ControlPoint Manual — versioned with the code; every worked example below is a REAL corpus job and its numbers are pinned by the test suite.
4 — Adjust
What it does
One click runs the least-squares adjustment: free first (internal consistency), then constrained to your held control — final coordinates are always adjusted TO control, never to the arbitrary frame the angles came in. Every observation type gets its own error factor (directions, distances, zeniths — or levels vs tape transfers in the 1D module), and a contamination gate stops the software recommending a rescale while a known fault is still in the data.
Worked example — the 2HPX levelling champion
97 level observations, 76 stations, five benchmarks. Error factor σ̂₀ = 0.943, inside the 95% chi-square bounds — the a-priori weighting honestly describes the work. Compare the corpus sweep: the legacy default of 2.403 mm/km proved ~7× pessimistic on this instrument's jobs.
Theory in one paragraph
Least squares finds the coordinates that minimise the weighted sum of squared corrections to your observations. The error factor compares the corrections it needed against what your sigmas promised: ≈1 means honest weights; the chi-square bounds say how far from 1 is explainable by luck on this many observations.