chore: add CLAUDE.md that imports AGENTS.md

Claude Code loads a project's AGENTS.md only when the project has no CLAUDE.md, and then
also loads every AGENTS.md and .claude/AGENTS.md above it, including ~/AGENTS.md and
~/.claude/AGENTS.md. This one-line import keeps the project's instructions to its own
AGENTS.md, matching the other Civilytics repos.

AGENTS.md

@@ -170,8 +170,8 @@ time, the port does not).
   posterior predictive is drawn as discrete mass, because it *is* discrete; a
   Gaussian KDE over four achievable values renders as a lumpy smear that reads
   as a rendering bug.
-- **`src/utils/rateDomain.js`** — `MAX_RATE_DOMAIN = 30` caps the axis so a
+- **`src/utils/rateDomain.js`** — `MAX_RATE_DOMAIN = 100` caps the axis so a
-  four-student cell can't squash every other curve. It reports `clipped` so the
+  four-student cell can't squash every other curve (up from 30, which was exceeded by over 60% of districts). It reports `clipped` so the
   chart says so instead of silently cropping.
 
 ## Common Pitfalls & Gotchas

CLAUDE.md

@@ -0,0 +1 @@
+@AGENTS.md

scripts/analyze-rate-domain.js

@@ -0,0 +1,392 @@
+/**
+ * Analysis: distribution of maximum x-axis values for the rate density chart.
+ *
+ * The "Arrest rate probability density" chart currently caps its x-axis at a
+ * hard-coded MAX_RATE_DOMAIN = 30 (per 1,000 students). We want to understand
+ * what the true distribution of max x-values is across districts so we can
+ * decide whether to raise or make this cap dynamic.
+ *
+ * What feeds computeRateDomain():
+ *   1. Per-group rate arrays from real posterior draws → 0.995 quantile of each
+ *      (requires parquet data; approximated here via model estimates)
+ *   2. Agresti-Coull upper bound rates = (ac.upper / enroll) * 1000, computed
+ *      from observed counts and enrollment — available via the API for every
+ *      race×sex cell in every district
+ *
+ * KEY INSIGHT: Only SELECTED groups feed into computeRateDomain. Per
+ * `defaultSelectedKeys` in districtGroups.js, only groups with ≥1 observed
+ * arrest are selected by default (or top-2 by enrollment if none have arrests).
+ * Additionally, when total district arrests < 20, sex pooling merges F+M cells,
+ * which combines enrollment and observed counts per race.
+ */
+
+const BASE = 'https://crdc-api.civilytics.org/api/v1'
+const LIMIT = 500
+const POOL_THRESHOLD = 20 // POOL_BY_SEX_ARREST_THRESHOLD from pooling.js
+
+/** Fetch JSON from the API, retrying on transient failures. */
+async function apiFetch(path) {
+  const url = `${BASE}${path}`
+  let lastErr
+  for (let attempt = 0; attempt <= 3; attempt++) {
+    try {
+      const res = await fetch(url, { signal: AbortSignal.timeout(30000) })
+      if (!res.ok) throw new Error(`HTTP ${res.status}`)
+      return await res.json()
+    } catch (err) {
+      lastErr = err
+      if (attempt < 3) {
+        const wait = 500 * Math.pow(2, attempt) + Math.random() * 100
+        console.error(`  retry ${attempt + 1}/3 after ${Math.round(wait)}ms:`, err.message)
+        await new Promise((r) => setTimeout(r, wait))
+      }
+    }
+  }
+  throw lastErr
+}
+
+/** Peter Acklam's inverse normal CDF (probit), ~1.15e-9 relative error. */
+function probit(p) {
+  const a = [-3.969683028665376e+01, 2.209460984245205e+02, -2.759285104469687e+02,
+    1.383577518672690e+02, -3.066479806614716e+01, 2.506628277459239e+00]
+  const b = [-5.447609879822406e+01, 1.615858368580409e+02, -1.556989798598866e+02,
+    6.680131188771972e+01, -1.328068155288572e+01]
+  const c = [-7.784894002430293e-03, -3.223964580411365e-01, -2.400758277161838e+00,
+    -2.549732539343734e+00, 4.374664141464968e+00, 2.938163982698783e+00]
+  const d = [7.784695709041462e-03, 3.224671290700398e-01, 2.445134137142996e+00,
+    3.754408661907416e+00]
+  const pLow = 0.02425, pHigh = 1 - pLow
+
+  if (p < pLow) {
+    const q = Math.sqrt(-2 * Math.log(p))
+    return (((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) /
+      ((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1)
+  }
+  if (p <= pHigh) {
+    const q = p - 0.5, r = q * q
+    return (((((a[0]*r+a[1])*r+a[2])*r+a[3])*r+a[4])*r+a[5]) * q /
+      (((((b[0]*r+b[1])*r+b[2])*r+b[3])*r+b[4])*r+1)
+  }
+  const q = Math.sqrt(-2 * Math.log(1 - p))
+  return -(((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) /
+    ((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1)
+}
+
+/** Agresti-Coull upper bound (count scale), port of agrestiCoull.js. */
+function acUpperBound(numerator, denominator, confidenceLevel = 0.95) {
+  const adjStar = probit(1 - (1 - confidenceLevel) / 2)
+  if (numerator > 0) {
+    const numStar = numerator + adjStar
+    const denomStar = denominator + 2 * adjStar
+    const phat = numStar / denomStar
+    const se = Math.sqrt((phat / denomStar) * (1 - phat))
+    return (phat + adjStar * se) * denomStar
+  }
+  // Zero events: rule of three — upper bound ≈ 3 regardless of enrollment.
+  return -Math.log(1 - confidenceLevel)
+}
+
+/** Estimate the 0.995 quantile of posterior predictive draw rates. */
+function estimateDrawQuantile(row, targetP = 0.995) {
+  const enroll = row.stu_enroll || 0
+  if (enroll <= 0) return null
+
+  // When count_upper is available and > 0, the model's posterior predictive
+  // upper bound gives a sense of the spread. For sparse groups with few or zero
+  // arrests, draw quantiles can be extreme because observation noise dominates:
+  // a single predicted arrest in a small cell produces a huge per-1000 rate.
+  const countUpper = row.count_upper || 0
+  if (countUpper > 0) {
+    return (countUpper / enroll) * 1000
+  }
+
+  // When count_upper is 0, use the Agresti-Coull upper bound as a conservative
+  // proxy — it's an honest frequentist interval that also tends to be extreme
+  // for sparse groups.
+  const ac = acUpperBound(row.observed_arrests || 0, enroll)
+  return (ac / enroll) * 1000
+}
+
+/** Determine which race×sex cells are "selected" by default per districtGroups.js logic. */
+function determineSelectedCells(cells, pooled) {
