How to measure a voltage without going to the lab

This is work in collaboration with Dirk van der Marel.

The figure above with its caption, from arXiv:2201.11883v1, shows what is claimed to be a "Measured voltage" MV(T) for CSH, or "carbonaceous sulfur hydride", a material reported to be a room temperature superconductor in Nature 586, 373 (2020). The "Measured voltage" (red curve) changes rapidly between the vertical dotted lines, supposedly indicating a "superconducting transition". The blue curve labeled UDB1(T) is claimed to be a "user defined background" which, in the transition region between the vertical dotted lines, is supposedly independent of MV(T), since only the "profile of the regions highlighted in blue" in the left panel were "used as part of the UDB1", as the Fig. caption explains.

In the following you will learn how to calculate MV(T) in the transition region starting from UDB1(T), without measuring anything.

1) Pick any line between 203 and 253 in this file: 160 GPa data, the "superconducting transition region" for that pressure, temperature range 169.5824K to 170.2829K. That file has the numerical data given in table 5 of arXiv:2111.15017 underlying the published susceptibility data in Nature 586, 373 (2020), "Room-temperature superconductivity in a carbonaceous sulfur hydride".
2) Select the values for:
line #, Temperature, n(T), "Measured Voltage", "Superconducting Signal", to be entered below.
3) Enter the values in what follows. Then, calculate "Non-measured Voltage" NMV(T) and compare with "Measured Voltage" MV(T)

Enter line # :
Enter Temperature :
Enter n(T) :
Enter "Measured Voltage" (MV) :
Enter "Superconducting Signal" (SS): Then, click on the boxes below to get the answers.
=
Note: the difference UDB1=MV-SS is the "user defined background method 1" defined in arXiv:2201.11883v1, which is supposedly independent of the "Measured Voltage" in the transition region.

Using T₀=170.2829, a=2.6164, b=-0.352704, c=-0.0984839, d=-0.126134:
=
=
=
Compare with MV(T): =
% difference: =

Note that starting from UDB1, a single integer number n(T) allowed you to calculate a "Non-measured Voltage" NMV(T) that reproduces the "Measured Voltage" MV(T) to 7 or 8 digit accuracy. Try replacing n(T) by any other integer and verify that the agreement is now 4 digits or less.
Example of how to do this (2 min movie). Then try it yourself for another line between 203 and 253. Did it work?

For details on this calculation and its implications, see https://osf.io/2gyj9 . An extended in-depth analysis of these and other data is given in IJMPB 2375001 (2022), and MRE 7, 048401 (2022), and EPL 137 36001 (2022), and Chem. Commun. 59, 5765 (2023).