Context
Research note extending Kim–Park’s explicit separation: the late-query reduction follows their strategy, and the recursive parity rules are adapted from their displayed grammar. The tree-addressed selection and residual-profile comparison are developed here; their novelty is not established.
Proof or evidence
Self-contained proofs and direct reduction in the manuscript. Finite semantic and rank checks corroborate the constructions; they do not prove an asymptotic lower bound.
Verification notes
Internal combined-proof audit on 5 September 2026; no independent expert review or formal verification claimed.
Limitations
- Equal profiles do not mean equal residuals or equal transition structures.
- The access exclusion uses Ko; the PEG consequence also uses Loff–Moreira–Reis.
- U's PEG membership and an intrinsic scaffold lower bound remain open.