Source: https://guthlabs.ai/docs/instruments/mohr-s-circle-for-3d-stress-principal-stresses/implementation/

instrument implementation / implementation-contract

# Mohr's Circle for 3D Stress (Principal Stresses) implementation

A source-bound implementation contract for Mohr's Circle for 3D Stress (Principal Stresses); 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**: t8-007

**Effect**: Computation or source lookup only

## Input and validation requirements

The extreme-magnitude vector exposes a numeric hazard: although the exact mathematical principal stresses are finite, binary64/JavaScript arithmetic overflows the τmax subtraction to Infinity, and cubic characteristic-equation coefficient formation can also overflow.

## 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": {
    "sigma_x": "0 MPa",
    "sigma_y": "0 MPa",
    "sigma_z": "0 MPa",
    "tau_xy": "0 MPa",
    "tau_yz": "0 MPa",
    "tau_zx": "0 MPa"
  },
  "expected_outputs": {
    "principal_stresses": [
      "0 MPa",
      "0 MPa",
      "0 MPa"
    ],
    "tau_max": "0 MPa",
    "canonical_exact_result": {
      "characteristic_polynomial": "lambda^3",
      "eigenvalues": [
        "0",
        "0",
        "0"
      ],
      "ordering": "sigma1 = sigma2 = sigma3 = 0"
    },
    "eigenvector_verification": {
      "A_v1": [
        "1.000000000",
        "0.000000000",
        "0.000000000"
      ],
      "lambda1_v1": [
        "0.000000000",
        "0.000000000",
        "0.000000000"
      ],
      "A_v2": [
        "0.000000000",
        "1.000000000",
        "0.000000000"
      ],
      "lambda2_v2": [
        "0.000000000",
        "0.000000000",
        "0.000000000"
      ],
      "A_v3": [
        "0.000000000",
        "0.000000000",
        "1.000000000"
      ],
      "lambda3_v3": [
        "0.000000000",
        "0.000000000",
        "0.000000000"
      ]
    },
    "spot_checks": [
      {
        "at": "zero tensor, eigenvalue 1",
        "input_side": 0,
        "answer_side": 0
      },
      {
        "at": "zero tensor, eigenvalue 2",
        "input_side": 0,
        "answer_side": 0
      }
    ]
  },
  "reference_data": {
    "stress_tensor": "[[0,0,0],[0,0,0],[0,0,0]] MPa",
    "eigenvectors": [
      "[1,0,0]",
      "[0,1,0]",
      "[0,0,1]"
    ]
  },
  "working": "A = [[0,0,0],[0,0,0],[0,0,0]] MPa.\n det(lambda I - A) = det([[lambda,0,0],[0,lambda,0],[0,0,lambda]]) = lambda^3.\n Therefore lambda = 0, 0, 0 MPa, so sigma1 = sigma2 = sigma3 = 0 MPa.\n tau_max = (sigma1 - sigma3)/2 = (0 - 0)/2 = 0 MPa.\n Verification: A times each coordinate-basis eigenvector is [0,0,0], equal to lambda times that eigenvector."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/mohr-s-circle-for-3d-stress-principal-stresses/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/mohr-s-circle-for-3d-stress-principal-stresses/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/mohr-s-circle-for-3d-stress-principal-stresses/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-tranche8/tranche8-results.json`