ALP-ttbar Toy MC v1.9 — Preregistration: Layer Geometry at Fixed Material for the All-Pixel Three-Dimensional Vertex Fit of Displaced Light ALP → e⁺e⁻

Preregistration of version 1.9 of a small, numpy-only toy Monte Carlo study motivated by the displaced-dielectron extension (Alimena et al., arXiv:2610.38932) of the top-associated long-lived ALP strategy of Rygaard et al. (JHEP 10 (2023) 138). This plan was frozen on GitHub before any v1.9 simulation or fit was run; the PDF reproduces the frozen README unchanged (SHA-256 9370cf0a0519d8075340655c1c181684b15557784f8a0a943b777059b6f40085) and adds two figures made only from the geometry definitions, an analytic resolution formula and published v1.6/v1.8 numbers. v1.8 found that the 17 MeV loss is set mainly by multiple scattering relative to the small opening angle, and that reducing the material helps. v1.9 asks whether the placement of the layers matters at fixed total material (f = 0.25, 3.8 T, z at every layer): G0 (v1.8 geometry), G1 (first pixel layer moved from 29 to 20 mm), G2 (eight pixel layers of half thickness instead of four) and G3 (both). An analytic estimate made in advance suggests at most about 17% better r–z resolution, partly offset by more material bands in the veto. Seven predictions (P1–P7), a sanity gate and three validations (U1–U3) are fixed in advance. Low-material trackers with many thin layers are pursued by next-generation concepts such as ALICE 3, ALICE ITS3 and the FCC-ee detectors; this toy only changes the layer radii and makes no statement about their performance. Independent personal project, not affiliated with the authors of the referenced papers or with any collaboration. GitHub: https://github.com/wspaik5/ALP_ttbar_Toy_MC_v1.9_Preregistration_Layer_Geometry