test(sampling): seed the sequential vs standard bootstrap uniqueness test (#223)

[Sean-Koval]

Closes #223

Problem

tests/sampling.rs::test_seq_bootstrap_and_ind_matrix ended with a Monte Carlo check (AFML Snippet 4.9): 100 unseeded sequential-bootstrap draws against 100 unseeded uniform draws on the book's three-label example, asserting avg_seq >= avg_std.

Exact enumeration of every draw path (27 uniform samples and 27 weighted sequential paths) gives:

	E[avg uniqueness]	sd
standard bootstrap	0.64198	0.15635
sequential bootstrap	0.70564	0.13858

The gap is 0.0637. At N = 100 the SE of the difference is 0.0209, so the gap was only about 3.0 SE. Simulating from the exact distributions (200,000 replications) gives a failure rate of 0.114%, about 1 in 880 runs, which matches the one-off failure reported in the issue.

Fix

• Both samplers now use seeded StdRngs: seq_bootstrap_with_rng for the sequential side and StdRng::random_range for the uniform side. The test is now deterministic.

• N is raised to 20,000, so the tolerances hold for any seed and survive a change of RNG algorithm. The SE of the difference becomes 0.00148, and the test checks:

  • avg_seq - avg_std > 0.04 (the true gap is 0.0637, a 16 SE margin)
  • each mean within 0.01 of its exact value (more than 9 SE each)

  So the test still checks the AFML claim, and it also pins both expectations to their exact values rather than only their ordering.

• The reasoning is written up in a comment in the test.

Stability evidence

I ran a temporary test on a scratch branch through CI (workflow_dispatch, run 36374678402, tests job, Linux, debug). The scratch branch has since been deleted.

• Before (old logic, N = 100, avg_seq >= avg_std): 20 of 20,000 seeds fail (0.10%). A simulation from the exact distributions agrees: 228 failures in 200,000 runs (0.114%).
• After (new logic, N = 20,000, all three assertions): 0 of 200 seeds fail. Across those seeds the smallest gap was 0.0591 (the threshold is 0.04), and the largest deviations from the exact means were 0.0032 (standard) and 0.0034 (sequential), against a tolerance of 0.01.
• The committed test itself passes in the same run (test_seq_bootstrap_and_ind_matrix ... ok).

Other tests that assert on unseeded randomness (not changed here)

• crates/openquant/tests/docs_ef3m_examples.rs::ef3m_page runs M2N::mp_fit (25 runs, and each fit draws its starting p_1 from rand::rng()), then asserts the modal parameters are within 0.02 of the truth. There is no seeded EF3M API, so fixing this needs a *_with_rng variant of fit/single_fit_loop/mp_fit. That should be a follow-up.
• crates/openquant/tests/bet_sizing.rs::test_bet_size_reserve_fit_and_return_parameters calls bet_size_reserve_full, whose EM starts come from rand::rng(). It only asserts structural properties (sigma > 0, p in (0, 1), sizes in [-1, 1]), so it cannot fail by chance.
• crates/openquant/tests/ef3m.rs fit(...) tests only assert is_ok() and the parameter lengths.
• invalid_input.rs calls unseeded seq_bootstrap only for error paths and fully warmed-up samples, so its results are deterministic.
• No Python test uses unseeded np.random or random.

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