Source: https://guthlabs.ai/docs/instruments/trigonometric-identity-verifier-simplifier/implementation/

instrument implementation / implementation-contract

# Trigonometric Identity Verifier & Simplifier implementation

A source-bound implementation contract for Trigonometric Identity Verifier & Simplifier; 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**: t8-034

**Effect**: Computation or source lookup only

## Input and validation requirements

The verifier must explicitly reject undefined samples such as tan(pi/2), preserve absolute-value branch behavior in sqrt(sin(x)^2), and require an angle-unit convention. Otherwise it can return misleading finite values, an invalid global simplification, or a wrong identity verdict.

## 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": {
    "expression": "sin(x)^2 + cos(x)^2",
    "sample_points": [
      "x=0",
      "x=pi/6",
      "x=pi/4"
    ]
  },
  "expected_outputs": {
    "simplified_form": "1",
    "identity_verdict": true,
    "spot_checks": [
      {
        "at": {
          "x": 0
        },
        "input_side": 1,
        "answer_side": 1
      },
      {
        "at": {
          "x": 0.5235987756
        },
        "input_side": 1,
        "answer_side": 1
      },
      {
        "at": {
          "x": 0.7853981634
        },
        "input_side": 1,
        "answer_side": 1
      }
    ]
  },
  "reference_data": {
    "identity": "sin(x)^2+cos(x)^2=1",
    "domain": "all real x"
  },
  "working": "At x=0: sin(0)^2+cos(0)^2=0^2+1^2=1. At x=pi/6: (1/2)^2+(sqrt(3)/2)^2=1/4+3/4=1. At x=pi/4: (sqrt(2)/2)^2+(sqrt(2)/2)^2=1/2+1/2=1."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/trigonometric-identity-verifier-simplifier/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/trigonometric-identity-verifier-simplifier/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/trigonometric-identity-verifier-simplifier/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`