Tao later explained a shorter proof using Bohr sets and simultaneous approximation. A complete human check of Ho’s exact manuscript is not documented; Tao also flagged missing attribution.
Technical verification
Ho says he vetted the main ideas, which checks the central construction's outline but does not document a complete rigorous proof check. Sothanaphan's reported standard AI check and Tao's replacement exposition do not by themselves establish a complete check of Ho's original argument.
Human understanding
Ho explains the logarithmic-comb and block-deletion mechanism in detail; Tao independently explains the central idea using simultaneous approximation and Bohr sets.
Correction and publication history
Gives the sharp obstruction to growth for the integer-ratio question.
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