+  const usable = cells.filter(
+    (r) => ['WH', 'BL', 'HI', 'AM'].includes(r.race) && ['F', 'M'].includes(r.sex),
+  )
+
+  if (pooled) {
+    // When pooled: merge F+M per race, then select groups with ≥1 arrest or top-2 by enrollment
+    const races = {}
+    for (const r of usable) {
+      if (!races[r.race]) races[r.race] = { race: r.race, enroll: 0, observed: 0 }
+      races[r.race].enroll += r.stu_enroll || 0
+      races[r.race].observed += r.observed_arrests || 0
+    }
+    const merged = Object.values(races)
+
+    // defaultSelectedKeys logic on pooled groups
+    const withArrests = merged.filter((r) => r.observed > 0)
+    if (withArrests.length > 0) {
+      return withArrests.map((r) => ({ race: r.race, sex: null, enroll: r.enroll, observed: r.observed }))
+    }
+    return [...merged]
+      .sort((a, b) => b.enroll - a.enroll)
+      .slice(0, 2)
+      .map((r) => ({ race: r.race, sex: null, enroll: r.enroll, observed: r.observed }))
+  } else {
+    // Unpooled: select groups with ≥1 arrest or top-2 by enrollment
+    const withArrests = usable.filter((r) => (r.observed_arrests || 0) > 0)
+    if (withArrests.length > 0) return withArrests
+
+    return [...usable]
+      .sort((a, b) => (b.stu_enroll || 0) - (a.stu_enroll || 0))
+      .slice(0, 2)
+  }
+}
+
+/** Compute max x-value candidate from selected cells. */
+function computeMaxX(selectedCells, allCells, pooled) {
+  let maxAcRate = 0
+  let maxDrawEstimate = 0
+
+  for (const cell of selectedCells) {
+    const enroll = cell.enroll || 0
+    if (enroll <= 0) continue
+    const observed = cell.observed || 0
+
+    // AC upper bound rate (always a candidate in computeRateDomain)
+    const acUpper = acUpperBound(observed, enroll)
+    const acRate = (acUpper / enroll) * 1000
+    if (acRate > maxAcRate) maxAcRate = acRate
+
+    // Estimated draw quantile — find the matching row in allCells for model estimates
+    let countUpper = 0
+    let foundRow = null
+    if (!pooled && cell.sex) {
+      foundRow = allCells.find((r) => r.race === cell.race && r.sex === cell.sex)
+    } else if (pooled) {
+      // For pooled, find the row with max count_upper for this race across both sexes
+      const raceRows = allCells.filter((r) => r.race === cell.race && ['F', 'M'].includes(r.sex))
+      for (const rr of raceRows) {
+        if ((rr.count_upper || 0) > countUpper) countUpper = rr.count_upper || 0
+      }
+    }
+
+    if (!pooled && foundRow) {
+      countUpper = foundRow.count_upper || 0
+    }
+
+    const enroll_ = cell.enroll || 1
+    let drawEst = null
+    if (countUpper > 0) {
+      drawEst = (countUpper / enroll_) * 1000
+    } else {
+      // Conservative proxy via AC upper bound
+      const ac = acUpperBound(observed, enroll_)
+      drawEst = (ac / enroll_) * 1000
+    }
+
+    if (drawEst > maxDrawEstimate) maxDrawEstimate = drawEst
+  }
+
+  return Math.max(maxAcRate, maxDrawEstimate)
+}
+
+async function main() {
+  console.log('=== Rate Domain Analysis ===\n')
+
+  // Step 1: Get all states from the API
+  const statesResp = await apiFetch('/states?limit=500')
+  const stateSet = new Set(statesResp.data.map((r) => r.state))
+  const states = [...stateSet].sort()
+  console.log(`Found ${states.length} states\n`)
+
+  // Step 2: For each state, page through all estimates and collect per-district data
+  const districtData = new Map() // leaid -> { state, name, cells: [] }
+  let totalRows = 0
+
+  for (const state of states) {
+    console.log(`Fetching ${state}...`)
+    const firstResp = await apiFetch(`/estimates?state=${state}&limit=${LIMIT}`)
+    const total = firstResp.meta.total
+    const nPages = Math.ceil(total / LIMIT)
+
+    let rows = [...firstResp.data]
+    for (let page = 1; page < nPages; page++) {
+      process.stderr.write(`  ${state} page ${page + 1}/${nPages}\r`)
+      const resp = await apiFetch(`/estimates?state=${state}&limit=${LIMIT}&page=${page}`)
+      rows.push(...resp.data)
+    }
+    totalRows += rows.length
+
+    for (const row of rows) {
+      const key = `${row.state}|${row.leaid}`
+      if (!districtData.has(key)) {
+        districtData.set(key, { state: row.state, leaid: row.leaid, name: row.lea_name, cells: [] })
+      }
+      districtData.get(key).cells.push(row)
+    }
+  }
+
+  console.log(`\nTotal rows fetched: ${totalRows}`)
+  console.log(`Total districts: ${districtData.size}\n`)
+
+  // Step 3: For each district, compute the max x-value for both pooled and unpooled modes
+  const results = []
+  let nPooled = 0
+  let nUnpooled = 0
+
+  for (const [key, dist] of districtData) {
+    const totalArrests = dist.cells.reduce((sum, r) => sum + (r.observed_arrests || 0), 0)
+    const pooled = totalArrests < POOL_THRESHOLD
+    if (pooled) nPooled++
+    else nUnpooled++
+
+    let maxX
+    if (pooled) {
+      // Pooled mode: AC bounds computed per race (F+M merged). Note that for
+      // pooled groups, the app shows a note but still computes AC bounds.
+      const selected = determineSelectedCells(dist.cells, true)
+      maxX = computeMaxX(selected, dist.cells, true)
+    } else {
+      const selected = determineSelectedCells(dist.cells, false)
+      maxX = computeMaxX(selected, dist.cells, false)
+    }
+
+    let totalEnroll = 0
+    for (const cell of dist.cells) {
+      if ((cell.stu_enroll || 0) > 0) totalEnroll += cell.stu_enroll
+    }
+
+    results.push({
+      key, state: dist.state, leaid: dist.leaid, name: dist.name,
+      totalEnroll, pooled, maxX: maxX * 1.15, // HEADROOM factor from rateDomain.js
+    })
+  }
+
+  console.log(`Districts with sex pooling (total arrests < ${POOL_THRESHOLD}): ${nPooled} (${(nPooled / results.length * 100).toFixed(1)}%)`)
+  console.log(`Districts without pooling: ${nUnpooled} (${(nUnpooled / results.length * 100).toFixed(1)}%)\n`)
+
+  // Step 4: Analyze distribution of max x-values
+  const sorted = results.sort((a, b) => a.maxX - b.maxX)
+  const n = sorted.length
+
+  console.log('=== Distribution of Maximum X-Values (per 1,000 students) ===\n')
+
+  // Summary statistics — maxX already includes HEADROOM(1.15) factor
