Source: https://guthlabs.ai/docs/instruments/taylor-maclaurin-series-generator/implementation/

instrument implementation / implementation-contract

# Taylor / Maclaurin Series Generator implementation

A source-bound implementation contract for Taylor / Maclaurin Series Generator; 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**: t8-023

**Effect**: Computation or source lookup only

## Input and validation requirements

The generator must reject centers where the function or required derivatives are undefined, must detect nondifferentiable branch switches, and must require an explicit angle-unit convention. Otherwise it can emit undefined coefficients or materially incorrect expansions.

## 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": "exp(x)",
    "center_a": "0",
    "order_N": 3,
    "evaluation_points": [
      "0.5000000000000000",
      "-1.000000000000000"
    ]
  },
  "expected_outputs": {
    "canonical_exact_symbolic_result": "P_3(x)=1+x+x^2/2+x^3/6",
    "spot_checks": [
      {
        "at": "x=0.5000000000000000",
        "input_side": 1.6487212707001282,
        "answer_side": 1.6458333333333333
      },
      {
        "at": "x=-1.000000000000000",
        "input_side": 0.3678794411714423,
        "answer_side": 0.3333333333333333
      }
    ],
    "remainder_estimate": "Not determinable from the specification because no remainder method or derivative bound is supplied."
  },
  "reference_data": {
    "interpretation": "order_N means terms k=0 through k=N",
    "exact_function_values": {
      "exp(1/2)": "e^(1/2)",
      "exp(-1)": "e^(-1)"
    },
    "exact_polynomial_values": {
      "P_3(1/2)": "79/48",
      "P_3(-1)": "1/3"
    }
  },
  "working": "Derivatives of exp(x) are all exp(x), so at a=0 every derivative equals 1. Therefore P_3(x)=1/0!+x/1!+x^2/2!+x^3/3!=1+x+x^2/2+x^3/6. At x=0.5: 1+0.5+(0.5^2)/2+(0.5^3)/6=1+0.5+0.125+0.0208333333333333=1.6458333333333333. The original value is exp(0.5)=1.6487212707001282. At x=-1: 1-1+1/2-1/6=1/3=0.3333333333333333. The original value is exp(-1)=0.3678794411714423."
}
````

## Other records

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