Light is fixed from either side

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.

And from the other side, because composition is not assumed commutative until it is checked.

Proposition

∀ v ∈ sample, same (add v light) light = true

Proof

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_fixed_from_either_side

Proved in the same file

• Light is the fixed point
• 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

All machine-checked theorems