Are altimeters calibrated to ISA geopotential altitude or ISA geometric altitude? Altimeters convert a pressure measurement to an indication of altitude. When set to standard pressure setting (1013.25 hPa / 29.92"Hg), they assume the atmosphere is according to the ICAO Standard Atmosphere (ISA) and indicate the altitude accordingly. However, ISA has two altitude definitions; geometric altitude and geopotential altitude. 

The ICAO Standard Atmosphere is a model of the atmosphere up to 80 kilometres high, based on the perfect gas law and the hydrostatic equation.  In order to deal with the effects of reduction of gravity with height, it uses the concept of geopotential altitude H: 

$$H= \frac{1}{g_0}\int_0^hgdh$$

with:


$h = \textrm{geometric altitude}$
$H = \textrm{geopotential altitude}$
$g_0 = 9.80665\textrm{ m/s, mean gravitational acceleration at mean sea level}$
$g = \textrm{local acceleration of gravity (height dependent)}$


Gravity is given by :

$$g = g_0 \left(\frac{r_e}{r_e + z}\right)^2$$
with:


$r_e = \textrm{the radius of the earth}$


And thus the relation between geopotential altitude and geometric altitude is given by: 

$$H = h\frac{r_e}{r_e+h}$$
And
$$h = H\frac{r_e}{r_e-H}$$

In the ISA model, the properties of the atmosphere (pressure, temperature, density) are all calculated with respect to geopotential height. 

For a geopotential height of 12 500 meters (41 010.5 ft), which corresponds to a geometric height of 12524.6 meters (41091.3 ft), the ICAO atmosphere gives a pressure of 178.648 hPa. 

My question is: what will a perfectly calibrated altimeter indicate when the pressure is 178.648 hPa? Does it indicate 41 010.5 ft (the geopotential altitude) or does it indicate 41091.3 ft (the geometric altitude)? 

You might say that the difference is "only" 80 feet, but for RVSM operations that is quite significant. 

The ICAO standard atmosphere (as described in ICAO Doc 7488) does not give the answer (at least I couldn't find it). And it includes tables for every 500 meters of both geopotential and geometric altitude, so that does not make it easier. 

I'd like to know which altitude is indicated on an altimeter (ISA geopotential or ISA geometric) and where (in which official document) this is specified.
The TSO for Air Data Computers is TSO-C106. It specifies for the minimum performance standard "SAE Aerospace Standard 8002, Air Data Computer - Minimum Performance Standard."  

From AS8002:


  3.6 Altitude Reference:
  
  Calibration of the static air sensing mechanism for pressure altitude
  outputs (including baro-corrected if supplied) shall be to the
  geopotential altitude tables of U.S. Standard Atmosphere, 1976.


While this is a US standard, the FAA asserts it is in compliance with ICAO Doc 7488.  

For RVSM, additional requirements are levied against the installation primarily focused on reduction of static source error (SSE). That guidance is available in AC 91-85A.  

It's important to remember that absolute accuracy at altitude is not as important as everyone adhering to the same reference.