Source: https://guthlabs.ai/docs/instruments/integral-calculator-symbolic-numeric/implementation/

instrument implementation / implementation-contract

# Integral Calculator (symbolic + numeric) implementation

A source-bound implementation contract for Integral Calculator (symbolic + numeric); 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**: t8-021

**Effect**: Computation or source lookup only

## Input and validation requirements

The input 1/x over [-1,1] forces the quadrature to evaluate 1/0 and the ordinary definite integral is undefined. A calculator that returns a finite number, such as the Cauchy principal value 0, without explicitly identifying the principal-value convention would be incorrect.

## 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": {
    "function": "3*x^2 - 4*x + 1",
    "variable": "x",
    "bounds": null
  },
  "expected_outputs": {
    "antiderivative": "x^3 - 2*x^2 + x + C",
    "spot_checks": [
      {
        "at": 1,
        "input_side": 0,
        "answer_side": 0
      },
      {
        "at": 2,
        "input_side": 5,
        "answer_side": 5
      }
    ]
  },
  "reference_data": {
    "method": "Differentiate the proposed antiderivative and compare with the integrand."
  },
  "working": "Let F(x)=x^3-2*x^2+x. Then F'(x)=3*x^2-4*x+1. At x=1: original=3(1)^2-4(1)+1=0; answer-side derivative=3(1)^2-4(1)+1=0. At x=2: original=3(2)^2-4(2)+1=12-8+1=5; answer-side derivative=12-8+1=5."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/integral-calculator-symbolic-numeric/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/integral-calculator-symbolic-numeric/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/integral-calculator-symbolic-numeric/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`