Source: https://guthlabs.ai/docs/instruments/johnson-parabolic-formula-intermediate-columns/implementation/

instrument implementation / implementation-contract

# Johnson Parabolic Formula (Intermediate Columns) implementation

A source-bound implementation contract for Johnson Parabolic Formula (Intermediate Columns); deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t4-118

**Effect**: Computation or source lookup only

## Input and validation requirements

The zero-modulus input makes the Johnson expression and critical slenderness ratio undefined through division by zero. The instrument should explicitly reject E = 0 rather than return a numeric critical stress.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "yield_strength": {
      "value": 250,
      "unit": "MPa"
    },
    "elastic_modulus": {
      "value": 200000,
      "unit": "MPa"
    },
    "slenderness_ratio_KL_over_r": 0
  },
  "expected_outputs": {
    "critical_stress": {
      "value": 250,
      "unit": "MPa"
    },
    "critical_slenderness_ratio": 125.663706,
    "applicable_to_strict_less_than_range": true
  },
  "working": "Cc=√(2π²E/σy)=√(2π²×200000/250)=√(1600π²)=40π=125.663706. σcr=σy−[σy²/(4π²E)](KL/r)²=250−[250²/(4π²×200000)]×0²=250−0=250 MPa. Since 0<125.663706, the Johnson range check is true."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/johnson-parabolic-formula-intermediate-columns/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/johnson-parabolic-formula-intermediate-columns/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/johnson-parabolic-formula-intermediate-columns/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-tranche4/tranche4-results.json`