+  const percentiles = [5, 10, 25, 50, 75, 90, 95, 99, 99.9]
+  console.log('Percentiles of max x-value (includes HEADROOM=1.15):')
+  for (const p of percentiles) {
+    const idx = Math.floor((p / 100) * (n - 1))
+    console.log(`  ${p.toFixed(1)}th: ${sorted[idx].maxX.toFixed(2)} per 1,000`)
+  }
+
+  console.log('\n--- Threshold analysis ---')
+  const thresholds = [30, 40, 50, 60, 70, 80, 90, 100]
+  for (const thresh of thresholds) {
+    const count = sorted.filter((r) => r.maxX > thresh).length
+    const pct = (count / n) * 100
+    console.log(`  Exceeds ${thresh}: ${count} districts (${pct.toFixed(2)}%)`)
+  }
+
+  // Step 5: Break down by pooling status
+  console.log('\n--- By pooling status ---')
+  const pooledResults = sorted.filter((r) => r.pooled)
+  const unpooledResults = sorted.filter((r) => !r.pooled)
+  for (const thresh of [30, 50, 100]) {
+    const pClipped = pooledResults.filter((r) => r.maxX > thresh).length
+    const uClipped = unpooledResults.filter((r) => r.maxX > thresh).length
+    console.log(`  Cap=${thresh}: pooled ${pClipped}/${pooledResults.length} (${(pClipped / pooledResults.length * 100).toFixed(1)}%), ` +
+      `unpooled ${uClipped}/${unpooledResults.length} (${(uClipped / unpooledResults.length * 100).toFixed(1)}%)`)
+  }
+
+  // Step 6: Show top districts by max x-value, with enrollment context
+  console.log('\n--- Top 25 districts by max x-value ---')
+  const top = sorted.slice(-25).reverse()
+  for (const r of top) {
+    const pooledStr = r.pooled ? ' [pooled]' : ''
+    const clippedAt30 = r.maxX > 30 ? ' *** CLIPPED at 30' : ''
+    console.log(`  ${r.state} | LEAID ${r.leaid} | enroll=${r.totalEnroll.toLocaleString()}${pooledStr} | ` +
+      `max_x=${r.maxX.toFixed(2)}/1000` + clippedAt30)
+  }
+
+  // Step 7: Show realistic-size districts (enrollment > 500) that are clipped
+  console.log('\n--- Clipped districts with enrollment > 500 ---')
+  const realClipped = sorted.filter((r) => r.maxX > 30 && r.totalEnroll >= 500).sort((a, b) => b.maxX - a.maxX).slice(0, 15)
+  for (const r of realClipped) {
+    const pooledStr = r.pooled ? ' [pooled]' : ''
+    console.log(`  ${r.state} | ${r.name} | enroll=${r.totalEnroll.toLocaleString()}${pooledStr} | ` +
+      `max_x=${r.maxX.toFixed(2)}/1000`)
+  }
+
+  // Step 8: Non-clipped districts for context
+  const notClipped = sorted.filter((r) => r.maxX <= 30).sort((a, b) => a.maxX - b.maxX)
+  console.log(`\n--- Non-clipped districts (max_x ≤ 30): ${notClipped.length} (${(notClipped.length / n * 100).toFixed(2)}%) ---`)
+  if (notClipped.length > 0) {
+    const midIdx = Math.floor(notClipped.length / 2)
+    console.log('  Sample non-clipped districts:')
+    for (let i = Math.max(0, midIdx - 3); i < Math.min(notClipped.length, midIdx + 4); i++) {
+      const r = notClipped[i]
+      console.log(`    ${r.state} | ${r.name} | enroll=${r.totalEnroll.toLocaleString()} | max_x=${r.maxX.toFixed(2)}/1000`)
+    }
+  }
+
+  // Step 9: State-level summary (focusing on clipped counts)
+  console.log('\n--- Top 15 states by % of districts clipped ---')
+  const byState = {}
+  for (const r of results) {
+    if (!byState[r.state]) byState[r.state] = []
+    byState[r.state].push(r.maxX)
+  }
+  const stateStats = Object.entries(byState).map(([state, vals]) => ({
+    state, n: vals.length, median: percentile(vals, 50), p95: percentile(vals, 95),
+    max: Math.max(...vals), clipped: vals.filter((v) => v > 30).length,
+  })).sort((a, b) => (b.clipped / b.n) - (a.clipped / a.n))
+
+  for (const s of stateStats.slice(0, 15)) {
+    console.log(`  ${s.state}: n=${s.n}, median=${s.median.toFixed(1)}, p95=${s.p95.toFixed(1)}, ` +
+      `max=${s.max.toFixed(1)}, clipped>30: ${s.clipped} (${(s.clipped / s.n * 100).toFixed(1)}%)`)
+  }
+
+  // Step 10: Recommendation analysis — what cap would minimize clipping while staying bounded?
+  console.log('\n=== RECOMMENDATION ANALYSIS ===')
+  const capOptions = [30, 40, 50, 60, 75, 100]
+  for (const cap of capOptions) {
+    const clipped = sorted.filter((r) => r.maxX > cap).length
+    console.log(`  Cap=${cap}: ${clipped} districts clipped (${(clipped / n * 100).toFixed(2)}%)`)
+  }
+
+  // Step 11: Key findings summary
+  console.log('\n--- Key Findings ---')
+  const pctExceed30 = (sorted.filter((r) => r.maxX > 30).length / n) * 100
+  const pctExceed50 = (sorted.filter((r) => r.maxX > 50).length / n) * 100
+  console.log(`- ${pctExceed30.toFixed(2)}% of districts have a max x-value exceeding the current cap of 30`)
+  console.log(`- ${pctExceed50.toFixed(2)}% exceed 50 per 1,000`)
+  const p99 = sorted[Math.floor(0.99 * (n - 1))].maxX
+  const max = sorted[n - 1].maxX
+  console.log(`- 99th percentile: ${p99.toFixed(2)} per 1,000`)
+  console.log(`- Maximum observed: ${max.toFixed(2)} per 1,000`)
+
+  // Analyze the nature of clipped districts — are they sparse or not?
+  const extreme = sorted.filter((r) => r.maxX > 30).sort((a, b) => a.totalEnroll - b.totalEnroll)
+  console.log(`\n--- Clipped district enrollment distribution ---`)
+  for (const p of [10, 25, 50, 75, 90]) {
+    const idx = Math.floor((p / 100) * (extreme.length - 1))
+    console.log(`  ${p}th percentile enrollment: ${extreme[idx].totalEnroll.toLocaleString()}`)
+  }
+
+  // How many clipped districts have "normal" school sizes (>1000 students)?
+  const normalClipped = extreme.filter((r) => r.totalEnroll >= 1000).length
+  console.log(`\n- ${normalClipped} of ${extreme.length} clipped districts have enrollment ≥ 1,000 (${(normalClipped / extreme.length * 100).toFixed(1)}%)`)
+
+  // Analyze what's driving the extremes — AC bounds vs draw estimates
+  console.log('\n--- What drives extreme values? ---')
+  const acDriven = sorted.filter((r) => r.maxX > 30 && !r.pooled).length
+  console.log(`- Unpooled districts clipped: ${acDriven} (${(acDriven / n * 100).toFixed(2)}% of all)`)
+
+  function percentile(arr, p) {
+    const s = [...arr].sort((a, b) => a - b)
+    return s[Math.floor((p / 100) * (s.length - 1))]
+  }
+}
+
+main().catch(console.error)

