Paper A presents LFCT's galaxy-scale structural derivation, obtaining the radial-acceleration relation, flat outer rotation curves, and the baryonic Tully–Fisher relation from a constrained two-mode exchange geometry rather than from a baryon-plus-halo decomposition or a phenomenological interpolation law. In the galaxy regime, the three-mode architecture reduces to a TD–TS exchange problem with routing curvature (TR) subdominant. From the contract-sphere constraint, the unique radial scalings of the active modes, and the swap symmetry at the TD=TS balance locus, LFCT derives a canonical exchange kernel G(x) = √x/(1+√x) that yields g_obs = g_bar + √(a₀ g_bar), with kernel exponent 1/2 and BTFR slope exactly 4, both structurally fixed rather than fitted. Only one external dimensional anchor (the MOND acceleration scale a₀) is required; once fixed, all galaxy scaling laws follow as algebraic corollaries of two independent relations (RAR and BTFR). The paper further predicts a dwarf-galaxy offset of 1+π² ≈ 10.87 relative to the spiral baseline, arising from the K₆ symmetry structure of the three-mode closure. Empirical benchmarks include the galaxy-scale a_0 identification at 0.5% and the dwarf-galaxy offset at 2.1%.. The paper states clearly what is assumed, derived, and calibrated, and identifies five failure conditions that would genuinely break the framework. The full empirical validation suite — including the SPARC 171-galaxy test, three-tier kernel hierarchy, and regime-dependent tier preference — is presented in the companion Paper A2.