ALP-ttbar Toy MC v1.6: Post-registration Results for a Magnetic-Field and Material-Budget Scan of the Two-Hypothesis Vertex Fit for Displaced Light ALP → e⁺e⁻

Post-registration results of version 1.6 of an independent toy Monte Carlo series motivated by the displaced-dielectron study of long-lived axion-like particles in top-quark pair events (Alimena et al., arXiv:2610.38932), which extends the displaced-dimuon strategy of Rygaard et al. (JHEP 10 (2023) 138). The analysis follows the preregistration doi:10.5281/zenodo.23942338, which was frozen on GitHub and Zenodo before any v1.6 result was computed. It also confirms, at two further field values, the boundary reference distribution that replaced Wilks' theorem in v1.5. v1.5 (doi:10.5281/zenodo.23924862) found no gain from a two-hypothesis vertex fit at 17-50 MeV in a 3.8 T field. v1.6 repeats that analysis in eight preregistered configurations of the magnetic field (3.8 to 0.2 T) and a material scale factor (1 to 0.25), on a subsample. Limit degradation from conversions at 17 MeV (ctau = 1 mm): 127x at 3.8 T, 65x and 35x with half and a quarter of the material, but 155-188x at 2.0-0.2 T. Material is the effective handle: the 17 MeV loss falls roughly in proportion to the material, faster than the conversion yield alone, because bremsstrahlung and fake openings fall too. Lowering the field does not help the lightest ALPs: with little bending the conversion vertex resolution grows from 7.9 to 48 mm and the material veto stops working. At 100-200 MeV the chi-square separation improves strongly at low field (200 MeV without mass window: 130x to 52x), but the 1/B momentum resolution offsets this once the mass window is used; the best field is about 1 T. Four of seven predictions were confirmed (P1, P2, P3, P7) and three refuted (P4, P5, P6). Wilks' theorem, revisited. In v1.5 the preregistered chi2_1 null reference (Wilks' theorem) failed: with a free vertex the opening angle is identified only at second order and the null lies on a parameter boundary, so the correct reference is the mixture 1/2 chi2_0 + 1/2 chi2_1 (Chernoff 1954; Self and Liang 1987). v1.6 fixed this mixture as the reference in advance, and validation Y1 passed at 0.2 T and 2.0 T. The full v1.5 record (what was preregistered, what was observed, why Wilks' theorem does not apply, table and Figure 9) is reproduced in Appendix A of the PDF; the v1.5 failure stays recorded as a failed preregistered validation. Future directions: a three-dimensional vertex fit including the r-z opening; a Gaussian-sum filter with ACTS; a dimuon control study; extension to mu+mu- above 200 MeV and other long-lived-particle signatures, including ALPs from B-meson decays; a location-dependent material model; and calibrated test statistics, i.e. checking the regularity conditions before assuming Wilks' theorem and making the null reference selectable in the code (Wilks, Chernoff or Self-Liang boundary mixtures, reparametrisation, or pseudo-experiments), as already standard in collider searches (Cowan et al. 2011). The PDF is the report; the zip contains the full code, outputs and Figures 1-10 (same files as the GitHub repository). Independent personal toy study, not affiliated with the authors of the referenced papers, the CMS, LHCb or ALICE Collaborations, or the FCC study. Only qualitative trends and ratios are meaningful.