Unreliable reduced formula order

[Lattay]

Python version

3.13.5

Pymatgen version

2025.5.2

Operating system version

Fedora 25

Current behavior

Because of the choice of NaN for undefined electronegativities, the reduced_formula property of Composition is unreliable, further breaking systems like get_protostructure_label from matbench-discovery (https://github.com/janosh/matbench-discovery/blob/75f0ca207d9b60b64b65790b318e6680a9ac74c5/matbench_discovery/structure/prototype.py#L187-L188).

This is the consequence of NaN causing all comparision tests to be false, thus making the sorting order dependant.

Expected Behavior

The reduced formula is relied uppon by many hight throughput packages, thus it needs to be consistent.

Minimal example

Here is demonstration:

>>> import pymatgen.core
>>> pymatgen.core.Composition({"Zn":3,"Ar":1,"O":3}).reduced_formula
... warning about unphysical electronegativity
'Zn3ArO3'
>>> pymatgen.core.Composition({"Ar":1,"Zn":3,"O":3}).reduced_formula
... warning here
'ArZn3O3'

A simple solution would be to choose the equally unphysical yet consistently ordered float("+inf") value for "undefined" electronegativity.

Relevant files to reproduce this bug

No response