Taylor / Maclaurin Series Generator implementation

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

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