What was already known
Steinerberger’s full-chord construction gave O(L^(1/3)). Earlier discrepancy theorems supplied ingredients, but not the weighted and chord-length forms needed here.
AI involvement
Korsky chose the endpoint-pair strategy and source theorems. His later clarification credits GPT-5.5 with the retained weighted discrepancy adaptations and chord-length bound; Korsky wrote the proof.
The author's clarification specifically assigns the retained weighted technical lemmas, which make the stated bounds work, to GPT-5.5; the strategy was human.
Importance
Gives polylogarithmic upper and logarithmic lower bounds in the restricted full-chord model.
Limitations
The lower bound is disk-specific. The reported numerical disk and ellipse checks do not verify either theorem. The broader bounded-discrepancy question remains open.
Technical verification
The problem record reports numerical quadrature and sampling checks of the chord-crossing reduction and growth proxies, with stated errors, but explicitly says neither upper nor lower theorem was checked. Numerical tests do not count as a machine checking method under the curation rule.
Human understanding
Korsky identifies why endpoint pairs convert crossings to rectangles and explains how weighted discrepancy and chord-length control yield the two bounds; no central mechanism is reported unexplained.
Correction and publication history
Gives polylogarithmic upper and logarithmic lower bounds in the restricted full-chord model.
Read this published revision