The background budget behind Paper A's T6 kill condition: how often does an atmospheric-neutrino background alone throw an accidental multi-track cluster inside a search cone, at a given detector rate, cone size, coincidence window, and multiplicity threshold? Set the cuts and read off the expected false multiplet count over a survey livetime.
A search cone of radius θ subtends solid angle Ω = 2π(1 − cos θ). If the full up-going hemisphere (2π sr) sees a background rate R (events/yr), the cone sees a fraction Ω/2π of it, giving a cone background rate λ = R·(Ω/2π) in events/s. Over a coincidence window of duration w, the Poisson expectation is μ = λ·w, and the probability of an accidental multiplet of k or more tracks in one window is the Poisson upper tail
P(≥k) = 1 − Σi=0k−1 e−μμi/i!
which for the small μ typical of a background-free search reduces to the leading term μᵏ/k!. Multiplying by the number of independent windows in the survey livetime gives the expected count of accidental multiplets over the whole campaign — the number that must be small for a single confirmed multiplet to be trusted as a genuine trigger.
The number above is for one fixed window duration. A real search scans several candidate window lengths (Paper A notes generous headroom even after this correction), which multiplies the single-window false-alarm count by roughly the number of independent durations scanned. The trials note below applies a fiducial ×10 scan penalty to the expected count; it does not change the per-window μ or P(≥k) shown in the outputs above.
At the T6 fiducials — full-array ARCA background R = 10³ yr⁻¹ over the up-going hemisphere, 1° cone, 10³ s window, k = 3, 10 yr livetime — this tool gives λ ≈ 4.8×10⁻⁹ s⁻¹, μ ≈ 4.8×10⁻⁶, P(≥3) ≈ 1.9×10⁻¹⁷, ≈3.16×10⁵ independent windows per decade, and an expected false-multiplet count ≈ 6×10⁻¹² per decade — the same order of magnitude as Paper A's rounded headline of ~10⁻¹¹ per decade (Swanson 2026, "Macro Transcension Hypothesis," §7). The criterion is background-free by many orders of magnitude; the practical limit on T6 is exposure, not background.