Non-symmetry of biconstrained two-step reachability
Kriebel Alec · Zenodo (CERN European Organization for Nuclear Research) · 2026
We give a negative answer to the symmetry question for the universal finite-tripartite biconstrained two-step reachability function psi: the absolute difference at (13/27,14/27) and its swap is at least 1/108. For rational theta in (0,1), we prove the exact boundary formula psi(1-theta,theta)=1-theta/d(theta), where d is a minimum integer degree over positively rational weighted regular incidence templates. The credited seven-type example of Chudnovsky, Hompe, Scott, Seymour and Spirkl and its complement bound the two relevant integers by four, which makes equality impossible. The exact values, their ordering and the invariant minima are not evaluated. A self-contained four-page research note and portable exact verification supplement accompany the result. The matrix and weighted framework are prior work. A dated bounded literature audit found no earlier equivalent theorem but does not certify global novelty; the cited 2019 senior thesis was inaccessible. AI tools were used extensively in solving, verifying, literature research, writing and adversarial review. This is an unrefereed preprint and has not received external human peer review.