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The Complete Actual Induction State

Abstract

An actual induction state retains one supplied cycle and all data later consumed by the native recursion.

Definition 1.1 (One Cycle with Both Literal Boundary Orders).

Lean statement: D5/S3/Combinatorics/Graph/PrefixReversal/NativeActualInductionState.StateFor

Formalization. D5/S3/Combinatorics/Graph/PrefixReversal/NativeActualInductionState.StateFor (✓ std3).

Source. Repository-derived.

Commentary.

For a supplied frame, the state contains one actual Hamilton cycle in its marked domain, two disjoint cut groups with their exact native images, a joint partition and both restored partitions on that cycle. It records each distinguished endpoint as a literal port coordinate, the primary and opposite parity flags, and the retained protected-a, remaining-b and selected-c edge conditions. Its opposite frame is the canonical selected-order exchange. This structure specifies the data required by the recursion; existence is proved by the separate all-order construction.

References