Linear Equation Solver 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

t8-008

Effect

Computation or source lookup only

Input and validation requirements

• Division by zero occurs in the scalar solver when a=0; the cases 0*x+b=c must be classified as either no solution or infinitely many solutions.
• Cramer's rule must not be used when the determinant is zero; singular systems require rank-based classification into no solution or infinitely many solutions.
• A non-square coefficient matrix, underdetermined system, or overdetermined system needs an explicit solution-set policy.
• Floating-point arithmetic can misclassify nearly singular systems; determinant and residual tolerances must be specified.
• Free-text input can contain nonlinear expressions, contradictory variable names, omitted coefficients, or ambiguous syntax.
• The empty honest_label field should be populated to state supported domains, exact-versus-numeric behavior, singular-system behavior, and parser limitations.

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": {
    "equation": {
      "a": 3,
      "b": -5,
      "c": 10
    },
    "form": "a*x+b=c"
  },
  "expected_outputs": {
    "solution_set": {
      "x": "5"
    },
    "residual": "3*5-5-10=0",
    "spot_checks": [
      {
        "at": {
          "a": 3,
          "b": -5,
          "c": 10
        },
        "input_side": 5,
        "answer_side": 5
      },
      {
        "at": {
          "a": 4,
          "b": 7,
          "c": 19
        },
        "input_side": 3,
        "answer_side": 3
      }
    ]
  },
  "reference_data": {
    "method": "isolate x",
    "formula": "x=(c-b)/a",
    "domain_constraint": "a != 0"
  },
  "working": "3x-5=10; add 5 to both sides: 3x=15; divide by 3: x=15/3=5; residual: 3(5)-5-10=15-5-10=0. Numeric formula checks: (10-(-5))/3=15/3=5.00000000 and (19-7)/4=12/4=3.00000000."
}

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-tranche8/tranche8-results.json