The universal forgotten-action PEG question has a negative answer

Exact statement

Forgotten-action projections of deterministic visibly pushdown languages are exactly the context-free languages. Since Kim and Park exhibit $L=C^R\in\mathsf{LIN}\setminus\mathsf{PEG}$ , there exists a deterministic visibly pushdown language whose forgotten-action projection is not a PEG language. Therefore FPRD-C02 is resolved negatively.

StatusSource-attributed proof from FPRD-T91 and the Kim-Park witness theorem

External reviewFPRD-T91 is source-verified from Alur and Madhusudan; the PEG separation is imported from Kim and Park, arXiv:2608.29592v1. The short composition has not received specialist review.

Context

FPRD-C02 asked whether every deterministic visible language remains PEG-recognizable after its action tags are forgotten. FPRD-T91 had already identified the resulting class with CFL; the new CFL-not-subset-PEG theorem settles the universal question.

Hypotheses and scope

Projection forgets only call, return, and local tags and is letter-to-letter.
The tagged visibly pushdown automaton may be deterministic, as provided by FPRD-T91.

Proof or evidence

Take the Kim-Park language L=C^R in LIN minus PEG. Since LIN is contained in CFL and FPRD-T91 identifies CFL with deterministic visible projections, L has the required deterministic visible lift and refutes the universal statement.

Negative resolution of FPRD-C02 →

Verification notes

The local checker treats the two source theorems as imported facts and verifies only the composition and reversal orientation. It does not recheck either external formalization.

Limitations

The result is existential and does not construct the smallest possible visible lift.
It does not characterize which forgotten-action projections are PEG languages.
No independent priority claim is made beyond the FPRD formulation of the composition.

Open work

Replace the universal inclusion target with a characterization of the projected frontier subclasses lying in SCA and PEG.