Source: https://guthlabs.ai/docs/instruments/telescope-f-ratio/mechanism/

instrument mechanism / verified-clean

# Telescope f-ratio mechanism

The inspectable method record for Telescope f-ratio, kept separate from implementation and qualification.

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

## Model scope

The focal-ratio formula is correct under the stated unit and diameter assumptions. The instrument cannot receive an unconditional PASS because the claimed relative-speed output lacks a defined formula, and “speed” is not precisely labeled.

- f/# = focal_length/aperture is the standard focal-ratio formula, provided aperture means aperture diameter and both lengths use the same units.

- The specification claims an output of relative speed vs f/10 but provides no formula for it. The standard exposure-speed ratio assumption is relative_speed_vs_f10 = (10 / f_ratio)^2; this must be explicitly adopted.

- The term “speed” is potentially ambiguous: the calculated quantity is relative exposure/light-gathering speed, not a directly measured physical speed.

## Units and conventions

- Focal length and aperture diameter must be expressed in identical linear units before division; the result is dimensionless.

- Aperture is the entrance-pupil diameter, not aperture radius.

- The f/10 reference is dimensionless and fixed at 10.

- Test-vector relative speed uses the standard inverse-square relationship: (10 / f_ratio)^2.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "focal_length": 100,
    "focal_length_unit": "mm",
    "aperture_diameter": 50,
    "aperture_unit": "mm"
  },
  "expected_outputs": {
    "f_ratio": 2,
    "relative_speed_vs_f10": 25
  },
  "working": "f_ratio = 100 mm / 50 mm = 2. relative_speed_vs_f10 = (10 / 2)^2 = 5^2 = 25."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-aperture input produces an undefined f-ratio and should be rejected. The specification also leaves unit normalization unspecified, allowing a 1 m versus 100 mm input to be incorrectly computed as f/0.01 instead of f/10.

## Other records

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