Time Dilation Calculator mechanism

Model scope

NEEDS_REVIEW because the exact meaning of 'time difference' is ambiguous and the v unit mode is not specified as an explicit input field. With v interpreted as speed, Δt0 as proper time, Δt−Δt0 as the time difference, and |v|<c enforced, the formulas are correct. The honest-label restriction to special relativity and inertial frames is appropriate.

• The algebraic formulas are standard for inertial special relativity, but the output 'time difference' is undefined; this review assumes it means Δt−Δt0.
• The claim 'proper time vs dilated time for a relatively moving observer' should explicitly state that Δt0 is the proper time between the same two events and Δt is the coordinate time measured in a frame where those events occur at different locations.

Units and conventions

• c is the exact SI speed of light: 299792458 m/s.
• If v is supplied as a fraction of c, v=0.6 means 0.6c; if supplied in m/s, v must be converted using v/c.
• Δt0 and Δt use the same time unit; the vectors below use seconds.
• v is the nonnegative speed magnitude, not a signed velocity component.
• The formula requires |v|<c; no acceleration is included because the honest label is inertial special relativity.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "v": 0,
    "v_unit": "fraction_of_c",
    "delta_t0": 10,
    "time_unit": "s"
  },
  "expected_outputs": {
    "gamma": 1,
    "delta_t": 10,
    "time_difference": 0
  },
  "working": "v²/c²=0²=0. γ=1/√(1−0)=1. Δt=γΔt0=1×10 s=10 s. Time difference=Δt−Δt0=10−10=0 s."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The formula has an undefined point at exactly |v|=c and is non-real for |v|>c. A conforming calculator must explicitly reject these inputs; silently returning infinity, NaN, or a complex value would be a boundary-handling failure.

Other records

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