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

instrument mechanism / verified-clean

# Stellar Parallax Distance mechanism

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

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

## Model scope

The core reciprocal formula is standard, but the specification is incomplete because it accepts either arcsec or mas without defining unit handling and advertises ly and AU without specifying conversion formulas. These ambiguities must be resolved before approval.

- d(pc)=1/p(arcsec) is correct for positive parallax expressed in arcseconds, subject to the small-angle approximation.

- If the input is in milliarcseconds, the required formula d(pc)=1000/p(mas) is not stated explicitly.

- Formulas or conversion constants for the advertised outputs in light-years and AU are missing.

- The specification does not define behavior for zero or negative measured parallax, which can occur because of measurement noise.

## Units and conventions

- For parallax p in arcseconds, distance is d(pc)=1/p.

- For parallax p in milliarcseconds, distance is d(pc)=1000/p.

- Conversions used here are 1 pc=3.26156 ly and 1 pc=206264.806247 AU.

- Parallax must be a positive angle; zero is undefined and negative measured parallax is not a physical distance input.

- The parsec reciprocal formula uses the small-angle approximation; an exact geometric calculation would use d(AU)=1/tan(p in radians).

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "parallax": 0.1,
    "parallax_unit": "arcsec"
  },
  "expected_outputs": {
    "distance_pc": 10,
    "distance_ly": 32.6156,
    "distance_AU": 2062648.06247
  },
  "working": "1) d(pc)=1/0.1=10 pc. 2) d(ly)=10×3.26156=32.6156 ly. 3) d(AU)=10×206264.806247=2062648.06247 AU."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The instrument breaks or becomes hazardous at zero parallax because division is undefined, at very large parallax because the small-angle formula diverges from the finite-angle geometric result, and for negative parallax because signed arithmetic produces an unphysical negative distance unless the input is rejected or specially interpreted.

## Other records

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