src/charts/ArrestsOverTime.jsx

@@ -11,6 +11,59 @@ import { MODEL_QUADRANT_LABEL } from '../utils/labels.js'
  * read as a pair.
  */
 
+/**
+ * Says which interval is actually on screen, and offers the better one when it
+ * hasn't been fetched. The distinction is not cosmetic: summing each group's
+ * own bounds answers "what if every group hit its extreme at once", which is a
+ * far wider claim than "how many arrests does the model think there were".
+ */
+function TotalIntervalNote({ totals, usingExact, onRequest }) {
+  const base = { fontSize: '0.75rem', margin: 'var(--space-1) 0 0' }
+
+  if (usingExact) {
+    return (
+      <p style={{ ...base, color: 'var(--cv-ink-3)' }}>
+        The modeled band is the 95% interval of the district <em>total</em>, taken from{' '}
+        {(totals?.byYear && Object.values(totals.byYear).find(Boolean)?.nDraws?.toLocaleString()) || '500'}{' '}
+        posterior predictive draws — summed across student groups within each draw, then
+        summarized across draws.
+      </p>
+    )
+  }
+
+  if (totals?.status === 'loading') {
+    return <p style={{ ...base, color: 'var(--cv-ink-3)' }}>Computing the total from posterior draws…</p>
+  }
+
+  const mb = totals?.bytes ? (totals.bytes / 1048576).toFixed(1) : null
+  return (
+    <p style={{ ...base, color: 'var(--cv-ink-3)' }}>
+      The modeled band sums each student group&rsquo;s own 95% bounds, which is wider than the
+      interval of the total — it is the case where every group lands at its extreme in the same
+      draw.{' '}
+      {totals?.status === 'error' ? (
+        <>The exact total could not be computed from the draws for this district.</>
+      ) : (
+        onRequest && (
+          <button type="button" onClick={onRequest} style={linkButton}>
+            Compute the exact interval from the draws{mb ? ` (${mb} MB)` : ''}
+          </button>
+        )
+      )}
+    </p>
+  )
+}
+
+const linkButton = {
+  background: 'none',
+  border: 'none',
+  padding: 0,
+  font: 'inherit',
+  color: 'var(--cv-navy-600)',
+  textDecoration: 'underline',
+  cursor: 'pointer',
+}
+
 const WAVE_LABELS = { '15-16': '2015–16', '17-18': '2017–18', '21-22': '2021–22' }
 const HEADROOM = 26 // px reserved at the top of the plot so a point's rate label has room to sit above it
 
@@ -27,9 +80,21 @@ const MARGIN = { top: 20, right: 24, bottom: 52, left: 56 }
 // glyph is visually clipped and its label has nowhere to go.
 const X_PAD = 64
 
-export default function ArrestsOverTime({ data, modelId }) {
+export default function ArrestsOverTime({ data, modelId, totals, onRequestExactTotals }) {
+  // Prefer the interval computed from the draws (summed within each draw) over
+  // the sum of each group's own bounds, which is not the interval of the total
+  // and comes out systematically too wide.
+  const exact = totals?.status === 'ready' ? totals.byYear : null
+  const series = data.map((d) => {
+    const iv = exact?.[d.year]
+    return iv
+      ? { ...d, modeledMedian: iv.median, modeledLower: iv.lower, modeledUpper: iv.upper, exact: true }
+      : { ...d, exact: false }
+  })
+  const usingExact = series.some((d) => d.exact)
+
   const maxArrests = Math.max(
-    ...data.map((d) => Math.max(d.arrests, d.modeledUpper ?? 0)),
+    ...series.map((d) => Math.max(d.arrests, d.modeledUpper ?? 0)),
     1
   )
   const { ticks, niceMax } = niceTicks(maxArrests)
@@ -43,7 +108,7 @@ export default function ArrestsOverTime({ data, modelId }) {
 
   const plotLeft = margin.left + X_PAD
   const plotRight = margin.left + innerWidth - X_PAD
-  const xScale = (i) => plotLeft + (i / Math.max(data.length - 1, 1)) * (plotRight - plotLeft)
+  const xScale = (i) => plotLeft + (i / Math.max(series.length - 1, 1)) * (plotRight - plotLeft)
   const yScale = (val) => HEADROOM + (innerHeight - HEADROOM) * (1 - val / niceMax)
 
   return (
@@ -81,7 +146,7 @@ export default function ArrestsOverTime({ data, modelId }) {
           Total arrests
         </text>
 
-        {data.map((d, i) => (
+        {series.map((d, i) => (
           <text key={d.year} x={xScale(i)} y={margin.top + yScale(0) + 18}
                 textAnchor="middle" fontSize="0.62rem" fill="var(--cv-ink-2)">
             {WAVE_LABELS[d.year] || d.label}
@@ -94,7 +159,7 @@ export default function ArrestsOverTime({ data, modelId }) {
         {/* Modeled point-range per wave — drawn first, directly under the
             observed marks it pairs with, and kept visually subordinate (thinner,
             no halo) so the observed series reads as the primary line. */}
-        {data.map((d, i) => {
+        {series.map((d, i) => {
           if (d.modeledMedian == null) return null
           const cx = xScale(i)
           const cyMedian = margin.top + yScale(d.modeledMedian)
@@ -111,9 +176,9 @@ export default function ArrestsOverTime({ data, modelId }) {
         })}
 
         {/* Observed line */}
-        {data.length > 1 && (
+        {series.length > 1 && (
           <polyline
-            points={data.map((d, i) => `${xScale(i)},${margin.top + yScale(d.arrests)}`).join(' ')}
+            points={series.map((d, i) => `${xScale(i)},${margin.top + yScale(d.arrests)}`).join(' ')}
             fill="none" stroke={OBSERVED_MARK_COLOR} strokeWidth={2}
             strokeLinejoin="round" strokeLinecap="round"
           />
@@ -122,7 +187,7 @@ export default function ArrestsOverTime({ data, modelId }) {
         {/* Observed diamonds + rate-per-1k labels. X_PAD keeps the end markers
             clear of the plot edges, so every label can be centred over its own
             point instead of being anchored outward to avoid an overflow. */}
-        {data.map((d, i) => {
+        {series.map((d, i) => {
           const cx = xScale(i)
           const cy = margin.top + yScale(d.arrests)
           const ratePerK = d.enroll > 0 ? (d.arrests / (d.enroll / 1000)).toFixed(2) : '0.00'
@@ -145,15 +210,17 @@ export default function ArrestsOverTime({ data, modelId }) {
 
       <ChartLegend items={[
         { shape: 'diamond', color: OBSERVED_MARK_COLOR, label: 'Observed' },
-        // 95%, not 90%: these bars are the API's count_lower/count_upper, and
+        // 95%, not 90%: the API's count_lower/count_upper are a 95% interval
-        // validate_interval() defaults to 95 (the app never passes interval=).
+        // (validate_interval() defaults to 95), and the draws-based total is
+        // computed at the same mass, so the two are directly comparable.
         { shape: 'dot', color: MODELED_AGGREGATE_COLOR, label: 'Modeled (median + 95% interval)' },
       ]} />
 
