Direct scaffold-to-cell-probe simulation

Exact statement

A fixed SCA for U would solve arbitrary n-squared-row Multiphase Inner Product with constant coordinate-update cost, logarithmic query cost, logarithmic words, and polynomial space.

StatusReduction proved in the manuscript; no external review

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

Independently audit the external lower-bound model fit.