ALP-ttbar Toy MC v1.7 — Preregistration: Three-Dimensional Two-Hypothesis Vertex Fit (Adding the r–z Opening Angle) for Displaced Light ALP → e⁺e⁻

Preregistration (frozen before any v1.7 result) of version 1.7 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). It is the first preregistration in the series to apply the calibrated-test-statistics procedure proposed in v1.6: the regularity conditions of each test are checked and the null reference distributions are fixed in advance. v1.5 and v1.6 (doi:10.5281/zenodo.23952888) used only the transverse view, where a free vertex absorbs a small ALP opening angle and bremsstrahlung makes about 10% of conversions look opening-angle-like. In the r-z view the tracks are not bent, a vertex shift cannot absorb a polar opening, bremsstrahlung barely changes the polar angle, and conversions have almost no polar opening. v1.7 adds z measurements (pixel layers, 25 um; a stereo-strip variant as secondary) and an r-z two-hypothesis fit on top of the unchanged transverse fit. A secondary variant with z measured at every layer (V-allpixel), a toy stand-in for the all-pixel trackers of next-generation concepts, was added before any computation. The document fixes in advance the longitudinal simulation (separate random stream, so the transverse hits are identical to v1.5/v1.6), the sequential 3D fit, the selection, a sanity gate, validation criteria (Z1-Z3) and seven predictions (P1-P7). Reference distributions: chi2_1 for the regular r-z test (Wilks), 1/2 chi2_0 + 1/2 chi2_1 for the transverse boundary test (v1.5), and 1/2 chi2_1 + 1/2 chi2_2 for their sum. A related-work section notes that using the r-z opening (delta cot theta) against conversions and 3D vertex fitting are standard, and that all-pixel trackers are pursued by ALICE 3 and the FCC-ee concepts, and limits the claim to this search. The PDF reproduces the frozen README unchanged (SHA-256 b538ea630b620aa881ca46f57320b530db439700e63c7ec0c50841e1d1ec3beb) and adds two figures made only from analytic formulas and truth-level quantities of the published v1.5 samples. No v1.7 simulation or fit had been run when it was written. The zip contains the same files as the GitHub repository; the repository history shows the first commit and the amendment that added V-allpixel and P7, both before any computation. 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.