חוסר תקינות של חוקיות קצב-על-קצב באנרגיה חיובית

תקציר מקורי באנגליתarXiv:2609.13476v1 Announce Type: cross Abstract: At a 2021 AIM workshop, Guo conjectured that the positive square energy s+ = E+_2 should inherit the familiar edge-addition monotonicity of the spectral radius, rho(G + uv) >= rho(G). That conjecture was subsequently shown to fail at p = 2. Tang, Liu, and Wang then introduced positive p-energy, proved nonmonotonicity for every 1 <= p < 3, and in version 3 of their preprint (26 March 2025) explicitly conjectured that monotonicity should hold for p >= 3. We disprove this conjectured high-exponent extension completely: for every real p > 2 there are infinitely many connected graphs G and nonedges uv such that E+_p(G + uv) < E+_p(G). Together with the Tang-Liu-Wang counterexamples below 3, this shows that no exponent p >= 1 restores the spectra