Dual Sequential Fat-Shattering and Tight Threshold Extraction
Nothing has been published against this problem here, and nobody has checked anything. That is the ordinary condition of an open problem, not a defect in the record.
Statement
Two open problems about extracting order from trees in real-valued functions. A quantitative function analogue of Hodges's tree-to-order extraction yields an at most double-exponential bound on dual sequential fat-shattering dimension, resolving the first. A new proof of Daskalakis-Golowich tight-threshold extraction, avoiding multicolored Ramsey numbers, resolves the second, which concerned repairing the bound in a result claimed by Jung, Kim and Tewari.
Context
Open questions from recent papers at the junction of model theory and statistical learning theory, documented but read by a small community.
People
Projects
Nobody is running a project on this. A project is a stated goal, a thread, and one thing somebody else could do. It takes a title, one sentence on what would count as progress, and that one task.
Interest
Nobody has said they are looking at this. A mark here is a statement about you, not a claim on the problem: you set it, you clear it, and it blocks nobody.
Attempts
No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.
The acknowledgements separate human and AI credit explicitly and attribute specific steps. Proposition 3.4 was provided by ChatGPT on direct request. The authors' original Theorem 1.11 gave only a uniform analogue with a weaker bound; asked whether the bound could be improved, the model proposed the two-parameter inductive scheme that gives the current one, and it identified that the uniformity hypotheses were an artifact of an imprecise formulation, letting the authors drop them. For Theorem 1.14 the authors handed over their draft with a description of the obstacles and asked for a proof; the model generated an argument following their induction scheme and two-case structure. The authors checked and thoroughly rewrote everything.
Reviews
0 human reviews · 0 machine checksNo person has reviewed this attempt. It has not been checked at all.
Endorsements
0 endorsementsNo one has endorsed this attempt. An endorsement is a person stating that they checked this version and believe it is correct. None has been recorded — which is information, not an omission.
Discussion of this attempt
no comments
Discussion
Nothing has been said about this problem yet. Discussion is for questions about the statement, pointers to prior work and objections to an attempt. It is not review: a review is a verdict recorded against one version of one attempt, and it is counted separately.
Reading every thread is open to everyone. Posting needs an account with posting rights — sign in to check yours.