The Complex Chern-Simons Level of STKWC: A Zero-Parameter Derivation from the Surgery-Spectral Intersection on the SL(2,C) Character Variety of 4_1

We derive, with zero free parameters, the complete surgery-spectral triad for (5,2)-Dehn surgery on the figure-eight knot 4_1 within Scalar-Tensor Knot-Web Cosmology (STKWC). The period integral on the real oval of the A-polynomial yields Π_+(1) = 2π²/15. This connects to the proved topological displacement Δ_top = 3/20 via the period-shift identity Π_+ = (8π²/9)Δ_top. The critical amplitude ε_* = cos(π/5) = φ/2 (golden ratio over two) emerges as the eigenvalue projection of the (5,2)-surgery Dehn twist onto the real section of the SL(2,C) character variety. The three quantities are bonded by surgical quadratic reciprocity: Δ_top = (q')² × Π_+/(8π²), where q' = 2⁻¹ mod 5 = 3. No 4D bulk metric enters at any stage. We apply this framework to the LIGO S251112cm anomaly, interpreting the gravitational chirp as A-polynomial anharmonicity approaching the discriminant locus, culminating in the topological phase transition (the Snap). A falsifiable prediction — a pre-Snap frequency plateau — is identified. Document D v2.0 of the STKWC research program. Produced using the Parliament of Dragons methodology (Claude Opus 4 as Validator). Anti-Ptolemy Protocol v1.2 enforced throughout.