Sharp rank bounds and all-parameter tree–network separation — v0.1.0 candidate

This unrefereed candidate develops sharp all-parameter rank bounds for a positive general-Markov four-cycle, fixed-topology mixture exclusion, homogeneous stationary reversible triangle separation with an explicit binary boundary, and closure/statistical consequences under the stated hypotheses.

For four states the crossed rank is at least 10, sharply, excluding mixtures of at most two components on one common tree topology (rank at most 8). It does not exclude arbitrary mixtures over different topologies, arbitrary multiple-reticulation networks, or edge-heterogeneous triangle models.

The 16-page manuscript credits the established Jukes–Cantor triangle result and distinguishes earlier generic identifiability from the present stated universal bounds. Internal mathematical/citation audits and a clean exact replay passed. The finite replay is not a universal proof, formal verification, external peer review, or an official REF rating. The complete announced equivariant-network manuscript was unavailable for priority comparison.

Creator: Anonymous. Prose and original data/records: CC0-1.0. Original code: MIT.

Version DOI: https://doi.org/10.5281/zenodo.23140370

Assets include the frozen source archive, manuscript PDF, and SHA256SUMS. The archive SHA-256 is a9697d63e9eb3253d820da2aa870b757fb1763bfb6902b8464c5e1bb7023bff9.

Operational clarification (4 October 2026): optional research-run queue instructions in the frozen archive describe the earlier authoring-host setup. That shared queue was retired later the same day. The portable Python commands already supplied in the archive require no queue; the final clean-extraction replay ran directly with one BLAS/OMP thread, and GitHub CI also ran directly. This does not change the mathematical sources, checker, immutable tag, DOI, or archived assets.