Source: https://guthlabs.ai/docs/instruments/relativistic-velocity-addition-calculator/mechanism/

instrument mechanism / verified-clean

# Relativistic Velocity Addition Calculator mechanism

The inspectable method record for Relativistic Velocity Addition Calculator, kept separate from implementation and qualification.

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

## Model scope

The instrument can pass after the input convention is resolved. Recommended contract: accept signed dimensionless beta values u and v in (-1,1), compute u'=(u+v)/(1+uv), and label the output as a fraction of c. Alternatively change the input contract to physical velocities and retain uv/c², while explicitly specifying c and output units. The honest label should state collinear one-dimensional relativistic velocity composition, not a general frame-relative velocity calculator.

- The stated inputs are fractions of c, but the formula u'=(u+v)/(1+uv/c²) is dimensionally correct only when u and v are velocities in physical units such as m/s. For dimensionless fractions beta_u=u/c and beta_v=v/c, the formula must be beta'=(beta_u+beta_v)/(1+beta_u beta_v).

- The phrase two frames moving relative to each other is ambiguous: plus-sign velocity composition is appropriate for successive collinear boosts with a specified sign convention, while a direct frame-coordinate velocity transformation commonly uses (u-v)/(1-uv/c²).

- The formula requires explicitly stated one-dimensional, collinear motion and signed velocities; arbitrary vector velocities are not supported by this scalar expression.

## Units and conventions

- For the supplied input contract, u and v are dimensionless signed fractions of c, so c cancels and must not appear in the denominator; output u' is also a signed fraction of c.

- If the implementation instead accepts velocities in m/s, c must be supplied numerically in matching units, typically c=299792458 m/s, and the stated uv/c² formula is then dimensionally valid.

- Inputs should normally satisfy |u|<1 and |v|<1 when expressed as fractions of c; the sign indicates the collinear direction.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "u": 0.6,
    "v": 0.5,
    "units": "fractions_of_c"
  },
  "expected_outputs": {
    "u_prime": 0.8461538462,
    "u_prime_exact": "11/13",
    "units": "fraction_of_c"
  },
  "working": "u'=(u+v)/(1+uv)=(0.6+0.5)/(1+(0.6)(0.5))=1.1/(1+0.3)=1.1/1.3=11/13=0.8461538462."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The formula returns an undefined 0/0 result at u=1, v=-1 unless the input is rejected. It also produces a superluminal numerical result for an input just beyond the physical validity boundary, u=0.5 and v=1.001, contrary to the stated no-superluminal-result behavior unless validation rejects that input.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/relativistic-velocity-addition-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/relativistic-velocity-addition-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/relativistic-velocity-addition-calculator/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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`