Series Convergence Tester 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

t6-036

Effect

Computation or source lookup only

Input and validation requirements

The ratio-test path has an explicit 0/0 trap for the identically zero series and must reject or reroute that input. Boundary cases with ratio limit 1 also require a different test, and a sign/indexing convention changes the reported sum for alternating series.

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": {
    "general_term": "a_n=(1/3)^n",
    "n_start": 1,
    "test_selection": "ratio",
    "partial_sum_terms": 5
  },
  "expected_outputs": {
    "verdict": "convergent",
    "convergence_type": "absolute",
    "test_used": "ratio",
    "ratio_limit": "1/3",
    "partial_sum_S5": "121/243",
    "partial_sum_S5_decimal": 0.4979423868312757,
    "infinite_sum": "1/2",
    "infinite_sum_decimal": 0.5
  },
  "working": "a_1=1/3, a_2=1/9, a_3=1/27. First ratio: |a_2/a_1|=(1/9)/(1/3)=1/3. Second ratio: |a_3/a_2|=(1/27)/(1/9)=1/3; therefore L=1/3<1, so the series converges absolutely. S_5=1/3+1/9+1/27+1/81+1/243=(81+27+9+3+1)/243=121/243=0.4979423868312757. Using the geometric-series sum, S=(1/3)/(1-1/3)=(1/3)/(2/3)=1/2=0.5."
}

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-tranche6/tranche6-results.json