Supplement to Document D: Independent Verification of Δ_top via the Surgery Linking Form and Contrast-Native Derivation of the Filling Correction

This supplement to Document D (DOI: 10.5281/zenodo.19287163) provides three results concerning the topological displacement Δ_top = 3/20 for (5,2)-Dehn surgery on the figure-eight knot 4₁ within Scalar-Tensor Knot-Web Cosmology (STKWC). (1) An independent derivation of Δ_top = 3/20 from the quadratic refinement of the surgery linking form, yielding the universal filling correction Δ_fill = q̄/(4p) where q̄ = q⁻¹ mod p. This algebraic/arithmetic path is independent of the period-integral derivation in Document D. (2) A scope clarification for Document D's Theorem 3 ("surgical quadratic reciprocity"): the formula (q')²·Π₊(1)/(4π²N) is specific to (5,2)-surgery on 4₁ and does not generalize to other slopes via the fixed full-oval period Π₊(1) = 2π²/15. The universal formula for arbitrary primitive (p,q) is q̄/(4p). (3) A reformulation of the filling correction within C0 (Contrast Calculus), the relations-first ontology underlying STKWC. Surgery is defined as contrast freezing — trivializing the holonomy along a chosen peripheral cycle. The filling correction emerges as residual cyclic curvature on an abstract rank-2 contrast lattice, requiring no 3-manifold. The agreement between the analytic/physical path (Document D) and the algebraic/arithmetic path (this supplement) constitutes independent verification that the (2+1)-dimensional Chern–Simons theory on the degeneracy surface ε = 0 produces invariants consistent with canonical surgery theory. Three open problems are formulated: a generalized surgery-dependent period formula, the non-abelian extension of C0 to SL(2,ℂ), and Two-Path verification for other hyperbolic knots. Computational verification performed within the Parliament of Dragons multi-AI methodology (Claude/Anthropic, ChatGPT/OpenAI, Gemini/Google DeepMind). Notes: Part of the STKWC preprint series. Document D Supplement v1.0.