Advance Both Actual Native Boundary Templates on One Cycle
Abstract
Advance Both Actual Native Boundary Templates on One Cycle.
Theorem 1.1 (Restore Both Orders Without Reselecting the Witness).
Lean statement: D5/S3/Combinatorics/Graph/PrefixReversal/NativeSimultaneousBoundaryState.native_actual_simultaneous_boundary_state
Proof. Machine-checked in Lean as D5/S3/Combinatorics/Graph/PrefixReversal/NativeSimultaneousBoundaryState.native_actual_simultaneous_boundary_state (✓ std3). ∎
Source. Repository-derived.
Commentary.
A concrete previous joint and two-half state, its literal distinguished native ports and boundary templates, and the actual updated parent joint partition earn both next restored partitions and endpoint templates on the same supplied Hamilton cycle. The old order roles exchange. The next endpoint laws and route factorizations are conclusions, while the old state and actual new joint partition remain premises.