Bilateral Resolution of Boundary Observational Symmetry in Canonical ACRF-4: Exact Sign-Pair Separation and the Open Global Reconstruction Problem

This research note establishes an exact distinction between boundary-edge observability and bilateral consequence accessibility in canonical finite ACRF-4, a mathematical realization of Registration Theory. The canonical successor equations possess a global-current-reversal symmetry under which retained-edge boundary histories and edge-only active responses remain identical. The note proves this observational obstruction algebraically. It then demonstrates that the previously established matched receiver-isolation response resolves this ambiguity for an explicit family of admissible states. The signed bilateral mean-response difference is nonzero and changes sign under current reversal. These findings complement the October 10, 2026 interval-certified local boundary-reconstruction results. Together they distinguish local observability, global observational symmetry, and bilateral consequence separation. The universal reconstruction implication—whether equality of combined admissible boundary and bilateral responses guarantees equality of complete host-consequence signatures—remains open and is identified as the next mathematical research target. Version 0.1 is a timestamped research draft containing exact finite-model propositions, their proofs, and explicitly stated limitations. It does not claim a universal reconstruction theorem, a derivation of physical spacetime, or a universal propagation speed.