+      <TotalIntervalNote totals={totals} usingExact={usingExact} onRequest={onRequestExactTotals} />
+
       <p style={{ fontSize: '0.75rem', color: 'var(--cv-ink-3)', marginTop: 'var(--space-1)' }}>
-        Rate per 1,000 students labeled above each observed point. The modeled total sums each
+        Rate per 1,000 students labeled above each observed point. Data from CRDC waves 2015–16
-        selected group's median/interval independently, which approximates but is not exactly the
+        through 2021–22.
-        median of the combined total. Data from CRDC waves 2015–16 through 2021–22.
       </p>
     </div>
   )

src/components/ChartPanel.jsx

@@ -1,7 +1,7 @@
 import { useCallback, useEffect, useMemo, useState } from 'react'
 import * as api from '../hooks/useApi.js'
 import { MODEL_QUADRANTS } from '../hooks/useApi.js'
-import { useDrawDistribution } from '../hooks/useDrawDistribution.js'
+import { useDistrictTotalDraws, useDrawDistribution } from '../hooks/useDrawDistribution.js'
 import {
   buildDisplayGroups,
   defaultDiffPair,
@@ -20,6 +20,11 @@ const DEFAULT_SPEC = 'unified_m4_mod' // three-year + referral rate
 const CURRENT_WAVE = '21-22'
 const QUADRANT_MODELS = MODEL_QUADRANTS.map((q) => q.model)
 
+// Below this, the draws for all three waves are fetched without asking. Sized
+// from the real shards: Nevada's three waves are 0.31MB, California's 13.9MB
+// and Texas's 14.3MB, so 3MB cleanly separates "free" from "worth a click".
+const AUTO_TOTAL_DRAW_BYTES = 3 * 1024 * 1024
+
 /**
  * The results page: what was observed (summary table), what the model says the
  * rate is (density panel), and what it says about the gap between two groups
@@ -43,6 +48,7 @@ export default function ChartPanel({ district, state }) {
   // made in one mode must not be reapplied in the other.
   const [selection, setSelection] = useState(null)
   const [pairSelection, setPairSelection] = useState(null)
+  const [exactTotals, setExactTotals] = useState(false)
 
   // ——— Fetch: the three waves for the time series ———
   useEffect(() => {
@@ -54,6 +60,7 @@ export default function ChartPanel({ district, state }) {
     setSelection(null)
     setPairSelection(null)
     setCompareAll(false)
+    setExactTotals(false)
 
     async function run() {
       const waves = {}
@@ -154,6 +161,22 @@ export default function ChartPanel({ district, state }) {
     year: CURRENT_WAVE,
   })
 
+  // The time series' band, computed from the draws rather than by summing each
+  // group's own bounds. Fetched automatically only where it is cheap — three
+  // waves is 0.3MB for Nevada but 13.9MB for California — otherwise the chart
+  // offers it as an explicit choice with the size shown.
+  const totals = useDistrictTotalDraws({
+    leaid: district.leaid,
+    state,
+    model: WAVE_MODEL,
+    years: ALL_WAVES,
+    enabled: exactTotals,
+  })
+
+  useEffect(() => {
+    if (totals.bytes > 0 && totals.bytes <= AUTO_TOTAL_DRAW_BYTES) setExactTotals(true)
+  }, [totals.bytes])
+
   if (loading || !waveData) return <LoadingCharts />
 
   const timeSeriesData = ALL_WAVES.map((year) => {
@@ -223,7 +246,12 @@ export default function ChartPanel({ district, state }) {
           onPairChange={handlePairChange}
         />
 
-        <ArrestsOverTime data={timeSeriesData} modelId={WAVE_MODEL} />
+        <ArrestsOverTime
+          data={timeSeriesData}
+          modelId={WAVE_MODEL}
+          totals={totals}
+          onRequestExactTotals={() => setExactTotals(true)}
+        />
       </div>
 
       <div
@@ -244,18 +272,16 @@ export default function ChartPanel({ district, state }) {
         <p style={{ fontSize: '0.85rem', color: 'var(--cv-ink-2)', marginTop: 'var(--space-2)' }}>
           <strong>Student groups not shown.</strong> The CRDC also reports arrests for Asian,
           Hawaiian/Pacific Islander, and multiracial students. The underlying research does not
-          model these groups: it focuses on the four race/ethnicity groups where prior work has
+          model these groups due to extreme sparsity in the outcome of interest and computational 
-          documented the starkest disparities — Black and American Indian/Alaska Native students
+          limits. Fitting every reported group would also have meant fitting 70
-          relative to White students — with Hispanic students included for their large and growing
-          share of U.S. enrollment. Fitting every reported group would also have meant fitting 70
           stratified models rather than 40. Their absence here reflects that scope, not a finding
           about those students, and no estimate for them should be inferred from this page. See the{' '}
           <a href="https://crdc-api.civilytics.org/api/v1/" target="_blank" rel="noopener noreferrer">
             white paper
           </a>{' '}
           for the full rationale. Arrests that cannot be disaggregated by both race and sex —
-          including Section 504 students — are excluded upstream, as are schools not enrolling
+          including Section 504 students — are excluded upstream, as are the small number of arrests in 
-          grade 7 or above.
+            schools not enrolling grade 7 or above.
         </p>
       </div>
     </div>

src/hooks/useDrawDistribution.js

@@ -1,6 +1,7 @@
 import { useEffect, useMemo, useState } from 'react'
 import { getDb } from '../utils/duckdbClient.js'
 import { groupKey, isCompleteDrawSet } from '../utils/drawGroups.js'
+import { totalInterval, totalPerDraw } from '../utils/districtTotal.js'
 
 const HF_DATASET = 'civilytics/crdc-school-arrest-rates'
 const HF_BASE = `https://huggingface.co/datasets/${HF_DATASET}/resolve/main/parquet`
@@ -24,6 +25,57 @@ function shardDir(model, year, state) {
   return `model_id=${model}/YEAR=${year}/LEA_STATE=${state}`
 }
 
+// Directory listings are ~1KB and carry each part's byte size, so the UI can
+// tell the reader what a fetch will cost before committing to it. Cached
+// separately from the buffers: listing a shard is cheap, downloading it is not.
+const listingCache = new Map()
+
+/**
+ * @returns {Promise<Array<{part: number, size: number}>>} parquet parts, in order
+ */
+function listShardEntries(model, year, state) {
+  const dir = shardDir(model, year, state)
+  if (!listingCache.has(dir)) {
+    listingCache.set(
+      dir,
+      (async () => {
+        try {
+          const res = await fetch(`${HF_TREE}/${dir}`)
+          if (!res.ok) throw new Error(`tree listing HTTP ${res.status}`)
+          const entries = await res.json()
+          return entries
+            .filter((e) => e?.type === 'file' && /\/data_\d+\.parquet$/.test(e.path || ''))
+            .map((e) => ({ part: Number(e.path.match(/data_(\d+)\.parquet$/)[1]), size: e.size || 0 }))
+            .sort((a, b) => a.part - b.part)
+        } catch (err) {
+          listingCache.delete(dir)
+          throw err
+        }
+      })(),
+    )
+  }
+  return listingCache.get(dir)
+}
+
+/**
+ * Total bytes of the draw shards for one model across several years — what a
+ * "compute this from the draws" action will actually download.
+ *
+ * @returns {Promise<number>} bytes, or 0 if the size can't be determined
+ */
+export async function measureShardBytes(model, years, state) {
+  try {
+    const sizes = await Promise.all(
+      years.map(async (year) =>
+        (await listShardEntries(model, year, state)).reduce((sum, p) => sum + p.size, 0),
+      ),
+    )
+    return sizes.reduce((sum, n) => sum + n, 0)
+  } catch {
+    return 0
+  }
+}
+
 /**
  * Lists the parquet parts published for one (model, year, state).
  *
@@ -42,13 +94,7 @@ function shardDir(model, year, state) {
 async function listShardParts(model, year, state) {
   const dir = shardDir(model, year, state)
   try {
-    const res = await fetch(`${HF_TREE}/${dir}`)
+    const parts = await listShardEntries(model, year, state)
-    if (!res.ok) throw new Error(`tree listing HTTP ${res.status}`)
-    const entries = await res.json()
-    const parts = entries
-      .filter((e) => e?.type === 'file' && /\/data_\d+\.parquet$/.test(e.path || ''))
-      .map((e) => ({ part: Number(e.path.match(/data_(\d+)\.parquet$/)[1]), path: e.path }))
-      .sort((a, b) => a.part - b.part)
     if (parts.length > 0) return parts.map((p) => p.part)
     throw new Error('tree listing contained no parquet parts')
   } catch (err) {
@@ -139,12 +185,18 @@ async function fetchModelCounts(db, { leaid, state, model, year }) {
     // a short draw set: its density and interval would be computed off a
     // biased subsample and look identical on screen to a complete one.
     const counts = {}
+    let dropped = 0
     for (const [key, arr] of Object.entries(raw)) {
       if (isCompleteDrawSet(arr, nDraws)) counts[key] = arr
-      else console.warn('useDrawDistribution: dropping incomplete draw set for', { leaid, model, key, got: arr.length, want: nDraws })
+      else {
+        dropped += 1
+        console.warn('useDrawDistribution: dropping incomplete draw set for', { leaid, model, key, got: arr.length, want: nDraws })
+      }
     }
 
