Seen (#364, FrogThai): the 中枢先兆者's shell hit the target and its orthogonal neighbours only — repro: a diagonal
neighbour (√2 ≈ 1.414 from the impact) took nothing, as did a tile two away; the reporter saw the 3×3 in the official game.
Official: PRTS 天赋 of both 先兆者 (one shared kit) 「弹道对半径1.2范围内的所有我方单位造成攻击力100%的无来源物理伤害（此弹道
不会强制击中主目标，碰撞无视迷彩）」. The landing is a 碰撞; PRTS 作战机制 §碰撞体积 (docs/SIM.md, constants.js): collider tests are
the common way and an ally's collider is a 0.25 circle — the rule the engine already applies to ranged enemies' reach.
Now (content/enemies/fly.js kitShell): an ally is hit when its collider touches the 1.2 circle — centre distance ≤ 1.45
(SHELL_REACH = SHELL_RADIUS + ALLY_COLLIDER_RADIUS): the impact tile and the 8 around it, never two tiles away. The
telegraph and the blast are drawn at that reach. [ASSUMED] for this shell (its text names the 碰撞); other content zones
keep their point radius as before. Golden: the three battles with a 先兆者 whose shells land beside a diagonal operator
(roster-001 中枢先兆者, roster-019 and diy-020 先兆者).
- server/sim/detmath.js: hypot (sqrt of the squares, rescaled outside 2^±500), powi (integer powers in double-double,
one rounding), sin / cos (fdlibm 5.3) and atan2 (fdlibm / FreeBSD msun) built only from correctly rounded IEEE
operations; the sim's Math.hypot / sin / cos / atan2 / pow calls go through it (65 files); eslint.config.js forbids
the approximated Math functions under server/sim and test/sim/detmath.test.js scans for them.
- sin / cos / atan2 are the algorithms V8 runs in Node, so the server's results stay; only hypot differs from V8's.
Golden: 2 moved — diy-027 (a hypot distance, damage +80) and coop3-ABYSS-5 (a later card pick from round 9, same end).
- Applied unchanged after review (Grok static review: MERGE; the diff read in full: no network, no new dependency).
- Tests: broad node --test 5155 / 5155 with the new file tracked (detmath 7 / 7, package 10 / 10); lint 0 errors,
typecheck, check:imports.
sganggs