I am not Richard but I get asked this question a lot on the carbon transfer forum. Here is basically how I understand the issue.
First, the correct syntax for entering data for the GRAY_CURVE command is as follows, with the example.
GRAY_CURVE="0;0 7;10 13;20 20;30 28;40 37;50 43;55 49;60 57;65 65;70 73;75 80;81 86;86 93;92 95;95 100;100"
However, this curve data can NOT be used with the LINEARIZE command, at least as I understand the matter.
There are three types of instruments used in measuring photo samples, densitometer, colorimeter and spectrophotometer.
A densitometer measures density. It measures the amount of light reflected or transmitted by a sample, then reports density as log or dot percent. The measurements of a densitometer can be used to create gray curves for linearizing QTR profiles, but these measurements can not be used to derive the LAB values that are necessary for linearizing with the LINEARIZE command.
A colorimeter measures a sample, then (from this data) computes LAB values internally by processing the measured data. Colorimeters are relatively inexpensive devices. Examples Datacolor Spyder Print 3 and 4 and Color Munki. Since the colorimeter can provide, via computation, LAB values, it can be used with the LINEARITY command with QTR profiles.
The most sophisticated, and expensive, color measurement instrument is a spectrophotometer, which measures the spectrum of a sample, reporting the reflectance or transmittance of a sample at regular intervals. The spectrum can be used to calculate all other measurements, such as density and LAB. Most spectrophotometers are capable of providing the LAB values, as well as other types of measurements. Examples are the X-Rite Eye One and Eye One 2. The LAB measurements given by a spectrophotometer can also be used with the LINEARITY command.