TA-TR-2026-22: changes from v1.0 to v1.1
Previous version: 1.0, DOI 10.5281/zenodo.23103274, 2 October 2026. Revision date: 3 October 2026. Original title and definitions retained.
- Strengthen the all-weight liminf coefficient from 1/(8 ln 3) to ln 2/(2 ln 3), a factor 4 ln 2, by applying the established Gavinsky–Lovett–Saks–Srinivasan read-k theorem. The asymptotic order remains 2^n/n^2.
- Replace the finite sufficient inequality with a read-degree/KL-divergence criterion and include two exact integer existence certificates.
- Define the paired tree family and raw comparison support. Prove a transition-word injection and one-rank/all-sweep constant-density theorem for the large-support class.
- Prove a conditional bottom-extension theorem preserving ANY specified paired parent, with an infinite compatible-family consequence on qualifying actual sparse row lifts.
- Add the exact actual-additive row-lift identity and an all-dimensional obstruction to uniform exponential tails in the unconditioned fair signed-tree model.
- Add a genuine integer-weight counterexample to exact conditional mean doubling, plus a rigorously conditional controlled-loss reduction.
- Supply separate exhaustive/sampled coverage statements, verifier sources, receipts and package hashes. Credit reused source tools and established mathematics.
The unrestricted positive-density conjecture remains open. Separate existential rank constructions are not combined without proof. No old DOI record, manuscript or archival receipt is overwritten. Unselected working classifications remain research notes.