perf(prover): default the cuda table scheduler to K = num_airs

[MauroToscano]

The cuda arm of table_parallelism() scales K by available_parallelism()
(cores * 2 / 3). Measured over 881 runs on two RTX 5090 boxes, that is the wrong
shape — not the wrong constant.

All eight core-count curves fit T(K) = S + max(Tmax, W/K) within run-to-run noise,
and the work K divides (W ≈ 5.3–8.0 s) is invariant to host core count over an 8×
range, to CPU model, and to rayon pool width. The decisive one: cutting
RAYON_NUM_THREADS 32 → 4 leaves W alone and merely doubles S, with the best K still
num_airs at every pool width. available_parallelism() sizes precisely that rayon
pool, so it is the wrong quantity to scale K by — K is not a thread count, each
table's work runs on the one global pool.

Worst case against the best measured K, over four core counts on both boxes:

rule	worst case
cores/3	+30.2%
cores*2/3 (what this replaces)	+13.0%
constant 12	+7.0%
num_airs	+1.6%

cores*2/3 fails where predicted: low core counts, K=2 at 4 cores (+13.0%), K=5 at 8
cores (+8.1%). No K below num_airs is significantly faster than num_airs anywhere
on either box (every such cell p ≥ 0.38 at n=8).

Taking the ceiling rather than solving for an optimum is right in both regimes of the
fit: if W/num_airs > Tmax more K strictly helps; if W/num_airs < Tmax the extra
drivers are floor-limited and cost nothing — the one staging slab is held 56% of wall
at K=31 and wall time still improves.

The old doc comment's mechanism ("in-flight tables mostly sit in GPU waits") is not
what happens — mean GPU utilisation never exceeded ~38% at any K — so it is rewritten
rather than re-tuned. What is meant to bound concurrency is memory admission rather
than a count: that is what VramGate is for.

auto_storage is held bounded

table_parallelism now takes num_airs and clamps to it, replacing the .min(num_airs)
the call site applied. auto_storage::decide keeps a bounded figure through the new
storage_estimate_parallelism(): peak_bytes sums the transient bytes of the top-k
tables, so an unbounded k there sums every table — measured +27% at 128 PAGE tables,
+44% at 512 — and would spill proofs to disk that fit in RAM. Its value is unchanged,
so no storage decision moves. Two tests pin both halves.

The CPU arm is untouched

cores / 3 stays. The sweep ran only on cuda builds, where the parallelized work is
device-bound; on a CPU-only build every table is pure host work and none of this
evidence transfers.

Evidence

The full sweep record — both rounds' write-ups, every result CSV and the re-runnable
harnesses, so every number above is checkable — lives in a gist to keep this diff
reviewable: https://gist.github.com/MauroToscano/54cdbf03da9a69517ae30c964efc2827
(filenames are the original scripts/profiling/table-parallelism-sweep/ paths
flattened with __; 00_INDEX.md maps the layout).

Honest limits

• One GPU model (RTX 5090) and one workload throughout: 6.8M cycles, 4 epochs at
  epoch-size-log2 21, ~31 tables. Production tables are much larger, so memory per
  concurrently-admitted table is larger and the auto_storage interaction is unverified
  at that scale — a big-block check is a merge gate, not something this PR establishes.
• Low-core legs are cache-confounded against round 1 (this box's taskset -c 0-7 is one
  CCD with 32 MB L3 vs the 3D part's much larger cache).
• W is inferred from T(1) − T(best), not instrumented per phase.
• Round 1's headline "knee K≈8" should not be quoted: the curve is S + W/K with no
  saturating resource, so a tolerance-knee is derived and reads 8 on one box and 16 on
  the other at the same 5% tolerance.

Verified

cargo fmt --check clean; cargo clippy --all-targets -p stark -p lambda-vm-prover
clean. auto_storage_tests 8 passed (needs --features disk-spill);
table_parallelism_stays_within_one_and_num_airs passes. The cuda-gated test and the
cuda arm itself cannot compile here — no local CUDA toolchain — so both were verified by
reading plus a non-cuda build.

[github-actions]

GPU Benchmark (ABBA) — c4132f815e vs main (14 pairs)

_{RTX 5090 · Vast.ai datacenter · prover/cuda · ethrex real block, continuations · drift-free A/B/B/A}

❌ Run failed. Last log lines: