`site_multiplicities` stores the orbit size of the analyzed cell, not the intrinsic Wyckoff multiplicity

[EBB2675]

Follow-up on #304, which introduced these quantities. Belongs under #219.

In schema_packages/model_system.py, the description of site_multiplicities (L 472-488) says the value is the multiplicity in the conventional cell and that it "remains the same" in primitive cells and supercells, being an intrinsic property of the Wyckoff position.

_compute_site_multiplicities (lines 858-893) instead counts, per atom, how many atoms share its equivalent_atoms index in whatever cell it was handed. Its own docstring (865-866) states this, so the disagreement is internal to the file.

Call sites diverge:

• Line 967 (resolve_analyzed_cell) is shared by both branches. The conventional branch gets get_equivalent_atoms_conventional() and therefore matches the description; the primitive branch does not.
• Line 1064 (resolve_bulk_symmetry) uses get_equivalent_atoms_original(), so ModelSystem.local_symmetry reflects whatever cell the parser produced.

Observed

fcc Cu, space group 225, single site 4a, three input cells:

input cell	original	primitive	conventional
primitive (1 atom)	1	1	4
conventional (4 atoms)	4	1	4
2x2x2 supercell (32 atoms)	32	1	4

Only the conventional column is invariant under the choice of input cell. The supercell reports 32, which is not a Wyckoff multiplicity of any position in space group 225.

Reproducer (spglib 2.7.0, matid 2.2.0, ASE 3.29.0)

from ase.build import bulk
from matid.symmetry import SymmetryAnalyzer

def site_multiplicities(equivalent_atoms):  # current implementation
    equiv = list(equivalent_atoms)
    return [equiv.count(equiv[i]) for i in range(len(equiv))]

for label, atoms in [('primitive', bulk('Cu', 'fcc', a=3.6)),
                     ('conventional', bulk('Cu', 'fcc', a=3.6, cubic=True)),
                     ('2x2x2', bulk('Cu', 'fcc', a=3.6, cubic=True) * (2, 2, 2))]:
    sa = SymmetryAnalyzer(atoms, symmetry_tol=0.1)
    print(label, site_multiplicities(sa.get_equivalent_atoms_original())[0])
# primitive 1 / conventional 4 / 2x2x2 32

Question

Which is intended?

Intrinsic (what the description promises): no extra spglib call needed. Multiplicity is fixed per Wyckoff letter within a space group, independent of the free parameters of a parametric position, so the map can be built once from the conventional cell:

conv_letters = [str(x) for x in sa.get_wyckoff_letters_conventional()]
conv_equiv = list(sa.get_equivalent_atoms_conventional())
mult_by_letter = {l: conv_equiv.count(e) for l, e in zip(conv_letters, conv_equiv)}
site_mults = [mult_by_letter[l] for l in letters_of_this_cell]

This gives 4a for both the primitive Cu cell and the supercell, 4a/4b for NaCl primitive, 2c for hcp Ti.

Per-cell orbit size (what the code computes): the description needs rewriting, and the quantity arguably wants a name that does not say "multiplicity", since equivalent_atoms already encodes the grouping.

Impact

test_compute_site_multiplicities (tests/test_model_system.py 1350-1375) uses synthetic equivalent_atoms arrays only, so it passes under either reading and does not pin the behaviour.

One dependency related minor question: if #241 (PyXtal for symmetry analysis) is on the near roadmap, the intrinsic multiplicity would come from PyXtal's Wyckoff tables rather than from a second pass over the conventional cell, so that decision may want to come first