Phase E Task 4. Medium-tier fill simulator per the design memo.
For each (level ∈ {L1,L2,L3}, side ∈ {Bid,Ask}):
λ(features) = exp(β · [1, spread_bps, L1_imb, OFI_5, log(τ+1)])
Per-snapshot Bernoulli fill probability for a posted limit order:
p = 1 − exp(−λ)
Market orders fill immediately at the opposite-side L1 quote (no slippage
modeled at medium tier). Closing actions (Side::None) return λ=0 — they
are handled separately in the env.
Scaffolding only. Task 5 fits the 30 coefficients (6 distributions × 5
features) from the 5.2M-trade historical tape. The skeleton constructor
uses β=0 → λ=1 → p≈0.632, a stable sanity default for early smokes.
Numeric guard: `linear.exp().min(50.0)` caps λ to prevent f32 overflow
under outlier features before fitting lands. Fitted models should stay
well below this cap in practice.
4 unit tests:
- skeleton_has_uniform_fill_prob (β=0 → p≈0.632 within 0.01)
- fill_prob_bounded_under_outlier_features
- lambda_cap_prevents_f32_overflow (β=100 outlier path)
- side_none_returns_zero_rate
`cargo test -p ml --lib env::fill_model`: 4 passed.
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