Source: https://guthlabs.ai/docs/instruments/sequence-series-explorer/implementation/

instrument implementation / implementation-contract

# Sequence & Series Explorer implementation

A source-bound implementation contract for Sequence & Series Explorer; 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**: t4-009

**Effect**: Computation or source lookup only

## Input and validation requirements

A naive geometric-sum implementation breaks at r=1 because the denominator r-1 becomes zero and produces 0/0. The instrument must switch to the constant-sequence sum branch. Negative signed differences also expose a convention risk if direction is not preserved.

## 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": {
    "type": "arithmetic",
    "a1": 7,
    "d": 3,
    "n": 5
  },
  "expected_outputs": {
    "term_list": [
      7,
      10,
      13,
      16,
      19
    ],
    "nth_term": 19,
    "partial_sum": 65,
    "closed_form": "aₙ=7+3(n−1)",
    "detected": "arithmetic"
  },
  "working": "Terms: a₁=7; a₂=7+3=10; a₃=10+3=13; a₄=13+3=16; a₅=16+3=19. nth term: a₅=7+(5−1)×3=7+12=19. Sum: S₅=5/2×(2×7+(5−1)×3)=5/2×(14+12)=5/2×26=65."
}
````

## Other records

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