Distance Modulus mechanism

Model scope

The core distance-modulus formula is standard and arithmetically correct, but the catalog claim is incomplete and unit/operation behavior is underspecified. The spec needs explicit inverse formulas for solving a missing m or M, a defined parsec-to-light-year conversion, and an extinction assumption before it can pass.

• The stated formulas are correct for distance modulus and its inversion when d is measured in parsecs: m−M=5·log10(d/10 pc) and d=10^((m−M+5)/5) pc.
• The input description says the instrument accepts a distance, but no formula is provided for calculating apparent magnitude m or absolute magnitude M from a supplied distance.
• The output description says 'missing magnitude', but no formula identifies whether the missing value is m or M or how to compute it.
• The formula does not include extinction, absorption, or bandpass corrections; it is valid only for an extinction-corrected apparent magnitude or an explicitly idealized no-extinction calculation.
• The requested distance unit is ambiguous: the formula directly returns parsecs, but no parsec-to-light-year conversion or precision is specified.

Units and conventions

• m and M are dimensionless astronomical magnitudes measured in the same photometric band and system.
• d in the logarithmic formula is a positive distance measured in parsecs; 10 pc is the reference distance.
• For light-year outputs, use 1 pc = 3.26156 ly unless a different catalog-wide conversion is specified.
• The apparent magnitude is assumed to be corrected for extinction, or extinction is assumed negligible.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "apparent_magnitude_m": 0,
    "absolute_magnitude_M": 0
  },
  "expected_outputs": {
    "distance_modulus": 0,
    "distance_pc": 10,
    "distance_ly": 32.6156
  },
  "working": "m−M = 0−0 = 0.\nd = 10^((0+5)/5) pc = 10^(5/5) pc = 10^1 pc = 10 pc.\n distance_ly = 10 pc × 3.26156 ly/pc = 32.6156 ly."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Invalid zero and negative distances reach logarithms outside their real-valued domain; a sign-convention reversal produces a radically different valid-looking distance, and extreme magnitudes could additionally overflow plain arithmetic.

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