feat(strategy): add nystrom landmark-column transform for low-rank data

[andriypolanski]

PR kind

• fix
• feat

Summary

New registered transform nystrom. Splits the M budget across col(A), row(A), col(B), and row(B) — the same four spaces rsvd sketches — but gathers random landmark columns/rows instead of random projections, then thin-QR into Q.
Basis FLOPs are ~2 N M² (QR only), not rsvd's ~2 N² M sketches.

Honest trade-off (GPU-measured): on --fill lowrank accuracy is 1.0000, VRAM and FLOPs beat exact, but latency is slightly above exact so the dominance gate scores 0 (not an improvement under the one rule). Versus rsvd at the
same accuracy/VRAM it is much faster and fewer FLOPs. Does not touch rsvd.

Fixes #193

Validation

• python -m strategy.smoke — nystrom and rsvd both PASS
• python -m pytest strategy/tests/test_nystrom.py tests/ strategy/tests/ eval/tests/ -q
  — 240 passed, 1 failed (tests/test_correctness.py::test_fp16_incore_tiled_parity,
  pre-existing fp16 tolerance flake; unrelated to strategy/)
• python -m eval … on NVIDIA GeForce RTX 5090 (see scorecard)

GPU Result (required for feat PRs only)

metric	value
accuracy	1.0000
time complexity	O(N²M) + O(N M²) QR; 2.3× fewer FLOPs vs exact
latency	2423.28 ms
VRAM usage	713.1 MiB

Regime measured: N=12000, dtype=fp32, fill=lowrank, data-rank=16, rank M=1500, device=RTX 5090, seed=0, pairs=3

Comparison (same couples)

metric	exact	rsvd	nystrom (this)
accuracy	1.0	1.0000	1.0000
latency	2301.35 ms	5491.87 ms	2423.28 ms
VRAM	2208.1 MiB	713.1 MiB	713.1 MiB
FLOPs vs exact	1×	1.8× fewer	2.3× fewer
verdict	baseline	not an improvement (latency ≥ exact)	not an improvement (latency ≥ exact)

Raw scorecard (paste python -m eval … output or --json)

$ python -m eval --n 12000 --pairs 3 --fill lowrank --data-rank 16 \
    --rank-m 1500 --transforms nystrom,rsvd --seed 0

[eval] device     : NVIDIA GeForce RTX 5090 (PyTorch/CUDA)
[eval] couples     : 3 x (12000 x 12000)  fill=lowrank  dtype=fp32
[eval] rank_m (M)  : 1500
[eval] transforms  : nystrom, rsvd

=== eval report (n=12000, 3 couples, fp32, fill=lowrank, M=1500, seed=0) ===
  complexity : normal O(N^3)   smart O(N^2 * M)  (M=1500 fixed -> ~O(N^2))
  exact      :  2301.35 ms   peak   2208.1 MiB
  transform   accuracy      latency   peakVRAM   FLOPx        score
  -----------------------------------------------------------------
  nystrom       1.0000    2423.28ms    713.1MiB    2.3x            0  (not an improvement: latency ≥ exact)
  rsvd          1.0000    5491.87ms    713.1MiB    1.8x            0  (not an improvement: latency ≥ exact)
  best (highest score): nystrom

# Companion --fill decaying-spectrum --data-rank 64 (same N/M/device/seed):
  nystrom       1.0000    2425.16ms    713.1MiB    2.3x            0  (not an improvement: latency ≥ exact)
  rsvd          1.0000    5491.46ms    713.1MiB    1.8x            0  (not an improvement: latency ≥ exact)

Checklist

• CPU-safe validation passed (strategy.smoke if relevant, plus pytest tests/ strategy/tests/ eval/tests/).
• My commits do not include Co-authored-by footers for coding agents such as Cursor, Codex, Claude, Copilot, or similar tools.
• If this is a feat PR, I ran the scorer on unseen couples — no hardcoding of seeds/matrices.
• If this is a feat PR, accuracy and latency come from the same run at the same dtype.
• If this is a feat PR, this is an improvement (every cost axis down, accuracy held) or I
  state honestly which axis it trades — see the one rule in CONTRIBUTING.md.
  (Honest: accuracy held; VRAM + FLOPs beat exact; latency is slightly above exact → score 0.)
• Correctness gates pass:
  python eval/tests/test_eval.py,
  python strategy/tests/test_subspace.py,
  python tests/test_correctness.py.
• If this is a feat PR, I named the device and dtype so a reviewer can reproduce the numbers.

[github-actions]

Gate chain passed. This PR is queued for the next batched GPU evaluation window.

[zeokin]

Approved — eval:L (first tiered frontier result on the low-rank track).

GPU re-measurement (RTX PRO 500 Blackwell, fp32, lowrank rank-16, n=8192, same seed 777):

• nystrom @ M=64: accuracy 0.99999, latency 0.230s, VRAM 260 MiB, 42x fewer FLOPs, score 17.11 (dominates exact on all axes).
• 3-way rsvd (current frontier, #156) @ M=64: score 12.85; @ M=48: score 13.51.
• nystrom beats the frontier by +33% at equal M=64, +27% at each method's natural M -> both clear the >=25% eval:L bar. Stable across 3 seeds (17.07-17.11).

Why it wins: nystrom's landmark-column basis (~NM^2, column gather + QR) is ~100x cheaper in FLOPs than rsvd's Gaussian sketch (~N^2M), so it's faster even using more columns. Merges cleanly (additive; keeps main's 3-way rsvd). Label: eval:L.