Q1 [partially_resolved] Boxed question, Section 2: For finite concept classes C, is RTD(C) in O(VCD(C)), i.e., does the RTD of a finite concept class never exceed its VCD by more than a constant factor c? | remains open: Prove RTD(C) ≤ c·VCD(C) for a universal constant c (or exhibit a sequence of finite classes with RTD/VCD → ∞); concretely, close the gap between the O(d^2) upper bound of Hu et al. 2017 and the 5/3 lower ratio of Chen-Cheng-Tang 2016, noting that any proof must go beyond the recursive greedy teachin
Q2 [partially_resolved] Equivalent reformulation stated in Section 2 (via Doliwa et al. 2014): For finite concept classes C, is TD_min(C) in O(VCD(C)), i.e., does the best-case teaching dimension of a finite concept class never exceed its VCD by more than a constant factor c? | remains open: Show that every finite class of VC dimension d contains a concept with a teaching set of size O(d) (or construct classes with TD_min/VCD unbounded); the O(d^2) bound of Hu et al. 2017 is the best known and the greedy k-point construction cannot improve it to O(d) for k ≤ ⌈cd⌉.
Q3 [resolved] Implicit sub-remark (Abstract and Section 3, not boxed): 'To date, no finite class C with RTD(C) > 3/2 VCD(C) has been found' -- does any finite class have RTD/VCD ratio exceeding 3/2? | remains open: Nothing for this sub-remark as such (ratio 5/3 > 3/2 is exhibited); whether any finite class achieves a ratio above 5/3, or whether the ratio is bounded at all, is subsumed by Q1.