Consolidate benchmarks around interpolative Gaussian inputs

[shinaoka]

Summary

• reduce the repository to three maintained cases: Fourier elementwise, rotated-anisotropic Gaussian elementwise global versus patched, and Gaussian MPO-MPO contraction global versus patched
• remove isotropic and smooth Gaussian families, TCI input generation, independent R sweeps, obsolete runners, Julia checks, stale design material, and old result profiles
• generate each Gaussian independently with two-dimensional multiscale interpolative decomposition and principal-axis unsafe points
• combine terms with deterministic balanced pairwise add-and-L2/SVD compression, then apply final relative-L2/SVD input tolerance 1e-6
• fix the patch cap at 128 and share atomic HDF5 input caches between the two Gaussian cases
• keep global and patched ACI elementwise arms while recording their internal residual metric separately from the common sampled relative-L2 validation metric
• update CI, documentation, report validation, and result metadata for the consolidated design

The future variational alternative to pairwise sum compression is tracked in tensor4all-rs issue tensor4all/tensor4all-rs#660.

Fresh benchmark profile

The committed linux-epyc-7713p profile was measured on an AMD EPYC 7713P 64-Core Processor, pinned to CPU core 0 with single-threaded Rayon and BLAS. No hostname is recorded.

Gaussian input points:

N	raw chi	compressed chi
2	32	16
8	50	24
32	64	41
128	99	64

All 48 records pass their accuracy gates. Maximum sampled relative-L2 error is 4.67e-6 for Gaussian elementwise and 2.11e-6 for Gaussian MPO contraction. Case 3 reuses the exact Case 2 cache keys at every point.

At compressed chi 64:

• elementwise global fit: 0.329 s
• elementwise patched fit: 4.084 s
• elementwise global ACI: 0.213 s
• elementwise patched ACI: 8.942 s
• MPO contraction global fit: 0.436 s
• MPO contraction patched fit: 0.299 s, 1.456x speedup

The cap does not bind through chi 64, so every recorded output remains one patch. The report states this directly through patch-count and maximum-patch-chi columns rather than claiming an asymptotic patching crossover.

Verification

• cargo fmt --all -- --check
• cargo clippy --locked --all-targets -- -D warnings
• cargo test --release --locked (21 passed)
• cargo check --locked --all-targets
• all three CI smoke runners, with Case 2 and Case 3 sharing one cache
• python3 scripts/report.py result/linux-epyc-7713p
• python3 -m py_compile scripts/report.py
• 48-record artifact and required-field audit
• git diff --check origin/main...HEAD
• branch contains current origin/main
• independent review: Correct-to-merge; all review findings and optional stale-code nits fixed