Source: https://guthlabs.ai/docs/instruments/limit-calculator/implementation/

instrument implementation / implementation-contract

# Limit Calculator implementation

A source-bound implementation contract for Limit Calculator; 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**: t8-022

**Effect**: Computation or source lookup only

## Input and validation requirements

The calculator is vulnerable at removable-discontinuity and branch-sensitive inputs: direct endpoint evaluation can report undefined instead of the correct limit, and a numeric approach can incorrectly collapse unequal one-sided limits into a single result. The infinity convention also requires explicit signed-direction handling.

## 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": "(x^2 - 1)/(x - 1)",
    "approach_point": "1",
    "direction": "two-sided"
  },
  "expected_outputs": {
    "canonical_exact_limit": "2",
    "indeterminate_form_at_substitution": "0/0",
    "limit": "2",
    "spot_checks": [
      {
        "at": 0.999,
        "input_side": 1.999,
        "answer_side": 2
      },
      {
        "at": 1.001,
        "input_side": 2.001,
        "answer_side": 2
      }
    ]
  },
  "reference_data": {
    "identity": "x^2 - 1 = (x - 1)(x + 1)",
    "domain_restriction": "x != 1"
  },
  "working": "Substitution gives (1^2 - 1)/(1 - 1) = 0/0. Factor: (x^2 - 1)/(x - 1) = ((x - 1)(x + 1))/(x - 1) = x + 1 for x != 1. Therefore lim_{x->1} (x^2 - 1)/(x - 1) = lim_{x->1}(x + 1) = 1 + 1 = 2. Spot check: at x=0.9990000000, (x+1)=1.9990000000; at x=1.0010000000, (x+1)=2.0010000000. The original expression is undefined exactly at x=1, but its limit is 2."
}
````

## Other records

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