Structural degree is maximally asymmetric under reversal

Exact statement

For the Kim-Park record-first witness C, delta_str(C)=infinity while delta_str(C^R)<infinity, and both C and C^R are linear context-free. Thus reversal can change an empty stationary transport spectrum into a nonempty one even within LIN.

StatusSource-attributed corollary of Kim-Park Theorem 4.19 and FPRD-T161

External reviewThe language-class separation is imported from Kim and Park, arXiv:2608.29592v1. FPRD Lab has not independently rerun their Lean artifact or rechecked the underlying cell-probe lower bound.

Context

FPRD-T161 makes finite canonical structural degree equivalent to scaffolding-automaton recognition. Kim and Park provide one linear language outside SCA whose reversal is inside SCA.

Hypotheses and scope

C is the record-first witness of Kim and Park, and C^R is its literal reversal.
Kim-Park Theorem 4.19 is used as an imported dependency.

Proof or evidence

Kim and Park prove C in LIN intersect PEG minus SCA and C^R in LIN intersect SCA minus PEG. Replacing SCA membership by finite structural degree through FPRD-T161 gives the claimed infinity-to-finite reversal.

Reversal-asymmetry corollary →

Verification notes

The local checker verifies the implication orientation and the two structural-degree conclusions. It does not verify the imported separation or its Lean formalization.

Limitations

This is a translation of an external theorem, not an independent separation proof.
It confirms nonclosure of PEG under reversal, not the separate palindrome question.
It does not characterize which linear languages have finite structural degree.

Open work

Use a deterministic visible lift of C as the hard calibration for intrinsic stationary-frontier invariants.