ALP-ttbar Toy MC v2.0: Series Overview (v1.0–v1.9) — What a Preregistered Toy Study Learned about Displaced Light ALP → e⁺e⁻ and Photon Conversions, and Open Questions for Full-Simulation Studies

Overview of versions 1.0 to 1.9 of a small, numpy-only toy Monte Carlo series motivated by the displaced-dielectron study of long-lived ALPs in top-quark events by Alimena et al. (arXiv:2610.38932), which extends the displaced-dimuon strategy of Rygaard et al. (JHEP 10 (2023) 138). No new simulation or fit: every number is taken from the published records, which are listed with their DOIs. The series asked, at toy level, how photon conversions in tracker material limit a search for displaced light ALPs decaying to e⁺e⁻, a limitation stated explicitly in the generator-level study, and what reduces it. In this toy, at 17 MeV and cτ = 1 mm the loss in reach from the conversion veto is about 2× without bremsstrahlung but 126–178× with it at nominal material; better electron fits and a two-hypothesis vertex fit barely change it; reducing the material is the only large handle (127× → 35× for a quarter of the material); measuring z at every layer adds to it (→ 27×); and the arrangement of the pixel layers at fixed material does not matter. Of 48 predictions frozen in advance (v1.2–v1.9), 32 were confirmed and 16 refuted. One preregistered validation failed instructively: in v1.5 the likelihood-ratio test did not follow Wilks' χ²₁, because the opening angle is identified only at second order and the null lies on a boundary; Wilks was replaced by the Chernoff / Self–Liang boundary result (½χ²₀ + ½χ²₁), and boundary-aware references were preregistered from then on and confirmed. The overview lists seven lessons, a dedicated section on the failed Wilks validation, six open questions that full or fast simulation could check, and related public work on next-generation low-material trackers (HL-LHC CMS Phase-2 and ATLAS ITk, ALICE ITS3, ALICE 3, FCC-ee IDEA/CLD, FCC-SEED). It turns the toy results into six suggestions for tracker studies, offered for discussion rather than as design recommendations: add a displaced, collimated e⁺e⁻ benchmark to layout studies; count material where displaced vertices occur; consider coarse z information in the outer tracker; treat the material veto as part of the design; note that for sub-mrad openings material reduction may matter more than electron-fit sophistication; and calibrate conversion-versus-decay discriminants. Planned next steps include an improved material veto, a dimuon control study, μ⁺μ⁻ above 200 MeV, ALPs from B-meson decays, other long-lived-particle signatures with displaced lepton pairs, and a lepton-collider toy geometry. The zip also contains the one-page overviews posted with earlier compilations, unchanged. Independent personal project by a non-specialist, not affiliated with the authors of the referenced papers or with any collaboration. Absolute numbers are not predictions for any real detector; only trends and ratios inside the toy are meaningful. GitHub: https://github.com/wspaik5/ALP_ttbar_Toy_MC_v2.0_Series_Overview