[audit 2026-07-09] General bugs for emulator interface and emulator-specific issues #451

Issues found by math-auditor: M - "major", m - "minor", h - "hygeine"

Forward-map wrapper

• M2 — predict ignores add_obs_noise_cov entirely; always returns Γ as the uncertainty of a deterministic map.
• M3 — predict crashes (DimensionMismatch) for any truncating output encoder.

General emulator interface

• M1 — with default noise_learn=true, add_obs_noise_cov=false still returns noise-inflated covariance and =true adds only the 1e-3 jitter — the flag's meaning is inverted relative to its docs
• m9 — passing an already-built MLT into a new Emulator only warns "already built. skipping...", but the constructor still fits a new encoder schedule to the new data, silently pairing old-encoder-trained models with new encoders.
• h10 — show.jl labels model count "(one per output dimension)" when it should say encoded output dimension; contradicts the adjacent Emulator display under truncating encoders.

GaussianProcess emulator

• m7 — add_obs_noise_cov=true adds alg_reg_noise·diag(Γ), silently dropping off-diagonal noise correlations; scale also wrong unless noise_learn=false.
• m10 — AGPJL ArgumentError message tells users the wrong parameter index (model_params[end-2] instead of [end-1]) and omits a value for log_std_noise.
• m11 — WhiteKernel semantics differ across backends at training-point coincidence (sklearn always zero cross-covariance; GPJL/AGPJL give σ²) — same hyperparameters, different predictions.
• h11 — _predict allocates Float64 buffers regardless of input eltype (silent Float32 demotion; blocks Dual numbers for GPJL/SKLJL), plus assorted dead variables/branches.

RandomFeature emulator (Scalar/Vector)

• M5 — documented optimizer option "prior" is silently ignored; the rebuild branch is provably dead.
• m1 — NICE correlation-noise level formula wrong by a scaling factor.
• m2 — latent data race (Threads.@threads shared read-modify-write) in mean_of_covs; currently unreachable but would silently corrupt \Gamma if the commented-out approx_σ2 code is re-enabled.
• m3 — coefficient-penalty observable drops the regularization factor λ relative to stated theory (matches only at the λ=1 default).
• m4 — predict docstrings claim noise-inclusive covariance, but default is add_obs_noise_cov=false (same trap direction as M1).
• m5 — scalar interface silently keeps only the diagonal of the output structure matrix while the vector interface uses the full matrix on identical input; no warning.
• h1 — tullio_threading = "tullio" hardcoded as a String where the API implies Bool; latent break on dependency update.
• h2 — docstrings document "prior_in_scale"/"prior_out_scale" options that are never read.
• h3 — objective RNG streams differ across multithread modes; seeded results change with JULIA_NUM_THREADS.
• h5 — cov_sample_multiplier's documented minimum (0.0) permits n_cov_samples ∈ {0,1}, producing NaN covariance downstream.