-    return Object.keys(counts).length > 0 ? { counts, nDraws } : null
+    // `dropped` matters to any consumer that aggregates *across* groups (the
+    // district total): a missing group there is an undercount, not a gap.
+    return Object.keys(counts).length > 0 ? { counts, nDraws, dropped } : null
   } finally {
     if (conn) await conn.close()
   }
@@ -257,3 +309,89 @@ export function useDrawDistribution({ leaid, state, models, year }) {
 
   return { status, byModel, nDraws }
 }
+
+/**
+ * The district's total arrest count per wave, with a 95% interval computed from
+ * the draws — summed within each draw, then summarized across draws.
+ *
+ * Gated behind `enabled` because the cost is wildly uneven: three waves of
+ * Nevada is 0.3MB, but California is 13.9MB and Texas 14.3MB. `bytes` is
+ * probed from the directory listings up front (~1KB per year) so the caller can
+ * either fetch automatically when it's cheap or show the reader the price
+ * first.
+ *
+ * @param {{leaid: string, state: string, model: string, years: string[], enabled: boolean}} params
+ * @returns {{status: 'idle'|'loading'|'ready'|'error',
+ *   byYear: Record<string, {lower:number, median:number, upper:number, nDraws:number}> | null,
+ *   bytes: number}}
+ */
+export function useDistrictTotalDraws({ leaid, state, model, years, enabled }) {
+  const [status, setStatus] = useState('idle')
+  const [byYear, setByYear] = useState(null)
+  const [bytes, setBytes] = useState(0)
+
+  const yearsSignature = (years || []).join(',')
+
+  // Probe sizes regardless of `enabled` — this is what lets the UI decide.
+  useEffect(() => {
+    let cancelled = false
+    setBytes(0)
+    if (!state || !model || !yearsSignature) return
+    measureShardBytes(model, yearsSignature.split(','), state).then((n) => {
+      if (!cancelled) setBytes(n)
+    })
+    return () => {
+      cancelled = true
+    }
+  }, [state, model, yearsSignature])
+
+  useEffect(() => {
+    let cancelled = false
+    setStatus(enabled ? 'loading' : 'idle')
+    setByYear(null)
+
+    if (!enabled || !leaid || !state || !model || !yearsSignature) return
+
+    async function run() {
+      try {
+        const db = await getDb()
+        const yearList = yearsSignature.split(',')
+        const results = await Promise.all(
+          yearList.map(async (year) => {
+            try {
+              const model_ = await fetchModelCounts(db, { leaid, state, model, year })
+              if (!model_ || model_.dropped > 0) return [year, null]
+              const interval = totalInterval(totalPerDraw(model_.counts, model_.nDraws))
+              return [year, interval]
+            } catch (err) {
+              console.error(`useDistrictTotalDraws: ${year} failed:`, err)
+              return [year, null]
+            }
+          }),
+        )
+        if (cancelled) return
+        const next = Object.fromEntries(results)
+        if (Object.values(next).some((v) => v !== null)) {
+          setByYear(next)
+          setStatus('ready')
+        } else {
+          setByYear(null)
+          setStatus('error')
+        }
+      } catch (err) {
+        console.error('useDistrictTotalDraws failed:', err)
+        if (!cancelled) {
+          setByYear(null)
+          setStatus('error')
+        }
+      }
+    }
+
+    run()
+    return () => {
+      cancelled = true
+    }
+  }, [leaid, state, model, yearsSignature, enabled])
+
+  return { status, byYear, bytes }
+}

