[SamuelBadr]

Adds a fourth maintained case, vertex_bse_contraction, as @shinaoka asked: a typical MPO-MPO contraction for two-particle vertices, the plain (unpatched) contraction.

The case

It contracts vertices of the single-impurity Anderson model as a Bethe-Salpeter equation does, Φ(ν, ν', ω) = Σ_ν₁ Γ(ν, ν₁, ω) χ0(ν₁, ω) F(ν₁, ν', ω): hadamard weights Γ by the bubble χ0 (diagonal in ω and ν₁), and partial_contract joins the result with F (contracting ν₁, diagonal in ω). Both steps are timed together, with two arms, zipup and fit (one sweep), truncating at τ/10 per bond. The error is the relative L2 error against the exact Φ at 4096 points; a run fails if it exceeds 10 τ.

The inputs are fixed data, so they are not generated: three ITensorMPS HDF5 files (τ = 1e-4, 1e-6, 1e-8; 60 MB together) are assets of the release vertex-bse-inputs-v1, which also describes their layout. The binary downloads a file once with curl into .cache/inputs/vertex_bse/ and reuses it afterwards; every run checks the file's structure and the result against the exact values. The default sweep is τ = 1e-4 and 1e-6; 1e-8 is opt-in.

AGENTS.md, the README, report.py (a Case 4 table and checks), run_all.sh and CI (a smoke run at τ = 1e-4) are updated accordingly. One new direct dependency, hdf5-metno (already in the graph through tensor4all-hdf5), to read the reference values. No result/ sweep is included.

Measured

One thread, AMD EPYC 9224 (a shared machine, so the times are indicative), tensor4all-rs a515738:

τ	input χ (Γ / F)	arm	time	relative L2 error	best attainable	peak memory of the process
1e-4	94 / 103	zipup	17 s	5.93e-5	5.89e-5	1.5 GB
1e-4	94 / 103	fit	33 s	5.92e-5	5.89e-5
1e-6	259 / 272	zipup	521 s	6.91e-7	6.74e-7	18 GB
1e-6	259 / 272	fit	821 s	6.82e-7	6.74e-7

"Best attainable" is the error of the exact contraction of the rounded inputs. τ = 1e-8 needs considerably more memory and was not run to completion. At this revision the fit starts from the zip-up result, so it costs at least as much as the zip-up.

Checked: cargo fmt --check, cargo clippy --all-targets -- -D warnings, cargo test --release, the download and cache path (a miss, then a hit), and report.py on the committed linux-ryzen-ai-9-hx-470 sweep plus these records.

The MPS groups store llim = -1 (no orthogonality center) because of tensor4all/tensor4all-rs#1041: load_mps rejects ITensorMPS's llim = 0.