Source: https://guthlabs.ai/docs/instruments/pediatric-growth-percentile-lookup/mechanism/

instrument mechanism / verified-clean

# Pediatric Growth Percentile Lookup mechanism

The inspectable method record for Pediatric Growth Percentile Lookup, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/pediatric-growth-percentile-lookup/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/pediatric-growth-percentile-lookup/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/pediatric-growth-percentile-lookup/qualification/>)

## 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`