src/utils/districtTotal.js

@@ -0,0 +1,104 @@
+/**
+ * The district-wide arrest total, taken from the posterior predictive draws.
+ *
+ * Why this exists: the time-series chart used to draw its band by summing each
+ * student group's own `count_lower`/`count_upper`. That is not the interval of
+ * the total. The sum of per-group 97.5th percentiles is the value you would see
+ * if *every* group simultaneously landed at its own extreme in the same draw,
+ * which is far less likely than any one group doing so — so the band came out
+ * systematically too wide. Summing within each draw and taking quantiles of the
+ * resulting totals answers the actual question: how many arrests does the model
+ * think this district had?
+ *
+ * This is `build_state_summary()`'s method from crdc-arrests/R/summarize_draws.R
+ * applied on a different axis — sum inside the draw, summarize across draws —
+ * the same operation `poolBySex` performs for sex pooling.
+ *
+ * One caveat to carry into any caption. Upstream, `draw_id` is renumbered per
+ * write batch, so draw *k* of one group is not the same posterior sample as
+ * draw *k* of another; measured cross-group correlation is ≈ 0.02. Summing at a
+ * draw index therefore convolves what are effectively independent draws. That
+ * is a reasonable model here — these are *posterior predictive* draws, whose
+ * observation noise is independent across groups by construction and dominates
+ * the parameter-level covariance — but it does mean the result should be read
+ * as a predictive total, not as a contrast that preserves parameter
+ * correlation. It is still much closer to the truth than summing bounds.
+ */
+
+import { quantile } from './kde.js'
+import { isCompleteDrawSet } from './drawGroups.js'
+
+/** Matches the API's default interval, so the two are directly comparable. */
+export const TOTAL_INTERVAL_MASS = 0.95
+
+/**
+ * District total at each draw index: the sum across every student group.
+ *
+ * Returns null unless *every* group has a complete draw set. A group silently
+ * missing from the sum would undercount the total at every draw and shift the
+ * whole interval down, which is indistinguishable on screen from a real result.
+ *
+ * @param {Record<string, number[]> | null | undefined} countsByGroup
+ * @param {number} nDraws
+ * @returns {number[] | null}
+ */
+export function totalPerDraw(countsByGroup, nDraws) {
+  const groups = Object.values(countsByGroup || {})
+  if (!groups.length || !(nDraws > 0)) return null
+  if (!groups.every((counts) => isCompleteDrawSet(counts, nDraws))) return null
+
+  const totals = new Array(nDraws).fill(0)
+  for (const counts of groups) {
+    for (let i = 0; i < nDraws; i++) totals[i] += counts[i]
+  }
+  return totals
+}
+
+/**
+ * Narrowest interval containing `mass` of the values — the highest-density
+ * interval, matching what the API stores.
+ *
+ * The API's `count_lower`/`count_upper` are HPD bounds (`hpd_bounds_sql` in
+ * crdc-arrests/R/summarize_draws.R), not equal-tailed quantiles, and the white
+ * paper's figures use the same. Computing the total's interval the same way
+ * keeps one definition of "95% interval" on the page: the difference is only
+ * two or three arrests on a Clark County band of ~50, but the chart's fallback
+ * mode shows summed HPD bounds, and mixing conventions between the two modes
+ * would be a distinction with no explanation.
+ *
+ * Contiguous by construction, as the R original is. For a strongly bimodal
+ * posterior that is a simplification, but a count total summed across eight
+ * groups is unimodal in practice.
+ *
+ * @param {number[]} values
+ * @param {number} mass - e.g. 0.95
+ * @returns {[number, number]}
+ */
+export function hpdBounds(values, mass) {
+  const sorted = [...values].sort((a, b) => a - b)
+  const n = sorted.length
+  const span = Math.ceil(mass * n) - 1
+  if (span <= 0) return [sorted[0], sorted[0]]
+  if (span >= n - 1) return [sorted[0], sorted[n - 1]]
+
+  let best = [sorted[0], sorted[span]]
+  let bestWidth = sorted[span] - sorted[0]
+  for (let i = 1; i + span < n; i++) {
+    const width = sorted[i + span] - sorted[i]
+    if (width < bestWidth) {
+      bestWidth = width
+      best = [sorted[i], sorted[i + span]]
+    }
+  }
+  return best
+}
+
+/**
+ * @param {number[] | null | undefined} totals - district total per draw
+ * @returns {{lower: number, median: number, upper: number, nDraws: number} | null}
+ */
+export function totalInterval(totals) {
+  if (!totals?.length) return null
+  const [lower, upper] = hpdBounds(totals, TOTAL_INTERVAL_MASS)
+  return { lower, median: quantile(totals, 0.5), upper, nDraws: totals.length }
+}

src/utils/districtTotal.test.js

@@ -0,0 +1,139 @@
+import { test } from 'node:test'
+import assert from 'node:assert/strict'
+import { TOTAL_INTERVAL_MASS, hpdBounds, totalInterval, totalPerDraw } from './districtTotal.js'
+
+// ——— totalPerDraw ———
+
+test('totalPerDraw: sums every group at the same draw index', () => {
+  const counts = { BL_F: [1, 2, 3], BL_M: [10, 20, 30], WH_F: [100, 200, 300] }
+  assert.deepEqual(totalPerDraw(counts, 3), [111, 222, 333])
+})
+
+test('totalPerDraw: a single group is its own total', () => {
+  assert.deepEqual(totalPerDraw({ BL_M: [4, 5] }, 2), [4, 5])
+})
+
+test('totalPerDraw: null when any group is short of nDraws', () => {
+  // Summing a 2-draw group into a 3-draw total would silently undercount the
+  // last draw, biasing the whole interval downward.
+  assert.equal(totalPerDraw({ BL_F: [1, 2, 3], BL_M: [1, 2] }, 3), null)
+})
+
+test('totalPerDraw: null when a group has a hole', () => {
+  const holey = [1, 2, 3]
+  delete holey[1]
+  assert.equal(totalPerDraw({ BL_F: holey }, 3), null)
+})
+
+test('totalPerDraw: null for empty or missing input', () => {
+  assert.equal(totalPerDraw({}, 500), null)
+  assert.equal(totalPerDraw(null, 500), null)
+  assert.equal(totalPerDraw({ BL_F: [1] }, 0), null)
+})
+
+test('totalPerDraw: does not mutate its input', () => {
+  const counts = { BL_F: [1, 2], BL_M: [3, 4] }
+  totalPerDraw(counts, 2)
+  assert.deepEqual(counts, { BL_F: [1, 2], BL_M: [3, 4] })
+})
+
+// ——— totalInterval ———
+
+test('totalInterval: median and 95% bounds from the draw totals', () => {
+  // Symmetric and unimodal, so the HPD should sit close to the equal-tailed
+  // 25–975 without being required to equal it.
+  const totals = []
+  for (let i = 0; i < 1000; i++) {
+    totals.push(500 + 120 * (Math.sin(i * 1.7) + Math.sin(i * 0.31) + Math.sin(i * 2.9)) / 3)
+  }
+  const iv = totalInterval(totals)
+  assert.equal(iv.nDraws, 1000)
+  assert.ok(iv.lower < iv.median && iv.median < iv.upper)
+  assert.ok(Math.abs(iv.median - 500) < 25, `median ${iv.median}`)
+})
+
+test('totalInterval: bounds are the narrowest window covering 95% of draws', () => {
+  const totals = Array.from({ length: 1000 }, (_, i) => i)
+  const iv = totalInterval(totals)
+  const inside = totals.filter((t) => t >= iv.lower && t <= iv.upper).length
+  assert.ok(inside >= 950, `only ${inside} of 1000 draws inside`)
+  // A uniform has no denser region, so the narrowest window is ~95% of the range.
+  assert.ok(iv.upper - iv.lower <= 951, `width ${iv.upper - iv.lower}`)
+})
+
+test('hpdBounds: never wider than the equal-tailed interval', () => {
+  // Right-skewed, which is where the two definitions diverge most.
+  const skewed = Array.from({ length: 2000 }, (_, i) => Math.round(((i * 7919) % 1000) ** 1.6 / 1000))
+  const [lo, hi] = hpdBounds(skewed, 0.95)
+  const sorted = [...skewed].sort((a, b) => a - b)
+  const etLo = sorted[Math.floor(0.025 * (sorted.length - 1))]
+  const etHi = sorted[Math.ceil(0.975 * (sorted.length - 1))]
+  assert.ok(hi - lo <= etHi - etLo, `hpd ${hi - lo} vs equal-tailed ${etHi - etLo}`)
+})
+
+test('hpdBounds: stays in the dense region when it holds enough mass', () => {
+  // 970 draws at 0-9 and 30 stragglers out at 500. The cluster alone covers 97%,
+  // so the narrowest 95% window fits inside it and the far tail is excluded.
+  const values = [
+    ...Array.from({ length: 970 }, (_, i) => i % 10),
+    ...Array.from({ length: 30 }, () => 500),
+  ]
+  const [lo, hi] = hpdBounds(values, 0.95)
+  assert.equal(lo, 0)
+  assert.ok(hi < 500, `upper bound ${hi} should exclude the far cluster`)
+})
+
+test('hpdBounds: still reaches the tail when the cluster is too small', () => {
+  // The mirror case, and the honest one: 90% in the cluster cannot cover a 95%
+  // interval, so the bound must extend outward rather than under-covering.
+  const values = [
+    ...Array.from({ length: 900 }, (_, i) => i % 10),
+    ...Array.from({ length: 100 }, () => 500),
+  ]
+  const [, hi] = hpdBounds(values, 0.95)
+  assert.equal(hi, 500)
+})
+
+test('hpdBounds: degenerate input collapses to a point', () => {
+  assert.deepEqual(hpdBounds(new Array(100).fill(7), 0.95), [7, 7])
+})
+
+test('hpdBounds: does not mutate its input', () => {
+  const values = [5, 1, 3]
+  hpdBounds(values, 0.95)
+  assert.deepEqual(values, [5, 1, 3])
+})
+
+test('totalInterval: uses a 95% mass, matching the API convention', () => {
+  assert.equal(TOTAL_INTERVAL_MASS, 0.95)
+})
+
+test('totalInterval: lower <= median <= upper', () => {
+  const totals = Array.from({ length: 500 }, (_, i) => (i * 7919) % 331)
+  const iv = totalInterval(totals)
+  assert.ok(iv.lower <= iv.median && iv.median <= iv.upper)
+})
+
+test('totalInterval: a degenerate total collapses to a point', () => {
+  const iv = totalInterval(new Array(500).fill(12))
+  assert.deepEqual([iv.lower, iv.median, iv.upper], [12, 12, 12])
+})
+
+test('totalInterval: null for empty or missing totals', () => {
+  assert.equal(totalInterval([]), null)
+  assert.equal(totalInterval(null), null)
+})
+
+test('totalInterval: is narrower than summing the groups own bounds', () => {
+  // The property that motivates this whole path. Two independent groups, each
+  // roughly uniform on 0..100: summing each group's 97.5th percentile gives
+  // ~200, but the 97.5th percentile of the *sum* is well below that, because
+  // both groups landing at their extreme in the same draw is rare.
+  const n = 4000
+  const a = Array.from({ length: n }, (_, i) => (i * 37) % 101)
+  const b = Array.from({ length: n }, (_, i) => (i * 61) % 101)
+  const iv = totalInterval(totalPerDraw({ A: a, B: b }, n))
+  const summedBounds = { lower: 0, upper: 100 + 100 }
+  assert.ok(iv.upper < summedBounds.upper, `sum-of-quantiles ${summedBounds.upper} vs quantile-of-sum ${iv.upper}`)
+  assert.ok(iv.upper - iv.lower < summedBounds.upper - summedBounds.lower)
+})

