Pediatric Growth Percentile Lookup mechanism

Model scope

The core LMS formula is standard, but the specification is not implementation-complete. It needs an authoritative table source, exact age and interpolation rules, the L=0 branch, explicit standard-normal-CDF conversion, measurement definitions, valid age ranges, and a BMI input definition. The educational/non-medical-advice label is appropriate but does not resolve these technical ambiguities.

• The LMS Z-score formula is standard when L, M, and S are valid parameters: Z=((X/M)^L-1)/(L*S). The implementation must also define the L=0 special case, Z=ln(X/M)/S.
• The percentile conversion is incomplete: it must explicitly specify percentile=100*Phi(Z), where Phi is the standard normal CDF.
• BMI cannot be computed from only one measurement value; BMI requires weight and height, BMI=weight_kg/(height_m^2), unless the supplied value is already BMI.
• The interpolation method between age rows is unspecified. Linear interpolation of L, M, and S is a possible convention but is not universally interchangeable with interpolation of Z-scores or chart centiles.
• The specification does not identify whether WHO or CDC tables are authoritative. WHO and CDC tables differ in age ranges, measurement definitions, and parameters.
• The term height is ambiguous for children under 24 months; WHO tables generally use recumbent length, while standing height is used for older children, with a conversion difference between them.

Units and conventions

• Age is expressed in completed or exact decimal months; the exact-age convention must be documented because growth parameters change rapidly in infancy.
• Weight is in kilograms, length/height and head circumference are in centimeters, and BMI is in kg/m^2.
• X, M, and the resulting measurement must use the same units; unit conversion must occur before applying the LMS formula.
• Sex is assumed to select the sex-specific WHO reference row; the specification must state whether this means sex at birth or another classification.
• Percentiles use the standard normal CDF: percentile=100*Phi(Z).

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "age_months": 24,
    "sex": "male",
    "measurement_type": "recumbent_length_cm",
    "value": 87.1
  },
  "expected_outputs": {
    "z_score": 0,
    "percentile": 50,
    "growth_chart_position": "50th percentile (median)"
  },
  "reference_data": {
    "source_convention": "WHO Child Growth Standards 2006, boys length-for-age LMS row at 24 months",
    "L": 1,
    "M_cm": 87.1,
    "S": 0.039,
    "normal_CDF": {
      "Phi(0)": 0.5,
      "source_convention": "NIST/standard normal distribution table"
    }
  },
  "working": "L=1, so Z=((X/M)-1)/S. X/M=87.1/87.1=1.000000. Z=(1.000000-1)/0.039=0.000000. percentile=100*Phi(0)=100*0.5=50.0%. This is exactly the tabulated median and the famous 50th-percentile entry."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification does not define age units or table validity boundaries, does not provide the required CDC/WHO LMS tables, and gives no special handling for L=0 or invalid powers such as 0 raised to a negative L. A literal implementation can therefore return undefined results or cannot perform the lookup at all.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json