CAS Simplifier / 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

t8-040

Effect

Computation or source lookup only

Input and validation requirements

The specification leaves domains, assumptions, cancellation restrictions, and square-root conventions unstated. An unconditional cancellation can incorrectly turn an undefined 0/0 value into 2 at x = 1, and an unconditional rewrite of sqrt(t^2) to t is wrong for negative t. These are concrete failure modes for a rule-based symbolic engine unless it preserves conditions and applies explicit conventions.

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": {
    "operation": "simplify",
    "expression": "(x^2 - 1)/(x - 1)",
    "evaluation_points": [
      "2.5000000",
      "-0.75000000"
    ],
    "boundary_check": "x=1"
  },
  "expected_outputs": {
    "canonical_result": "x + 1, subject to x ≠ 1",
    "boundary_result": "undefined at x=1 because the original expression is 0/0",
    "spot_checks": [
      {
        "at": 2.5,
        "input_side": 3.5,
        "answer_side": 3.5
      },
      {
        "at": -0.75,
        "input_side": 0.25,
        "answer_side": 0.25
      }
    ]
  },
  "reference_data": {
    "identity": "(x^2−1)/(x−1) = ((x−1)(x+1))/(x−1) = x+1 for x≠1",
    "domain": "x≠1"
  },
  "working": "At x=2.5: original=((2.5)^2−1)/(2.5−1)=(6.25−1)/1.5=5.25/1.5=3.5; simplified=2.5+1=3.5. At x=−0.75: original=((−0.75)^2−1)/(−0.75−1)=(0.5625−1)/(−1.75)=−0.4375/−1.75=0.25; simplified=−0.75+1=0.25. At x=1, the original denominator is zero, so the result is undefined even though the cancelled expression evaluates to 2."
}

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