Tetrahedral Emergent Gravity (TEG): Preliminary Galactic-Scale Evidence and Falsifiable Predictions for Next-Generation Instruments

Tetrahedral Emergent Gravity (TEG) proposes that the apparent gravitational excess at galactic scales is a geometric consequence of the discrete tetrahedral structure of the quantum vacuum, rather than evidence for dark matter. Starting from the single hypothesis that the quantum vacuum in R^3 selects tetrahedral coordination (z_fund = 4), the framework derives algebraically, without any adjustable parameters, the roughness parameter sigma_eff = 0.1088. The full derivation, detailed treatment of assumptions, eight open problems, and two explicitly falsified predictions are developed in the technical companion paper. The present paper has a narrower and more modest scope: to report preliminary galactic-scale evidence and to formulate three predictions that are testable with instruments currently operating in 2026-2027. Applied to 171 SPARC galaxies with sigma_eff = 0.1088 derived geometrically (zero fitting), TEG achieves RMSE = 0.152 dex. This is substantially worse than MOND (approx. 0.057 dex) and Lamba-CDM+NFW (approx. 0.051 dex), and is reported honestly. The structural distinction is that sigma_eff is derived rather than fitted; no other framework in the literature shares this property. A systematic z-sweep over 171 galaxies confirms z = 4 as the coordination number minimising observational error when sigma_eff(z) is fully derived at each z — zero fitting at any step. Three falsifiable predictions are derived from the same geometric chain: A +5% excess in the weak-lensing shear power spectrum at l >= 10^4, testable by Euclid at 5-sigma by 2027. An 8% central density deficit in cosmic voids relative to Lambda-CDM, testable with DESI void catalogues already public in 2026. A value H_0^TEG \approx 70.3 km s^-1 Mpc^-1 suggested by the algebraically derived codimension partial = 3 - ln 8 \approx 0.921 — presented explicitly as an algebraic conjecture whose numerical value is consistent with recent independent measurements, but which predates those measurements only in algebraic form and cannot be claimed as a genuine prediction until the full cosmological action of TEG is derived. Each prediction includes a quantitative falsification threshold.