Continued Fraction Converter 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-with-binding-errata

Evidence ID

t4-093

Effect

Computation or source lookup only

Input and validation requirements

The specification does not define validation for zero-denominator rational input or a sign convention for negative numbers. A compliant implementation must reject 1/0 and explicitly choose a negative-number convention; otherwise it can return undefined values or a convention-dependent continued fraction.

Required corrections

[
  {
    "vector": 4,
    "field": "cf_terms",
    "wrong": "[1,2,2,2,2,1,1,29]",
    "correct": "[1,2,2,2,2,2,1,1,29]",
    "cause": "dropped one 2; her own convergents list (correct, 9 entries) proves it"
  }
]

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "number": "415/93",
    "interpretation": "exact rational"
  },
  "expected_outputs": {
    "cf_terms": [
      4,
      2,
      6,
      7
    ],
    "convergents": [
      "4/1",
      "9/2",
      "58/13",
      "415/93"
    ]
  },
  "working": "Euclidean steps: 415=4*93+43; 93=2*43+7; 43=6*7+1; 7=7*1+0, so CF=[4;2,6,7]. With h_-2=0,h_-1=1 and k_-2=1,k_-1=0: h0=4*1+0=4, k0=4*0+1=1; h1=2*4+1=9, k1=2*1+0=2; h2=6*9+4=58, k2=6*2+1=13; h3=7*58+9=415, k3=7*13+2=93."
}

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
• tranche errata record