Source: https://guthlabs.ai/docs/instruments/distance-modulus/mechanism/

instrument mechanism / verified-clean

# Distance Modulus mechanism

The inspectable method record for Distance Modulus, kept separate from implementation and qualification.

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

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/distance-modulus/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/distance-modulus/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/distance-modulus/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-tranche2/tranche2-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`