On two questions of Qi on saturated filtrations

Jihao Liu, Haofeng Zhang

Abstract

We answer two questions of Qi [J. Reine Angew. Math. 830 (2026)] on the metric space of saturated filtrations, one affirmatively and one negatively. The main result of this paper was obtained by Chatgpt 5.5 pro, and the Danus system based on the Rethlas system.

Disclosure

“nuous in time, with H( · , 0) ≡ o• and H( · , 1) = id. In particular the argument uses neither a field assumption nor the geodesic structure of FilsR,m . Remark 1.5. The sketch of the proof of the main result of this paper was obtained by Chatgpt 5.5 pro, and later summed up, verified, and properly written by the Danus system, a specialized agent built on Rethlas and substantially more capable for fundamental mathematical research based on the Rethlas system. Human verification and”

PDF page 2
Classification
Substantial proof generation
Multiplier
10
Verified

Structural counts

Pages 6 pdf
Theorems 2 source
Lemmas 6 source
Propositions 0 source
Corollaries 0 source
Definitions 0 source
Displayed equations 32 source
Bibliography entries 4 source
Appendix pages 0 estimated

Count notes

  • Source counts use the expanded primary TeX file main_1_.tex.
  • Appendix pages include the first PDF page with an explicit Appendix heading through the final page.