The Hadronic Vacuum Polarization in the Bounce Frame: The Dispersion Sum Tested Under Counting Saturation

The bounce frame's counting rule (counting saturation) is tested against a third sum: the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment, a_mu^HVP,LO = 693.1(4.0) x 10^-10, a dispersion integral over hadronic states. The rule does not transfer, for four checkable reasons. (i) Support: 91.6% of the sum lies below sqrt(s) = 1.8 GeV, and the tail above the frame's own independence crossing E_ind = 3.02 x 10^9 GeV is bounded by 3.1 x 10^-17 x 10^-10, a fraction 4.5 x 10^-20 of the total; the regulated sum is the standard sum. (ii) Operand: the rule's trigger is a collective density of modes occupying a cell, while these addends are spectral weights of a two-point function fixed by unitarity and measured cross sections - a completeness sum over physical states, not an occupancy of virtual modes. (iii) The integral is ultraviolet finite (kernel ~ m_mu^2/3s) and infrared saturated; it is not a power-law-growing unsigned accumulation. (iv) R(s) >= 0, so any truncation subtracts, in the direction no live comparison has ever required. A hypothetical counting bound inside the hadronic domain is priced and excluded: a crossing at 2 GeV would shift the value by -50.0 x 10^-10, 12.5 times the published uncertainty. The vacuum grades are untouched: the dissolution stands as established on the frame's stated postulate, the surviving count has not been produced, and the vacuum catastrophe is not solved. The computation is deposited with the paper (muon_g2_counting.py); below 1.8 GeV the published data compilations are used directly.