{
  "version": 1,
  "approvedHierarchyDate": "2026-10-20",
  "scope": "All unordered four-number hands from 1 through 13, with repetition; each tile exactly once; +, −, ×, ÷ only.",
  "assignment": "Minimum level across every enumerated expression. Ties prefer nonnegative routes, then smaller intermediate values and fewer division/subtraction operations. Tie-breaking never changes the assigned level.",
  "interpretation": "Teaching-template difficulty, not observed solve time or an empirical player rating.",
  "levelRules": {
    "1": "Nonnegative integer routes using only addition/subtraction, or only multiplication.",
    "2": "Obvious cancellation or making/using 0 or 1 that leaves direct arithmetic; multiplication and exact division with intermediates no larger than 24; or one operation on two original tiles followed by multiplication.",
    "3": "Construct 2 × 12, 3 × 8, or 4 × 6, with preparation not requiring a higher-level operation.",
    "4": "Combine positive integer subtotals by addition, or correct an overshoot above 24 by subtracting 1 through 6. Harder preparation still raises the level.",
    "5": "Divide a whole number above 24 by an integer greater than 1, whether as the final step or while constructing a factor. Harder preparation still raises the level.",
    "6": "A multiplicative/divisive route needs to subtract more than 6 from an intermediate value above 24. Integer routes using negative intermediates are also kept here; no minimum-level representative needs negatives.",
    "7": "Any noninteger intermediate value. A hand reaches this level only if all of its solutions need fractions."
  },
  "operationalChoices": {
    "smallSubtractionCorrectionMaximum": 6,
    "positiveIntegerAdditionComplements": "Level 4, unless the whole route qualifies for Level 1 or 2.",
    "preparation": "A familiar final factor pair does not override harder intermediate division or subtraction.",
    "zeroAndOne": "Only simplify genuine identity operations; multiplying a difficult three-tile solution by an original 1 does not make that route easy.",
    "counts": "Each distinct number combination counts once. Deck frequencies are not weights. Unsolvable hands have no level."
  }
}