CCEGA Paper 17: The Hard Threshold as an Intrinsic Property of the Sen Tachyon Vacuum — Exact Derivation of κ(ρ) (v1.1)

Derives the exact density-dependent coupling κ(ρ) from the Sen tachyon field equation for the power-law form G_eff(ρ) = G(ρ_c/ρ)2/3. Shows that the divergence at ρ_c is intrinsic to the non-analytic structure of L ∝ φ1/2 at its vacuum — not a pathology but a critical point analogous to a second-order phase transition. v1.1 adds Section 6: Reconciliation with Exponential Coupling. The exponential form G_eff = G exp(−ρ/ρ_c), adopted in subsequent CCEGA papers (P25, P34, P43, P44), is more consistent with observational constraints. The key insight — intrinsic hard threshold from tachyon tension divergence — applies to both forms. P17 is not retracted; the power-law derivation remains valid and pedagogically important. Related: P25 v1.1 (doi:10.5281/zenodo.19284768), P34 v2.0 (doi:10.5281/zenodo.19766662), P43 v1.1 (doi:10.5281/zenodo.19394258).