Signed Spatial Profile Realization
Abstract
Signed Spatial Profile Realization.
Theorem 1.1 (Simultaneous realization in every spatial fibre).
Lean statement: D5/S3/ConceptDynamics/Spacetime/SignedProfileRealization.exists_signed_profile
Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/Spacetime/SignedProfileRealization.exists_signed_profile (✓ std3). ∎
Source. Repository-derived.
Commentary.
In every finite dimension, each finitely supported integer spatial profile is the selected spatial charge of a finite rich history. All archived events are current, occur at time zero, lie in the support of the profile, and have empty causality. The entire current region has zero spatial charge and is globally balanced. At each supported position, equally many positive and negative events are created, and the events whose sign agrees with the prescribed coefficient are selected. A zero profile gives an empty archive.