Golden Ratio & Fibonacci 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

t6-143

Effect

Computation or source lookup only

Input and validation requirements

• Division by zero or undefined output occurs for convergence ratios whose denominator is F0=0; the UI must define behavior for n<2.
• Non-integer, negative, NaN, infinite, or excessively large n values need validation because Fibonacci indexing and Binet's intended use are for nonnegative integers.
• Direct floating-point Binet evaluation can lose accuracy for large n through cancellation or overflow; exact integer recurrence or a numerically stable method is preferable.
• The initial values and indexing convention must be exposed in the implementation or fixed in the honest label.
• The spiral can be plotted with inconsistent geometry unless the formula, angular units, starting radius, center, orientation, and domain are specified.
• A purely floating-point implementation may display exact Fibonacci integers incorrectly once values exceed the safe integer range of JavaScript Number; BigInt or an explicit upper bound is needed.
• The current input specification only says “n terms” although the outputs include a ratio and a spiral graphic, whose required parameters are not specified.

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": {
    "n_terms": 8,
    "initial_values": {
      "F0": 0,
      "F1": 1
    },
    "indexing": "F0_through_F7",
    "ratio_definition": "F7/F6"
  },
  "expected_outputs": {
    "sequence": [
      0,
      1,
      1,
      2,
      3,
      5,
      8,
      13
    ],
    "finite_ratio": "13/8 = 1.62500000000",
    "phi": "(1+√5)/2 = 1.61803398875",
    "ratio_limit": "1.61803398875"
  },
  "working": "Start with F0=0 and F1=1. Iteration 1: F2=F1+F0=1+0=1. Iteration 2: F3=F2+F1=1+1=2. Continue: F4=2+1=3, F5=3+2=5, F6=5+3=8, F7=8+5=13. Thus the first 8 terms are [0,1,1,2,3,5,8,13]. The requested finite ratio is F7/F6=13/8=1.62500000000. The golden-ratio limit is φ=(1+√5)/2=1.61803398875."
}

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