Establish Cross-Buffer Key Uniqueness in the Historical One-T4 Implementation

Establish whether the historical one-T4 implementation performs globally correct cross-buffer de-duplication so that each Hash128 key is represented by exactly one candidate before threshold witnessing and final beam selection.

Background

The paper proves reduced-key top-B equivalence only for an abstract distributed pipeline that globally reduces every candidate key, routes records without races, and applies the final physical-layout tie order. The historical one-T4 implementation was audited against these obligations, but its Stream 4 processing appears to reduce physical sibling buffers separately rather than performing a global cross-buffer key reduction.

If identical keys can remain in multiple physical buffers, threshold witnesses may count one key more than once. That violates the distinct-key premise required by the conditional correctness theorem and leaves the historical implementation’s beam-selection correctness unresolved. The paper also notes a separate multi-rank in-place owner-scatter risk, but the cross-buffer uniqueness issue is the specific unresolved problem identified here.