Seen (PR #402, measured again on 0.2.2): TICK = 1/30 is not a binary fraction. An attack cooldown counted down from 1 s
stops at 2.1e-16 after thirty steps and the fire check `atkCd > 0` waited a 31st frame; 300 time gains of 1/30 SP add up
to 9.999999999999975 and `sp >= cost` charged a 10-SP skill a frame late. Over the 265 golden battles 30.85 % of the
consecutive attacks on a whole-frame interval came a frame late (control, other intervals: 0.09 %), and 4 157
end-of-tick states sat within 1e-9 under a cost. The engine already took timers within 1e-9 as done (skill timeLeft,
buffs, every() / after(), enemy abilities, nextCastAt, the 失衡 end); these two did not.
Official: PRTS 作战机制/sandbox 「帧对齐机制对攻速的影响」 — one frame = 1/30 s; since 2019-12-24 a non-integer frame count
is rounded (四舍五入); an exact 1 s is 30 frames under any rule.
Now: ai.js attackCountdown(cd, dt) (left within 1e-9 of 0 is 0) for the operators' cooldown (the canAct guard kept) and
the enemies' (not while stunned or hidden; the 0.2.2 失衡 swing cut untouched) — an enemy's whole-frame wind-up is exact
too (0.4 s: 12 frames, 13 before). The same countdown for the two strict `cd -= dt; if (cd > 0)` attack clocks of the
same shape: the 双眼皮 turrets (content/devices.js; BAT 4 s: 121 → 120 frames) and 寒檀's S2 icicles (0.5 s: 16 → 15).
SkillRuntime.gainSp takes SP within 1e-9 of the cost as full for every charge (a tiny negative remainder → 0);
_normalize compares the same way. Left as they are: a non-integer count still ends on the frame that crosses 0
(⌈30 × interval⌉ — the official 四舍五入 is an older, separate difference); the count-up content clocks that restart from
0 (bosses.js self-timers, kit auras — PR #402's list); attack / hurt SP (+1 on an integer cost) unchanged.
Tests: test/sim/tick-tolerance.test.js (new, 7: the PR's four adapted — residue, attackCountdown over bat 0.1–10 s ×
14 ASPD = ⌈30 × interval⌉, 1 s operator every 30 / 3 s ranged enemy every 90, time SP 4/10/16/20/30/50 at exactly 30 × N
gains for one and two charges — plus the 1.2 s / 1.25 s control (36 / 38), the turret at 0 layers (120) and 寒檀's
icicles (15); the four engine tests fail on the parent: 31 / 91, cost 4 at 121, 121, 16). The PR's seven test edits,
re-run: the same 8 assertions failed on the new timing and each edit passes on the parent and on the fix —
feedback2-surtr-stealth (count once no arrow is in flight), kits_alt_t2 拉普兰德 S1 (dummy ATK 300 → 250: 120 × 15 = her
1791 HP by 59.5 s), kits_alt_t6 (medic smoke at half HP; 余 S1 up to the first 燃烧 burst), op_jesca2 (the T6 shield
returns a tick after the cast), op_lmlee (hits before the burst), op_logos (count after the clear), op_narant (the first
attack thrown after the new enemies). node --test (with the golden of the next commit): 5703 tests, 5701 pass, 0 fail,
2 skipped; eslint 0 errors (135 warnings, the parent's 135); typecheck, check:imports, smoke ok.
feedback7 R23-TICK: golden for whole-frame attack intervals and SP costs (PR #402) — 281 of 283 scenarios move: roster 49/49, bonds 46/46, fields 22/22, matches 18/18, standins 10/10, diy 136/138; solo-NORMAL-1 now loses its Final Assault (below)
npm run golden:update on the previous commit. Every family moves because both sides attack on time (more enemy kinds
than operator forms sit on whole-frame intervals: 3 s, 4 s, 1 s …) and time SP charges a frame sooner. Measured over
the 265 battles: whole-frame consecutive attacks a frame late 30.85 % → 0.04 % (control 0.09 % → 0.13 %; 1 s gaps at
30 frames 256 → 3 776 of ~3 800, 3 s at 90 frames 0 → 6 657 of 6 657), SP float-short states 4 157 → 0. Moved battles'
totals: kills 10 647 → 10 625, leaks 12 398 → 12 445, deaths 2 913 → 2 944. Unchanged: diy-040, diy-069.
End results that flip (one frame cascades; the causes as measured with the matches' battles instrumented):
- solo-NORMAL-1: won → lost in round 14 (passed 14 → 13, team LP 8 → 0): the Final Assault on 卢西恩 (pool 390 000) runs
as before for two minutes (his 0.4 s wind-up a frame shorter), then the team's damage on the pool trails — 884 left
when the overtime drain (from 300 game s) takes the last of the 17 LP at 334 s; before, it emptied at 318 s, 8 LP left.
- solo-HARD-1: LP 10 → 12 — round 8 lets one more through (26 → 25; rounds 11–12 even it out) and the Final Assault ends
at 300.6 s, before the overtime drain (304.8 s and 2 LP before).
- solo-NORMAL-2: LP 9 → 25 — round 5 lets one more through (26 → 25, a coin less), the bot's shop path parts from round
6 and its later board (突袭, 232 layers at round 13 against 94) clears rounds 12–13 with no leak (7 + 18 before).
- coop2-NORMAL-3: team LP 63 → 68 — ai_1's round-13 battle leaks 1 instead of 6 (its round-12 leaker now goes to 联防).
- coop2-ABYSS-10-boosted: team LP 583 → 630 — the Final Assault ends at 606.6 s (639.6) and the Hidden Core at 335.9 s
(397.8): 47 LP less of overtime drain.
