fix: correct Guttman ring counts and speed up the search

[Atilaac]

Problem

compute_guttmann_rings contracted the T–O–T network into a T–T graph, discarding the bridging oxygens and adding an edge between every pair of formers on a shared oxygen. Three defects followed:

1. Phantom 3-rings from oxygen triclusters. An oxygen bonded to three formers contributed C(3,2) = 3 edges — a triangle — reported as a 3-ring. In the real network that walk re-enters the same oxygen three times, so it is not a ring at all. It inflates the 3-ring count, which is the structural marker for the D₂ Raman band, and it bites hardest in aluminosilicates and borosilicates.
2. Edge-sharing polyhedra were invisible. Two formers bridged by two oxygens produced the same edge twice, and nx.Graph collapses duplicates, so no 2-membered ring could be reported at any max_size.
3. No periodic closure check. Neighbour lists return atom indices under minimum image, so a path that leaves the cell and re-enters through the opposite face comes back to the same index and looked like a ring. It is a helix, and it over-counts large rings in small cells.

Alongside these: nx.all_shortest_paths swept the entire graph for every edge with no early stop, making the search O(E·V); the parallel path shipped the whole edge list once per edge; max_size filtered after the fact rather than bounding the search; and _ring_is_primitive was dead code that both the module docstring and the theory doc claimed was applied. It was not — and Guttman shortest-path rings are a looser set than primitive rings, so those claims were wrong either way.

Solution

The search now runs on the bipartite T–O atom network: formers and oxygens are both nodes, and the only edges are T–O bonds. Both graph defects dissolve mechanically rather than by special-casing — BFS paths are simple, so a path cannot route through the same tricluster oxygen twice, and two bridging oxygens are two distinct nodes forming a genuine four-node cycle.

Candidate cycles must now close in real space: the minimum-image bond vectors summed around the loop must vanish, at a 1e-6 Å tolerance. When every shortest closure through a bond fails that test, the search deepens two atoms at a time until it finds the shortest one that does close, the same behaviour as the RINGS reference implementation.

The BFS stops as soon as the level containing the target is complete, touching only nodes within the ring's own radius instead of the whole network. That is where the speedup comes from, and it also makes max_size almost free.

networkx is no longer used here or anywhere else in the repo, so the dependency is dropped. Deduplication now keys on the full T–O cycle, keeping rings that share formers but differ in bridging oxygens distinct.

Performance

System	max_size	Before	After
20Na2O–80SiO2, 300 atoms	12	0.017 s	0.008 s
20Na2O–10B2O3–70SiO2, 30,080 atoms	12	61.9 s	1.18 s
20Na2O–10B2O3–70SiO2, 30,080 atoms	40	64.3 s	1.15 s

Behaviour changes to be aware of

• Ring histograms change for every structure. Jobs already cached in SQLite hold prefix numbers and need ?rerun=all.
• n_cpus only engages above ~100,000 T–O bonds. Below that, the search stays sequential regardless, because starting worker processes costs more than it saves.
• Public signature, return type, and the T-atom size convention are unchanged.

[codecov]

Codecov Report

❌ Patch coverage is 95.02262% with 11 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...spy/src/amorphouspy/properties/structural/rings.py	95.02%	11 Missing ⚠️

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