Reconstruct the declared field from boundary measurements. The decoder uses the samples you supply, not the generator’s hidden coefficients.
Default field u = 2 + 3x + x² − y², plus βJ. At (1/5, −3/10, 1/3), J = -11/300. After k transport steps the preimage is x = A to the power −k applied to y. This view uses k = 0.
Generator reference at the source probe: 2.40333333. This is not an imported field’s true value. Reconstruction from the generator’s samples: 2.55000000. Residual against the twelve-node family: 1.332e-15. Absolute tolerance 0.000001. A large-magnitude field can fail this absolute test even when its relative error is small. Additional sample: not used. Recovered beta from the active samples: —.
Exact-model samples of u, which do not include β, beside the generator’s binary64 samples of u+βJ.