Long Division / Long Multiplication Stepper

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mathematics

Tranche

tranche-2

Evidence ID

t2-009

Ledger rows

1

No ledger note is attached.

Review findings

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.

Formula and scope findings

• 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.

Unit assumptions

• 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.

Boundary hardening

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.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "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."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche2/tranche2-results.json
• BOUNDARY_HAZARD_CATALOG.json