fix(search): order numbered headwords by numeric value

The final ranking tie-break compared headwords lexicographically,
so entries numbered with digits or CJK numerals sorted by text
instead of by number. Compare runs of digits or numeral characters
by their numeric value, saturating on very long runs.

app/src/main/java/com/example/research/core/util/NaturalSort.kt

@@ -0,0 +1,128 @@
+package com.example.research.core.util
+
+val NaturalStringComparator: Comparator<String> = Comparator { a, b -> compareNatural(a, b) }
+
+private const val NUMERAL_CAP = 1_000_000_000_000_000_000L
+
+private fun digitOf(c: Char): Int = when (c) {
+    '〇', '零' -> 0
+    '一', '壹', '壱', '弌' -> 1
+    '二', '貳', '贰', '弐', '弍', '兩', '两' -> 2
+    '三', '叁', '參', '参', '弎' -> 3
+    '四', '肆' -> 4
+    '五', '伍' -> 5
+    '六', '陸', '陆' -> 6
+    '七', '柒' -> 7
+    '八', '捌' -> 8
+    '九', '玖' -> 9
+    else -> Character.digit(c, 10)
+}
+
+private fun smallUnitOf(c: Char): Long = when (c) {
+    '十', '拾' -> 10L
+    '百', '佰' -> 100L
+    '千', '仟' -> 1000L
+    else -> 0L
+}
+
+private fun fixedTensOf(c: Char): Long = when (c) {
+    '廿' -> 20L
+    '卅' -> 30L
+    '卌' -> 40L
+    else -> 0L
+}
+
+private fun bigUnitOf(c: Char): Long = when (c) {
+    '万', '萬' -> 10_000L
+    '億', '亿' -> 100_000_000L
+    '兆' -> 1_000_000_000_000L
+    '京' -> 10_000_000_000_000_000L
+    else -> 0L
+}
+
+private fun isNumeralChar(c: Char): Boolean =
+    digitOf(c) >= 0 || smallUnitOf(c) > 0L || fixedTensOf(c) > 0L || bigUnitOf(c) > 0L
+
+private fun satMul(a: Long, b: Long): Long =
+    if (a != 0L && b > NUMERAL_CAP / a) NUMERAL_CAP else minOf(a * b, NUMERAL_CAP)
+
+private fun satAdd(a: Long, b: Long): Long = minOf(a + b, NUMERAL_CAP)
+
+private fun numeralValue(s: String, start: Int, end: Int): Long {
+    var total = 0L
+    var section = 0L
+    var pending = -1L
+    for (k in start until end) {
+        val c = s[k]
+        val digit = digitOf(c)
+        if (digit >= 0) {
+            pending = if (pending < 0) digit.toLong() else satAdd(satMul(pending, 10L), digit.toLong())
+            continue
+        }
+        val small = smallUnitOf(c)
+        if (small > 0L) {
+            section = satAdd(section, satMul(if (pending < 0) 1L else pending, small))
+            pending = -1
+            continue
+        }
+        val fixed = fixedTensOf(c)
+        if (fixed > 0L) {
+            section = satAdd(section, fixed)
+            pending = -1
+            continue
+        }
+        val base = satAdd(section, maxOf(pending, 0L))
+        total = satAdd(total, satMul(if (base == 0L) 1L else base, bigUnitOf(c)))
+        section = 0L
+        pending = -1
+    }
+    return satAdd(total, satAdd(section, maxOf(pending, 0L)))
+}
+
+private fun compareNatural(a: String, b: String): Int {
+    var i = 0
+    var j = 0
+    while (i < a.length && j < b.length) {
+        val ca = a[i]
+        val cb = b[j]
+        val asciiA = ca in '0'..'9'
+        val asciiB = cb in '0'..'9'
+        when {
+            !asciiA && !asciiB && isNumeralChar(ca) && isNumeralChar(cb) -> {
+                var endA = i
+                while (endA < a.length && isNumeralChar(a[endA])) endA++
+                var endB = j
+                while (endB < b.length && isNumeralChar(b[endB])) endB++
+                val diff = numeralValue(a, i, endA).compareTo(numeralValue(b, j, endB))
+                if (diff != 0) return diff
+                i = endA
+                j = endB
+            }
+            asciiA && asciiB -> {
+                var endA = i
+                while (endA < a.length && a[endA] in '0'..'9') endA++
+                var endB = j
+                while (endB < b.length && b[endB] in '0'..'9') endB++
+                var startA = i
+                while (startA < endA - 1 && a[startA] == '0') startA++
+                var startB = j
+                while (startB < endB - 1 && b[startB] == '0') startB++
+                val lengthA = endA - startA
+                val lengthB = endB - startB
+                if (lengthA != lengthB) return lengthA.compareTo(lengthB)
+                for (k in 0 until lengthA) {
+                    val diff = a[startA + k].compareTo(b[startB + k])
+                    if (diff != 0) return diff
+                }
+                i = endA
+                j = endB
+            }
+            else -> {
+                if (ca != cb) return ca.compareTo(cb)
+                i++
+                j++
+            }
+        }
+    }
+    return (a.length - i).compareTo(b.length - j)
+}

app/src/main/java/com/example/research/data/parser/SearchRanking.kt

@@ -1,6 +1,7 @@
 package com.example.research.data.parser
 
 import com.example.research.core.domain.model.IndexEntry
+import com.example.research.core.util.NaturalStringComparator
 import com.example.research.core.util.foldLatinDiacritics
 
 internal data class SearchRankingContext(
@@ -40,6 +41,11 @@ internal fun List<IndexEntry>.rankBySearchRelevance(
             entry = entry,
         )
     }
-        .sortedWith(compareBy({ it.matchTier }, { it.exactMatch }, { it.charCount }, { it.word }))
+        .sortedWith(
+            compareBy<SortKey> { it.matchTier }
+                .thenBy { it.exactMatch }
+                .thenBy { it.charCount }
+                .thenBy(NaturalStringComparator) { it.word }
+        )
         .map { it.entry }
 }