Function forward_model_from_base_xs 

pub fn forward_model_from_base_xs(
    energies: &[f64],
    base_xs: &[Vec<f64>],
    resonance_data: &[ResonanceData],
    thicknesses: &[f64],
    temperature_k: f64,
    instrument: Option<&InstrumentParams>,
) -> Result<Vec<f64>, TransmissionError>

Compute a transmission spectrum from precomputed unbroadened cross-sections.

Applies Doppler broadening and Beer-Lambert using cached base XS, then resolution broadening on the total transmission (issue #442). This skips the expensive Reich-Moore calculation, making it suitable for use inside TransmissionFitModel::evaluate() when temperature is a free parameter.

The full pipeline runs on the auxiliary extended grid (boundary extension + resonance fine-structure points) so that Doppler AND resolution broadening have adequate quadrature support and correct boundary handling; the data-grid points are extracted LAST. This mirrors the non-cached forward_model and broadened_cross_sections_for_transmission exactly — previously this cached path collapsed σ to the coarse data grid before resolution broadening, degrading the convolution near the grid edges and around narrow resonances.

Pipeline:

1. Per isotope: build σ on the extended grid (cached data-grid values + freshly-evaluated auxiliary points), Doppler-broaden on the extended grid
2. Accumulate total attenuation on the extended grid: Σᵢ nᵢ·σ_{D,i}
3. Beer-Lambert: T = exp(−attenuation) on the extended grid
4. Resolution: T_broad = R ⊗ T on the extended grid (when instrument present)
5. Extract the data-grid points