feat(examples): play scenarios and accuracy sliders on the chart data page

[nichinichisou0609]

The chart data page (examples/songs/) gets play scenarios and accuracy sliders. With the defaults, its figures match the current page exactly.

Commits

1. fix(examples): the chart data page guide renders its definition lists; hedged wording. These are the pending working-tree edits:
   • the definition lists of guide sections 06 and 07 render again;
   • the texts name the decompiled client as their source and defer to other sources;
   • the footer shows the source and versions;
   • the score figures are described as the Gekisou Live best case.
2. feat(examples): play scenarios and accuracy sliders on the chart data page.
3. docs(examples): the chart data page guide gives the rank 1 to rank 5 ratio.

Scenarios

• Gekisou Live (default). Each of the three Gekisou ranges has its own rank from 1 to 5. The default is rank 1 everywhere, labelled as the best case. Other ranks follow linearly from the rank-1 seeds (ranking.js scenarioSeed):
  • base_r = (score − Σ rankBonus_i + Σ trunc(rangeScore_i · p_i(r_i) / 100)) / power
  • w_r[k] = w[k] + Σ (p_i(r_i) − p_i(1)) / 100 · rangeWeights[k][i]
• Free Live (gk=free). Gekisou is off and the figures come from offSeeds. Charts with more than 3 fevers, which Gekisou Live cannot play, still get figures here.
• Missing data. If the data lacks a field, the matching option is disabled and marked "数据待更新" / "data pending" (scenarioData). Rank 1 in Gekisou Live uses the current seeds.

Accuracy

Both sliders update the table, the frontier and the chart details while they move. Both are approximations, and neither models combo breaks.

• Great share q. Applies to every note and scales every score by 1 − 0.2q (greatFactor). It replaces the old Great input of the event ranking.
• Just rate j (Gekisou Live only). Interpolates linearly between the all-Just seeds (score, rangeScore) and the all-Perfect run (scorePerfect, rangeScorePerfect).
  • The rank bonuses are recomputed as trunc(interpolated range score × pct / 100), then multiplied by g(q).
  • The skill weights inside each range are scaled by the same ratio. This is also an approximation.

Score ranks

Free Live keeps the solo thresholds (requiredScore).

In Gekisou Live, the client compares the room's summed score with trunc(√(5/n) · R_battle · n). The page adds a room size n from 1 to 5 (default 5) and assumes every player scores the same as you, so you need trunc(√(5/n) · R_battle · n) / n ≈ √(5/n) · R_battle (roomThreshold / rankThreshold(row, rank, room)).

Chart details

The chart details have their own scenario panel, and the figures redraw in place. In Gekisou Live the details show both reported scores: the one with Gekisou, and the one without it that is kept as the song's best score, which is about the Free Live score.

Guide (Chinese and English)

• New section 2 covers the scenarios and ranks.
• The judgements section becomes 判定与准率 / Judgements and accuracy and covers both sliders.
• The score ranks section explains the room assumption.
• The event figures are recomputed for Gekisou Live at rank 1 in a room of 5: SS on Expert needs 270k to 2.05M power, and the median relative residual of the fit is about 32 %.
• The "in the works" wording is gone. Model results are stated "by this model".

Query

New parameters: gk=free, rk=<r>[,<r>,<r>], jr=<Just percent> and n=<players>. gr keeps its meaning. All of them are left out at their defaults.

Data

The fields follow the final schema of the scenario data (deck d4abb52, nnnotes 7bfa26b):

• ranges[i].rankBonusPercents
• seeds[].rangeWeights[kind][k][i]
• seeds[].scorePerfect, which includes the rank-1 bonuses of its own range scores
• seeds[].ranges[i].rangeScorePerfect
• offSeeds[]

A null rangeWeights, or a null entry for a kind, leaves that chart without figures for ranks other than 1 and for Just rates below 100 %. Older files without these fields still load; the new options are then disabled and marked "data pending".

For the Just rate, the page recomputes the rank bonus on the interpolated range score, as the product decision specifies. Interpolating the two finished bases instead differs by less than 1 point per range: at most 1.8 points on the real data.

Checks

• npm test: 557 passing. New songs-page tests cover:
  • rank 1, j = 1, q = 0 matching the previous implementation value for value;
  • Free Live reading offSeeds;
  • the rank formula and the Just/Great interpolation against hand computations;
  • the room thresholds;
  • the rk query round trip.
• npm run typecheck passes.
• node scripts/build.mjs --check passes.

Checks on the real scenario data (read only):

• Default scenario. Rank 1 everywhere, j = 1 and q = 0 give the same figures as the previous joinCharts / chartRows on all 340 charts, value for value.
• Free Live. It reads offSeeds: every one of the 340 charts has figures, with base = offSeeds[0].score / P₀ and the weights exactly as stored.
• Other ranks. For ranks 5,5,5 and two mixed rank vectors, base equals a hand computation from the raw fields (difference 0).
• Random ranks. On 1376 seeds with rankCheck, the linear prediction matches deck's own predicted with the same residual as at rank 1 (median 0), and every whole-live exact is within its bound (at most 0.5 bound).
• Just rate. At j = 0 the base equals scorePerfect. In non-Just ranges rangeScorePerfect == rangeScore.
• Rank 1 vs rank 5. The no-skill base at rank 1 is 1.25 to 1.65 times the base at rank 5 (median 1.46). The guide now says so.

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