Hi, Mike,

  I heard more than once a remark that if a space telescope 
will go to an cis-lunar space of L2, it can see millions
of black holes. Number "millions" caught my ear.

  Following reasoning in your paper https://doi.org/10.3847/1538-4357/ab2bed
we assume that a 4m EHE will have SEFD 2D4 Jy at 245 GHz. Paired 
with phased ALMA with SEFD 150 mJy and recording at 128Gbps,
its 1-sigma sensitivity will be 0.88 sqrt ( 2.D4*1.5D2/(2*32D9) ) = 6 mJy.
One can detect a point-like source if its brighter 7 sigma
or 40 mJy for one second of integration time. Observing for 30 sec, the 
detection limit drops to 40/sqrt(30) = 7 mJy. SEFD of LMT, APEX are 
at best 4000 Jy. LMT/EHE baseline is a factor of sqrt(4000/150) = 5 less
sensitive. A 35 mJy source can be detected for 30 sec at 128Gbps at 
that baseline.

  Figure 5R in your paper https://doi.org/10.3847/1538-4357/ac2eb5 
provides a plot of source count at a given "horizon-scale" flux density.
I took a rule and got an approximate number of the total number (thick
black line) from that graph:

100 mJy:    1
 10 mJy   ~20
  1 mJy  ~400

  These numbers seem to me reasonable. That means that observing in
favorite conditions we can detect up to ~40 sources. Compare 
with > 20,000 sources we have detected and imaged at ground-ground 
baselines at 1.4-8 GHz. In order to claim detection of a ring, one need 
to have sensitivity at least a factor of 2-3 greater than the detection 
limit. That means that at best, an EHE/ALMA interferometer can 
potentially detect rings at one-two dozens of source provided, ... 
a long number of conditions.

  In a nutshell, although EHE can see millions of AGNs, the number of 
sources a 4m-EHE/phasedALMA instrument can detect at 245 GHz is 
measured in dozens, not in millions. In order to detect one million
sources, one need to reach a detection limit at a ~10 microJy level. 
A pair of space antennas with a diameter 1km is needed for that.
The number of detectable sources at lower frequencies is of course, 
much greater, although it is measured in hundreds or thousands, 
not in millions for an interferometer 4 meter space antenna + ground.
  
  An inflatable 30-m class space antenna will improve sensitivity
by a factor of 30/4 = 7.5 and increase the number of detectable sources
at 245 GHz to several hundreds.

Leonid
2022.01.14_12:21:30