Split metric
The displayed congruence is an exact normal form of the stated local Lorentzian two-plane relation.
Four Dual Forms · F 01
Gravity Light
Metric invariance and fixed null directions
Abstract
Gravity measures interval. Light propagates along the null relation of that interval. A recurrence matrix and an oriented area form generate a symmetric split metric with two fixed null directions. Its metric flow is a Lorentzian boost and its mirror reverses that boost. Every chosen Lorentzian two-plane of spacetime has this root as an explicit normal form.
A_Lorᵀ η₁,₁ A_Lor = G = [Q, Ω]
zᵀGz = 0
LₛᵀGLₛ = G
Record
Shared verifier
The finite verifier checks the root and companion paper relations. Its recorded output remains attached.
Local inclusion
The curved-spacetime inclusion ιₓ and curved boost remain the stated field-level extension, not an additional empirical result.
Scope
Claim boundary. The exact result is the local two-plane normal form under the stated isometric inclusion into a Lorentzian spacetime metric. The paper preserves the native metric and null conditions; it does not supply a new observational comparison.