Source: https://guthlabs.ai/docs/instruments/base-n-number-system-converter/mechanism/

instrument mechanism / verified-clean

# Base-N & Number System Converter mechanism

The inspectable method record for Base-N & Number System Converter, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The positional conversion claim is broadly standard, but the Roman and especially Egyptian-fraction claims are underspecified. The empty honest_label should be replaced with an explicit scope such as supported base syntax, exactness/precision policy, canonical Roman range, and the chosen Egyptian-fraction algorithm.

- Positional expansion/collapse is appropriate for bases 2-36, but the specification does not define the digit alphabet and case rules, validation of digits, signed numbers, or handling of finite versus repeating fractional expansions.

- A Roman numeral symbol lookup table alone is insufficient: the formatter/parser must define standard subtractive pairs, canonical output rules, valid range, and treatment of zero, negatives, and values above the supported range.

- Egyptian-fraction conversion is claimed but no Egyptian-fraction algorithm is specified. The result is non-unique unless a convention such as greedy unit-fraction decomposition is required.

- The input description only mentions number and source/target base, but Roman-numeral and Egyptian-fraction modes require an explicit mode and representation contract.

## Units and conventions

- All values are dimensionless exact integers or rational numbers; no physical-unit conversion is involved.

- A positional numeral in base b represents the sum of digit times b raised to each place value, with b an integer from 2 through 36.

- For these vectors, base digits use 0-9 followed by A-Z, case-insensitively, and fractional parts are interpreted as exact finite base expansions.

- Roman numerals use canonical modern notation with subtractive pairs IV, IX, XL, XC, CD, and CM, and the supported positive range is assumed to be 1 through 3999.

- Egyptian fractions are assumed to mean positive rational numbers represented as a sum of distinct positive unit fractions, using the greedy algorithm.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "mode": "positional",
    "number": "0",
    "source_base": 10,
    "target_base": 2
  },
  "expected_outputs": {
    "converted": "0",
    "value_in_source_base": 0
  },
  "working": "0 in base 10 has no nonzero place values. The same value in every positional base is 0, so 0_10 = 0_2. This is the zero-value boundary case."
}
````

## Failure boundary

- Reject source or target bases outside the inclusive range 2-36, and reject digits whose numeric value is at least the base.

- Define behavior for lowercase versus uppercase digits and for signs, whitespace, malformed radix points, and multiple radix points.

- A finite fraction in one base may require a repeating expansion in another base; the implementation needs a repeating notation, precision limit, or explicit exact-fraction output policy.

- Protect against integer overflow or loss of exactness in JavaScript Number arithmetic; BigInt or rational arithmetic may be required for exact conversions.

- Roman numeral parsing must reject noncanonical or invalid subtractive forms and define behavior for zero, negative values, and values greater than 3999.

- Egyptian fractions can have multiple valid decompositions; without a stated algorithm and canonicality rule, outputs cannot be uniquely verified.

- Egyptian-fraction input must reject a zero denominator and define behavior for zero, negative, improper, or non-reduced fractions.

- Repeated division by the radix must terminate for integer conversion, but fractional conversion can fail to terminate without a stopping policy.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/base-n-number-system-converter/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/base-n-number-system-converter/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/base-n-number-system-converter/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`