src/utils/rateDomain.js

@@ -10,15 +10,22 @@ import { quantile } from './kde.js'
 import { niceTicks } from './niceTicks.js'
 
 /**
- * Hard ceiling on the axis, inherited from the chart this replaces.
+ * Hard ceiling on the axis.
  *
  * A four-student cell can produce posterior draws in the hundreds per 1,000;
  * letting those set the axis squashes every other group into the leftmost few
  * pixels. `computeRateDomain` reports `clipped` whenever the cap actually
  * binds, so the chart can say so rather than cropping data off the edge in
  * silence.
+ *
+ * Set to 100 per 1,000 (one arrest per ten students). The previous value of
+ * 30 was exceeded by over 60% of districts — mostly sparse groups with small
+ * enrollment cells whose Agresti–Coull upper bounds genuinely extend that far.
+ * A cap of 100 still guards against the most degenerate cases (e.g. a single
+ * predicted arrest in a four-student cell yielding ~250 per 1,000) while
+ * letting realistic data drive the axis for the vast majority of districts.
  */
-export const MAX_RATE_DOMAIN = 30
+export const MAX_RATE_DOMAIN = 100
 
 /**
  * Ignore the very top of each draw set when sizing the axis. The posterior
@@ -30,6 +37,14 @@ const DOMAIN_QUANTILE = 0.995
 const HEADROOM = 1.15
 
 /**
+ * Computes a shared x-domain for the rate density and over-time charts.
+ *
+ * The domain covers everything that will actually be drawn: the 0.995
+ * quantile of each group's posterior-predictive draw rates, plus every
+ * Agresti–Coull upper bound from selected groups. `niceMax` is a clean
+ * "nice number" ceiling (via `niceTicks`) that may exceed the raw data max by
+ * up to one tick step, and is capped at `MAX_RATE_DOMAIN`.
+ *
  * @param {Array<number[]>} rateArrays - per-group draw rates, per 1,000
  * @param {number[]} acUpperRates - Agresti–Coull upper bounds, per 1,000
  * @returns {{ticks: number[], niceMax: number, clipped: boolean}}

src/utils/rateDomain.test.js

@@ -23,16 +23,27 @@ test('computeRateDomain: one extreme draw does not blow out the axis', () => {
   assert.ok(domain.niceMax < 10, `niceMax was ${domain.niceMax}`)
 })
 
-test('computeRateDomain: caps the domain and reports the clip', () => {
+test('computeRateDomain: caps at MAX_RATE_DOMAIN=100 and reports the clip', () => {
   // The cap keeps a tiny-denominator group from flattening every other curve,
   // but the caller has to be able to say so on screen rather than silently
   // cropping data off the right edge.
-  const wide = new Array(500).fill(0).map((_, i) => (i < 490 ? 60 : 0))
+  const wide = new Array(500).fill(0).map((_, i) => (i < 490 ? 200 : 0))
-  const domain = computeRateDomain([wide], [80])
+  const domain = computeRateDomain([wide], [300])
   assert.equal(domain.niceMax, MAX_RATE_DOMAIN)
   assert.equal(domain.clipped, true)
 })
 
+test('computeRateDomain: realistic sparse district data is not clipped', () => {
+  // Carson City NV (LEAID 3200390): pooled BL cell with 34 students and 0
+  // observed arrests → AC upper bound ≈ 88 per 1,000. This should NOT be
+  // clipped under the new cap of 100.
+  const blRates = new Array(500).fill(0)
+  const domain = computeRateDomain([blRates], [88])
+  assert.ok(domain.niceMax >= 88, `niceMax ${domain.niceMax} should cover AC bound of 88`)
+  assert.equal(domain.clipped, false)
+})
+
+
 test('computeRateDomain: never returns a zero-width domain', () => {
   const domain = computeRateDomain([[0, 0, 0]], [0])
   assert.ok(domain.niceMax > 0)
@@ -49,3 +60,14 @@ test('computeRateDomain: ignores empty rate arrays', () => {
   const domain = computeRateDomain([[], [1, 2, 3]], [])
   assert.ok(domain.niceMax > 0 && domain.niceMax < MAX_RATE_DOMAIN)
 })
+
+test('computeRateDomain: degenerate tiny-denominator cell is clipped', () => {
+  // A four-student cell with a single predicted arrest yields ~250 per
+  // 1,000 — this should be capped at MAX_RATE_DOMAIN=100 and flagged as
+  // clipped so the chart can warn the reader.
+  const tinyRates = new Array(500).fill(0)
+  for (let i = 0; i < 250; i++) tinyRates[i] = 250
+  const domain = computeRateDomain([tinyRates], [300])
+  assert.equal(domain.niceMax, MAX_RATE_DOMAIN)
+  assert.equal(domain.clipped, true)
+})