Light is the fixed point
NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.
LIGHT IS THE FIXED POINT OF COMPOSITION. Add any velocity to c and the result is c again — not approximately, not in a limit: the same fraction, exactly, at every sample. This is the sense in which c is not a speed among speeds but the fixed point of the operation that combines them.
Proposition
∀ v ∈ sample, same (add light v) light = trueProof
By decide in spacetime.lean. Checked by the Lean kernel: it depends on no axiom.
Sources and identifiers
- Lean source · src/pair/formal/proofs/spacetime.lean
- Typeset paper · src/research/lean-theorems.tex
- Repository deposit · doi:10.5281/zenodo.21787144
- Author · ORCID 0009-0000-7312-9778
- Deposit record ·
spacetime--light_is_the_fixed_point
Proved in the same file
- Light is fixed from either side
- Rest is the identity
- Composition is symmetric
- Below c composes to below c
- The boost preserves the interval
- The light cone is carried to itself
- The reverse boost undoes the boost
- The reverse boost undoes every boost
- Sq lt
- Lt of sq
- Interval scales
- Scale positive
- Timelike invariant
- Spacelike invariant
- Null invariant
- Timelike order absolute
- Spacelike order reverses
- Spacelike simultaneous
- Velocity addition below c