Long Division / Long Multiplication Stepper mechanism

Model scope

The honest pedagogical label is appropriate, but the instrument needs an explicit operation model, integer-versus-decimal division policy, sign convention, precision policy, and divisor-zero validation before the formulas can be verified as fully specified.

• The specification gives a procedural description ('classic grade-school algorithm') rather than an explicit formula or defined semantics for each operation.
• For integer division, the standard expected relationship should be dividend = divisor × quotient + remainder, with divisor != 0 and 0 <= remainder < abs(divisor); these constraints are not stated.
• The inputs permit decimals, but quotient-and-remainder semantics for decimal division are undefined. A decimal result could be represented as an exact decimal quotient, a truncated quotient with a decimal remainder, or a scaled-integer calculation.
• Negative-number behavior is unspecified, including whether the remainder follows Euclidean division or the programming-language remainder convention.
• Multiplication does not produce a remainder, so the output schema must distinguish multiplication results from division quotient/remainder results.

Units and conventions

• Inputs are dimensionless numeric values; no physical units or unit conversions apply.
• The division test vectors use integers, with exact integer quotient and remainder semantics.
• The decimal multiplication vector treats decimal literals as exact base-10 values, not binary floating-point approximations.
• For production-safe integer arithmetic, inputs should be constrained to values exactly representable by the implementation, such as JavaScript safe integers, unless arbitrary-precision arithmetic is used.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "operation": "division",
    "dividend": 847,
    "divisor": 23
  },
  "expected_outputs": {
    "quotient": 36,
    "remainder": 19
  },
  "working": "23 goes into 84 three times: 3 × 23 = 69; 84 - 69 = 15. Bring down 7 to make 157. 23 goes into 157 six times: 6 × 23 = 138; 157 - 138 = 19. Therefore quotient = 36 and remainder = 19. Check: 23 × 36 + 19 = 828 + 19 = 847."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero divisor produces an undefined result and must be rejected. Signed division also has a convention-dependent result unless the quotient and remainder sign rules are explicitly specified.

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-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json