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

instrument / verified-clean

# Distance Modulus

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

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

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/distance-modulus/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/distance-modulus/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/distance-modulus/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/distance-modulus/qualification/>)

## Ledger state

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

**Area**: Earth & Space

**Tranche**: tranche-2

**Evidence ID**: t2-017

**Ledger rows**: 1

No ledger note is attached.

## Review findings

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.

### Formula and scope findings

- 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.

### Unit assumptions

- 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.

## Boundary hardening

**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.

## 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": {
    "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."
}
````

## 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`