Mass bracket massA aMinus < 1 < massA aPlus (square roots compared
through rational squares; massA a = (1 + a + 4√(1+a²) - √(25+a²))/6, margins ≈ 1.2e-6 and 5.7e-6),
and 549/500 < log 3 from 2 log 3 = 3 log 2 + log (1 + 1/8). Written from scratch.