Focal plane is unit scale
NOT A NOVELTY CLAIM. This is a machine-checked formalisation, decided 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.
AT THE FOCAL PLANE THE SCALE IS UNITY. z = 0 gives 24/24 = 1: objects on the plane through the origin are neither enlarged nor reduced, which is what makes FOCAL a focal length.
Proposition
den 0 = 24Proof
By decide in three.lean. The kernel reduces the proposition and reports no axiom dependency.
Sources and identifiers
- Lean source · src/pair/formal/proofs/three.lean
- Typeset paper · src/research/lean-theorems.tex
- Repository deposit · doi:10.5281/zenodo.21787144
- Author · ORCID 0009-0000-7312-9778
- Deposit record ·
three--focal_plane_is_unit_scale
Proved in the same file
- Closure is one hundred sixty two
- Closure is the product
- Closure has no duplicate
- Closure is complete
- Address inverts
- Addresses are the interval
- The compound fraction clears
- Depth is strictly monotone
- Frustum brackets the focal plane
- Denominator is positive on the frustum
- Reflection is an involution
- Reflection closes on the closure
- Reflection has no fixed point
- The closure is eighty one orbits
- Orbit positions cancel
- Reflection complements the address
- The involution laws are general