同一片夜空One Sky

總分Score = round(1000 × raw ÷ raw_標準解std)，raw = (w_D·D + w_R·R + w_C·C) × P。標準解（出題時對預報版搜出來的計畫）永遠是 1000 分；分數只在伺服器算，同一份計畫永遠同分。The standard plan (searched on the forecast when the challenge was set) always scores 1000; scores are computed on the server only, and the same plan always gets the same score.

D 深度depth = min(1.5, log₂(1 + S/N ÷ S/N_標準解std))，S/N = √n_pix · Σq·S·t ÷ √Σq·((S+B)·t + RN²)，n_pix = A_ref ÷ 像素尺度pixel scale²。比的是同一塊天空（固定面積），大像素灌不了分；拼接取跟目標相交各格裡最差的那格。It compares a fixed patch of sky, so big pixels cannot inflate it; mosaics take the worst tile that touches the target. 粗估Rough estimate

R 解析resolution = min(1, FWHM 需求req ÷ FWHM)，FWHM = √(seeing_eff² + 繞射diffraction² + 追蹤tracking²)，下限 2 × 像素尺度 × bin（彩色相機再 ×2）；seeing 乘 X^0.6（Roddier 1981）。floored at 2 × pixel scale × bin (×2 again for colour cameras); seeing scales as X^0.6 (Roddier 1981). 粗估Rough estimate

C 構圖framing = 目標範圍落在任一格裡的比例（2,000 個取樣點，同模擬器的拼接幾何）。the fraction of the target extent inside any tile (2,000 sample points, same mosaic geometry as the simulator).

P 瑕疵defects = 核心飽和 ×0.85；不導星又超過赤道儀單張上限 × 上限 ÷ 單張（最低 0.5）。core saturation ×0.85; unguided subs over the mount limit × limit ÷ sub (floor 0.5). 遊戲規則Game rule

每張保留率Sub retention q = c_開始start × exp(−Σ(1−c)·Δt ÷ 600 s)：c 是無厚雲比例；單張越長，遇雲整張作廢的期望損失越大。透明度低於報廢門檻、太陽在 −18° 以上、月亮在天上（照亮 > 10%）、目標低於 max(山稜線, 10°) 的張數不算；消光 0.2 mag/airmass 只作用在訊號。c is the cloud-free fraction; the longer the sub, the more you expect to lose to clouds. Subs below the transparency threshold, in twilight (Sun above −18°), with the Moon up (> 10% lit) or with the target below max(ridge, 10°) do not count; extinction 0.2 mag/airmass dims the signal only. 遊戲規則Game rule

引擎Engine rough-1・規則rules sn-a1。物理是望遠鏡工作台的粗估公式移植到伺服器（physics_rough），不是精密模型。The physics is the Telescope Workbench’s rough model ported to the server (physics_rough), not a precise model.