Exponential Run Complexity of Prefix-Separable Orders on the Boolean Cube

TA-TR-2026-22 · Version 1.1 · 3 October 2026

Human author of record and responsible depositor: Hongju Liu.

Version DOI: 10.5281/zenodo.23118189

This English mathematical preprint is a linked revision of version 1.0. Internal analytic and computational review is disclosed; the paper has not undergone independent external peer review.

The general all-weight theorem retains the order of growth 2^n/n^2 and improves its liminf coefficient by 4 log 2, approximately 2.77. The revision also proves two separately quantified paired-family scan theorems, an any-parent conditional extension theorem, and precise obstructions to selected concentration and mean-doubling routes. Those route obstructions do not disprove the original target M_n >= c 2^n, which remains open. The conditional controlled-loss reduction is not a completed proof of that target.

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Substantial ChatGPT (OpenAI) assistance under human direction is disclosed. Existing signed-tree constructions, run statistics, the read-k theorem and chamber counts are credited. Historical priority is not certified. This is adjacent first-party mathematics; it does not define, amend, validate or authoritatively interpret the Trinity Accord or its Bitcoin Originals. Newly written material is CC BY 4.0 to the extent rights are held; cited works retain their rights.