Source: https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/implementation/

instrument implementation / implementation-contract

# Column Buckling — Euler Critical Load implementation

A source-bound implementation contract for Column Buckling — Euler Critical Load; 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**: t4-106

**Effect**: Computation or source lookup only

## Input and validation requirements

The specification has no numerical slender-column validity threshold or Johnson-formula branch, so it cannot reliably classify the formula's applicability near the slender/short-column transition. It also produces undefined results for zero length unless the input is rejected, and negative K has an unresolved convention that can cause either silent normalization or invalid lookup behavior.

## 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": {
    "E_Pa": 200000000000,
    "I_m4": 0.000008,
    "A_m2": 0.004,
    "L_m": 3,
    "K": 1
  },
  "expected_outputs": {
    "Pcr_N": 1754596.34,
    "sigma_cr_Pa": 438649084.45,
    "slenderness_ratio": 67.08204
  },
  "working": "r = √(I/A) = √(0.000008/0.004) = √0.002 = 0.0447214 m. KL/r = (1×3)/0.0447214 = 67.08204. Pcr = π²EI/(KL)² = 9.8696044×200000000000×0.000008/(3)² = 9.8696044×1600000/9 = 1754596.34 N. σcr = Pcr/A = 1754596.34/0.004 = 438649084.45 Pa."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/column-buckling-euler-critical-load/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`