feat(bo): Bayesian optimization with a Gaussian process model, log-EI and a Latin hypercube design

[tachsin]

The first part of batch B in the optimization plan: Bayesian optimization, for expensive black-box functions. It follows the decisions in #381 and #379.

Foundations:

• Portable erf, erfc and the scaled erfcx in math.
• Real::latin_hypercube.
• EI, log-EI, PI and UCB, with their gradients, in algorithm::bo::acquisition. Log-EI's gradient goes through the Mills ratio, with an asymptotic series below z = −64, its coefficients checked with mpmath.

model::gp, public and marked unstable for one release:

• Gaussian process regression with a constant mean, profiled at its GLS estimate (Jones et al. 1998, eq. 5), and an ARD Matérn 5/2 or squared exponential kernel.
• Hyperparameters by maximum log marginal likelihood, with genoxide's own L-BFGS-B and GPML eq. 5.9's gradient, from several seeded starts.
• predict and predict_with_gradient.
• Checked against GPML: eqs. 2.20, 2.25-2.26 with Algorithm 2.1, 2.30, 4.17, 5.8 and 5.9.

Bo:

• A Latin hypercube of 2(n + 1) points first, then one point per generation: the model is fitted, then log-EI is maximized from 1,000 raw samples and 10 L-BFGS-B starts with its analytic gradient.
• Acquisitions: log-EI (default), EI, PI and UCB.
• Output::Standardize (default) or Output::Log, for objectives like Goldstein-Price.
• It never asks a point twice. Invalid points enter the model at the worst valid value.
• Re-evaluation and checkpoints; the same bits on every thread count.

Noise: none by default, which differs from the plan. The jitter is the only nugget, so the model interpolates deterministic functions. Learned noise blurred the minimum: within 80 evaluations over 20 seeds, f* + 1e-4 was reached by:

Problem	Noise-free	Learned noise
Branin	20/20	14/20
Six-hump camel	20/20	17/20
Hartmann 3	20/20	12/20

Noise::Learned stays available for noisy functions.

In Python and the CLI: gx.Bo and gx.model.gp.GaussianProcess; type = "bo".

The bayesian_optimization example: Branin, with the posterior mean and log-EI drawn per step in a new surrogate plot. It ends 2.1e-5 above the global minimum after 31 evaluations, using a final L-BFGS-B polish on the GP mean and one evaluation. Rust and Python give identical output and traces.

Tests:

• The GP against hand-worked formulas to 1e-13.
• Every gradient against finite differences.
• Branin, six-hump camel, Hartmann 3, and Goldstein-Price with Log, each reaching f* + 1e-3.
• Reproducibility, checkpoints and validation.
• Two portable_runs entries, and a Rust and Python cross-check.

Coming in B2: batch BO (Kriging believer, constant liar), AsyncEngine, constrained BO, integer genes, and their examples.