- coop2-NORMAL-14-standins: team LP 41 → 40 — ai_0's round-13 battle lets one 潜伏者 through (23 → 22).
- roster-016: cleared at 220.3 s → time-out at 230 s (主角阵营角色 leaks instead of falling; kills 101 → 105, leaks 26 → 22).
- roster-041: time-out → cleared at 189.0 s, perfect (the last 粉碎攻坚组长 falls inside the 190 s).
- bond-suntShip-high: cleared at 164.2 s → time-out at 190 s (kills 11 → 13, deaths 4 → 2).
- standin-04: perfect → 10 leaks (deaths 8 → 10; 萨卡兹大剑组长 / 萨卡兹穿刺手 / 澪 get through).
- diy-005 / diy-008 (艾丽妮 / 赫拉格): cleared at 225.3 s → time-out at 230 s (a last 宿主重装士兵 / 深池方阵指挥官 walking).
- diy-127 (白铁 / 酒神): time-out → cleared at 225.8 s (deaths 7 → 13, leaks 57 → 72).
- diy-131 (死芒): perfect → 1 leak (a 掠海漂移体).
The other matches keep their ends (solo-FUNNY-1/2, solo-HARD-2, solo-ABYSS-1/2, coop2-HARD-4, coop3-ABYSS-5,
coop4-FUNNY-6, coop4-ABYSS-7, coop2-NORMAL-8-serverrun, solo-HARD-9-boosted, coop2-NORMAL-70-diy). PR #402's own
0.2.1 table (coop2-NORMAL-14-standins loss → win, solo-HARD-2 / solo-ABYSS-2 earlier exits) was measured before §27 and
does not repeat here.
- 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.
The 「投石车」 is 自制投石机 (enemy_10162_mnctpt), the 「蒸汽地板」 the 排气格栅 smog (隐匿 to enemy ranged attacks). PRTS
天赋 「索敌不受阻挡影响」: the blocker exception (a blocked enemy attacks its blocker whatever its selectability) does not
apply to it. New enemy profile field `blockFree` (spawns.js): attackTargets selects as if unblocked, canTargetAlly
refuses a 隐匿 / 迷彩 blocker to it, sortAllyTargets puts no blocker first. Other enemies unchanged.
Golden: standin-06 (the bounty catapult, blocked by 忍冬, now shoots by 仇恨值 — checked instrumented).
Tests: test/sim/feedback5-catapult-smog.test.js (3; 2 fail on the parent). Docs: DESIGN §25.18.7, docs/SIM.md.
Review follow-up to the water / tactical point change.
- Re-orienting 伺夜 / 缪尔赛思 in place while hand and temp are full could leave
a placed 狼群 / 流形 outside the new range (it had nowhere to go and stayed
put). The re-orientation is now refused with HAND_FULL when a summon it
would leave out has no stack and no free slot. On the other paths
(promotion, an owner moved with no room) such a summon leaves the board and
its stack comes back at the next round start (grantTokensFor), so no
out-of-range placement reaches the battle.
- Citation corrected: the 深水区 rule comes from the PRTS page 深水区 (地形信息
tile_deepsea: 部署类型 全部位, 地形机制 "拒绝部署（待补充）"), corroborated by
PRTS 作战机制 (地形标记 AdvancedBuildableMask lists 深水). There is no PRTS
page 地形.
- grid.js: the tie-break note now says what changed on 战场#08 (no gate
route; a few off-route smoothed steps of the boss field go around the water).
- Documented the known limit of the inactive act1 m05: its 特制水上平台 tiles
are deployable in the prep's deploy map only; the sim does not model the
canoes and keeps those tiles non-standable.
- gameLogic.summonRange reuses facing.js rangeTiles.
- #1 近地悬浮 enemies count as air units (Unit.isFlying): ground-only attacks, splash, terrain and traps skip them;
PRTS 不可对空 skill effects made ground-only; 掠海漂移体 / 吉兆飞鳞 drop modes; the bot plans them as air
- #2 an operator knocked out before 联防 is fielded and force-exited (PRTS 强制退场): it lies on its tile with the
redeploy ring and redeploys (full timer [ASSUMED]); partners, observers and the server fallback included
- #3 element audit of every operator, item and enemy: 海嗣 numbers are official; bursts are 无来源, 元素脆弱 only
raises 元素伤害, 元素抗性 applied, 盟约·辅助干员 fills all three gauges, 菲莱 / 哈洛德 / 纯烬 / enemy kits fixed
- #4 blocking by the official contact radius (0.7071): another operator in contact takes over at once when the
blocker dies, withdraws or is stunned; melee blockers attack what they block
- #5 enemy target order per PRTS 索敌: blocker, special priority, taunt, last deployed; initial deploy 从上到下>从左到右,
operators before summons; special priorities break ties by taunt then deploy order
- #6 act2 m01's normal-field blower machines (row 13) are drawn in the normal / 联防 views
- #7 Final Assault prep legality reads the player's half of the boss field (fence tiles deployable); all 11 stages
audited against the official level files
- #8 regular settings gear; #9 the prep camera keeps the bench and temp rows clear of the shop bar on phones
- #10 huge bosses have the official 4.95 × 2.95 hit area (sim/body.js) and are 自缚 / unblockable
- #11 至简 costs 1: 购买价格为N's bb.price is a discount off the tier price, applied before other price effects
- DESIGN §19 and the normative §3 / §5 / §6 / §7 lines, SIM / META / DATA / PLAYING updated; 2595 unit tests and
every browser suite green; dev recordings regenerated
sganggs