Advance the Complete Actual State
Abstract
The same parent joint partition earns both restored orders and all retained edge invariants.
Theorem 1.1 (Construct the Next Strong State).
Lean statement: D5/S3/Combinatorics/Graph/PrefixReversal/NativeActualStrongStateStep.strong_state_from_same_parent
Proof. Machine-checked in Lean as D5/S3/Combinatorics/Graph/PrefixReversal/NativeActualStrongStateStep.strong_state_from_same_parent (✓ std3). ∎
Source. Repository-derived.
Commentary.
The current joint partition and both actual prior boundary orders earn a complete next state. Its graph map preserves raw vertices, its primary and opposite parity flags exchange, and its distinguished flag flips. The Hamilton property, literal boundary coordinates, all three partitions and all three retained-edge invariants remain attached to the same mapped parent cycle.