33.62 turns neutron magnetic-moment gradient coupling into a tightening court: with one frozen spin-precession readout, blinded ±G scans, and a preregistered even–odd decomposition, μ_n or g_n must show an even-symmetry drift dominated by k2 × G² while k1 remains consistent with zero and the proton stays the odd-symmetry comparator.
Use this section as a compact machine-readable EFT reference.
33.62 turns neutron magnetic-moment gradient coupling into an even-function court. The admissible claim is not that any curvature under switching proves neutron ontology, but that a reversible gradient can leave the neutron readout unchanged under sign reversal while the amplitude grows mainly with G². That creates a clean contrast with the proton’s odd-symmetry linear response.
Measurement uses one preregistered decomposition aperture. The hard ledger includes μ_n or g_n from the spin-precession readout, the sign and magnitude of G under one repeatable calibration, the matched-pair even and odd components Δμ_n,even and Δμ_n,odd, the quadratic coefficient k2 from Δμ_n,even versus G², the linear coefficient k1 from drift versus G, and the residual structure that decides whether a linear-only model leaves systematic curvature.
The workflow freezes the gradient court before any verdict. A stable neutron instrument keeps the readout chain fixed, G is generated by a reversible external configuration with at least three magnitudes and both directions, geometry and the allowed model family are preregistered, gradient labels stay blinded during extraction, and interleaved +G, −G, 0 sequences with a fixed settling window suppress slow drift while ensuring that switching changes only the gradient configuration.
Controls must prove both sensitivity and decomposition logic. Under the same +G/−G/0 cadence, the proton should remain odd-dominant rather than even-dominant; a near-zero-gradient configuration should erase systematic dependence on pseudo-gradient labels; a geometry-matched low-gradient surrogate should strongly weaken or erase k2; and permutation of +G and −G labels must collapse the apparent quadratic scaling if the result is genuine.
Support requires stable even symmetry at matched |G|, Δμ_n,odd consistent with zero, a non-zero k2 that replicates across batches or days, k1 consistent with zero inside the preregistered window, and clean separation from proton, surrogate, and near-zero controls. Falsification follows from systematic +G/−G mismatch, a non-zero odd component, vanishing or unstable k2, linear dominance, or controls that reproduce comparable curvature. The named adversaries are magnetic-field gradients and geometric-phase artifacts, switching-linked thermal or mechanical stress, and extraction or window bias.
So the chapter closes only one tightened neutron magnetic-moment even-gradient ledger aligned with the V02/V08/V09 laboratory audit lane. It may not become a neutron ontology verdict, a magnetic-moment ontology, or a force-law rewrite. Its clean onward value is to hand an odd/even gradient-separation grammar to 33.63 and 33.64.