PAPER-FBT08C: QGT Velocity Ratio and the Pre-Spacetime Origin of Propagation

This bridge paper develops a pre-spacetime interpretation of velocity inside the Fracture–Berry–Tension framework. The guiding idea is that velocity is more primitive than the later separation between space and time: before an effective Lorentzian spacetime has been reconstructed, one may still define a propagation ratio as a comparison between metric distinguishability and Berry-phase readout. The main input is the quantum-geometric tensor used in FBT06A, Q = gread +i/2Ωread. Its real part gread measures local readout distinguishability, while its imaginary part Ωread measures Berry curvature and phase rotation. The present paper proposes that the normalized ratio between these two components, evaluated along admissible readout directions, provides a pre-spacetime velocity ratio.More precisely, for two admissible readout directions u, v, define υQ(u, v) := |Ωread 󰁳 (u, v)|/gread(u, u)󰁳gread(v, v). On a K¨ahler-compatible readout chart, where Ωread(u, v) = gread(Jreadu, v), the Cauchy–Schwarz inequality gives 0 ≤ υQ(u, v) ≤ 1. Thus the QGT itself supplies a finite dimensionless propagation ratio before a spacetime metric is reconstructed. The symplectic nature of Ωread and the K¨ahler pairing (u, Jreadu) give this construction a deep geometric meaning: the velocity ratio measures how close a given readout directionpair is to the optimal symplectic pairing, and the upper bound corresponds to maximal saturation of this pairing relative to the readout metric. The paper further relates this QGT ratio to the non-central tension Casimir of FBT01D.If TXY Z = XeX + Y eY + ZeZ is the non-central tension readout vector, then the Casimir-like quantity CT = X2 + Y 2 + Z2 is interpreted as the QGT real-part norm CT = gread(TXY Z, TXY Z) after the appropriate non-central projection. The imaginary part of the QGT supplies the phase-readout channel associated with the central S-sector. After finite vacuum calibration, the dimensionless QGT ratio gives an effective propagation speed veff = c∗ υQ ≤ c∗. The role of the present paper is therefore not to derive the numerical value of the physical speed of light, nor to replace the cone reconstruction of FBT08A. Rather, it supplies a QGT-level explanation for why a finite propagation ratio is natural before the spacetime split.