Sequence & Series Explorer 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

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

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