fix: calculate chart scores with song formulas and hidden note weights

scripts/collect-exact-charts.mjs

@@ -1,6 +1,7 @@
 import { mkdir, readFile, writeFile } from 'node:fs/promises';
 import { execFileSync } from 'node:child_process';
 import path from 'node:path';
+import { formulaScoreMetadata } from './song-score-formulas.mjs';
 
 const sourceOrigin = process.argv[2] ?? 'https://dreams.wf-calc.net';
 const outputDirectory = path.resolve('static/data/charts');
@@ -237,14 +238,18 @@ async function worker() {
     const releaseTime = Number(music?.startTime);
     const notes = flattenEvents(chartData);
     const measuredCalibration = scoreCalibrationByKey.get(`${item.songId}::${item.difficulty.toLowerCase()}`);
+    const difficultyLevel = difficultyLevelByKey.get(`${item.songId}::${item.difficulty.toLowerCase()}`) ??
+      (Number.isFinite(item.difficultyLevel) ? item.difficultyLevel : null);
+    const formulaMetadata = formulaScoreMetadata(item.songId, item.difficulty, difficultyLevel, notes.length, music?.liveScoreCoefficientPermil, chartData.source?.sha256);
     const output = {
       schemaVersion: 1,
       songId: item.songId,
       difficulty: item.difficulty.toLowerCase(),
       durationSeconds: sourceEntry?.durationSeconds ?? Math.ceil(notes.at(-1)?.timeSeconds ?? 0),
-      // 실측이 있으면 우선하고, 없을 때만 채보 가중치와 계산기 고유 상수로 추정한다.
+      // 검증된 공식 우선. 참고 분모가 없는 채보만 기존 실측/추정으로 대체한다.
       scoreRatio: measuredCalibration?.scoreRatio ?? calibratedScoreRatio(chartData),
       scoreCalibrationSource: measuredCalibration ? 'measured' : 'local-estimated-v1',
+      ...formulaMetadata,
       notes,
       specialStartSeconds: (chartData.sp_activation_events ?? [])
         .sort((left, right) => left.slot - right.slot)
@@ -268,6 +273,7 @@ async function worker() {
       durationSeconds: output.durationSeconds,
       scoreRatio: output.scoreRatio,
       scoreCalibrationSource: output.scoreCalibrationSource,
+      ...(output.scoreFormula ? { scoreFormula: output.scoreFormula } : {}),
       totalNotes: notes.length,
       singerType: output.singerType,
       singerCharacterIds: output.singerCharacterIds,