Modular Exponentiation Calculator mechanism

Model scope

The catalog description is not honest as written because the formula omits the final modulo reduction and the domain constraints are absent. The empty honest_label is a concern: the instrument should explicitly state that it is a toy/coursework calculator unless it has rigorously bounded, arbitrary-precision behavior suitable for cryptographic-sized integers.

• The stated formula is not correct as an integer equality: the product of the selected residues must itself be reduced modulo m, i.e. result = (Π (b^(2^i) mod m)) mod m.
• The formula does not explicitly define the square-and-multiply accumulator update, including reducing after every multiplication.
• The supported domain is unspecified; square-and-multiply requires an integer exponent e >= 0 and a positive integer modulus m > 0.
• The promised step-by-step binary-exponent trace has no specified format or required intermediate values.

Units and conventions

• Base, exponent, and modulus are dimensionless integers; no physical units or unit conversions apply.
• The exponent is a nonnegative integer.
• The modulus is a positive integer; m = 0 is invalid.
• For ordinary arithmetic, inputs should be within exact-integer limits. JavaScript Number arithmetic is not exact for all large integers, so arbitrary-precision BigInt or an explicit safe-integer limit is required.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "base": 5,
    "exponent": 13,
    "modulus": 23
  },
  "expected_outputs": {
    "result": 21,
    "trace": {
      "exponent_binary": "1101",
      "squared_residues": [
        {
          "bit": 0,
          "value": 5
        },
        {
          "bit": 1,
          "value": 2
        },
        {
          "bit": 2,
          "value": 4
        },
        {
          "bit": 3,
          "value": 16
        }
      ],
      "selected_bits": [
        0,
        2,
        3
      ],
      "accumulator_values": [
        5,
        20,
        21
      ]
    }
  },
  "working": "13 = 2^3 + 2^2 + 2^0 = 1101_2. b^(2^0) mod m = 5^1 mod 23 = 5. b^(2^1) mod m = 5^2 = 25, 25 mod 23 = 2. b^(2^2) mod m = 2^2 = 4. b^(2^3) mod m = 4^2 = 16. Select bits 0, 2, and 3: accumulator = 1 × 5 = 5; then 5 × 4 = 20; then 20 × 16 = 320; 320 mod 23 = 21."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification does not define behavior for modulus 0 or define the residue convention for negative bases. Modulus 0 must be rejected, and raw JavaScript remainder semantics produce -2 for base -3, exponent 3, modulus 5 whereas the standard least-nonnegative modular result is 3.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json