Matching conditional profiles with different access costs

Exact statement

Terminal-marker hard and easy families have equal residual counts at every update cut and query prefix, including after any fixed initial update segment, and matching probability multisets under uniform completions. Their access-cost separation uses Ko's lower bound.

StatusProfile identities proved; access exclusion depends on Ko

External reviewNone documented for this work.

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.

Manuscript proof and evidence →

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.

Open work

Seek an independent review of the construction and its novelty.