Source: https://guthlabs.ai/docs/instruments/summation-product-notation-evaluator/implementation/

instrument implementation / implementation-contract

# Summation & Product Notation Evaluator implementation

A source-bound implementation contract for Summation & Product Notation Evaluator; 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**: t4-021

**Effect**: Computation or source lookup only

## Input and validation requirements

The evaluator has an undefined-result failure mode when an expression such as 1/k includes k=0; it must reject the input instead of producing a numeric result. Geometric closed-form evaluation also requires a separate r=1 branch because the ordinary formula divides by 1-r.

## 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": {
    "operation": "sum",
    "expression": "k",
    "index": "k",
    "lower_bound": 1,
    "upper_bound": 10
  },
  "expected_outputs": {
    "numeric_total": 55,
    "closed_form_match": true,
    "closed_form": "N(N+1)/2"
  },
  "working": "Direct sum: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55. Closed form with N = 10: N(N+1)/2 = 10×11/2 = 110/2 = 55."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/summation-product-notation-evaluator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/summation-product-notation-evaluator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/summation-product-notation-evaluator/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-tranche4/tranche4-results.json`