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    {
      "category": "Roads",
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    {
      "category": "Roads",
      "program": "Road Widening - Primary Roads",
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    },
    {
      "category": "Roads",
      "program": "Road Widening - Secondary Roads",
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      "candidateBoundaryMeters": 713.9152610779518,
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      "sensitivityMinimum25mBicImprovement": 0.4926277731544815
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      "status": "Insufficient observations for breakpoint search"
    }
  ],
  "method": {
    "bands": "Within-PAP approximately equal-count length bands, up to eight, targeting at least 20 observations per band; duplicate observed lengths are never split.",
    "changeRule": "At least 20 observations in each consecutive populated band of the same category and official PAP; median density differs by at least 2×. A descriptive screen, not a significance test.",
    "breakpointModel": "Within one PAP: continuous piecewise log(allocation)=intercept+slope*log(length)+hinge at a data-derived candidate boundary. Compare against single-slope log allocation model with BIC.",
    "candidateBoundaries": "Geometric midpoints between adjacent observed distinct lengths with at least 20 records per side; at most 31 candidates spaced across eligible distinct-length boundaries.",
    "minimumModelRecords": 80,
    "minimumRecordsEachSide": 20,
    "minimumModelLengthMeters": 10,
    "bicImprovementScreen": 6,
    "bootstrapRepetitions": 100,
    "bootstrapSeed": 20271011,
    "limits": [
      "Density=allocation/length; declining density can follow mechanically from a fixed budget.",
      "Quantile-band counts and 2×/BIC screens are editorial exploratory choices, not calibrated corruption thresholds.",
      "Models use total allocation rather than density to reduce the arithmetic-denominator trap.",
      "Bootstrap votes measure selection stability in this sample, not the probability of a real engineering threshold.",
      "Dependence between allocation occurrences, unknown width/terrain/structures and non-random missing lengths remain uncontrolled.",
      "Sub-10m rows stay visible in bands but are excluded from model fits; ≥25m sensitivity is reported.",
      "Multiple exploratory program/boundary searches are not confirmatory significance tests; no p-values or multiplicity-adjusted claims are made.",
      "Sparse bridge/FMR data cannot establish an engineering threshold. No pooled cross-category rate model."
    ]
  }
}