**NOTES AND MINOR CORRECTIONS**

ON THE PROOF OF LEMMA 1 IN APPENDIX A:  The definition of g_i(y) as an infimum should be ignored (it is a holdover from a simplified version of the lemma).  Instead one should appeal to, e.g., the result of J. Czipszer & L. Geher from 1955 (https://link.springer.com/article/10.1007/BF02021278) to obtain the necessary extension of each coordinate function \tilde{g}_i.  This further requires that \Delta satisfies, e.g., all three properties listed in section 3 of Czipszer & Geher's paper.  These assumptions should be implicitly assumed about \Delta throughout.


ON THE PARTITION OF UNITY UTILIZED IN APPENDIX F (Proof of Proposition 6):  A nice proof that the "spike" functions defined in appendix F really do form a partition of unity can be found in Lemma 3.6 of Pan, Hutter, and Bolcskei (https://arxiv.org/pdf/2407.01250).


Please do reach out with any additional questions/corrections/issues concerning this paper.

Mark Iwen, March 10, 2025