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Manuscript V@1 · V.tex · figure · e7ddf37d

Signed cubic transfer structure

Contrast: the Newton–wave cubic form › Transfer behavior · lines 3420–3452

V@1#fig:cubic-transfers

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metricscalarrepresented quantumdefect / unresolvedsupport / scope

Schematic. Eight sign sectors, σa=±1\sigma_a=\pm 1.

σ₁p₁σ₂p₂q = σ₁p₁+σ₂p₂, r=|q|σ₃p₃w
initial and source amplitudesd[Zinit]+d[Zsrc]=0d[Z^{\mathrm{init}}]+d[Z^{\mathrm{src}}]=0
cyclic symmetrization into KfσK_f^\sigma
Equal signs: ρ12=O(r2)\rho_{12}=O(r^2), J12=O(r)J_{12}=O(r), locally bounded.
Opposite signs: a generally surviving r−2r^{-2}, locally integrable in three transverse dimensions.
∣Kfσ∣≤CfR5(1+∑i<j∣σipi+σjpj∣−2)|K_f^\sigma|\le C_f R^5\bigl(1+\sum_{i<j}|\sigma_i\mathbf p_i+\sigma_j\mathbf p_j|^{-2}\bigr)
Pair singularities add, not multiply. No additional finite-time frequency pole.

Signed cubic transfer structure. Each ordered stress pair contributes initial and sourced metric amplitudes whose divergences cancel in the total. Equal-sign transfers have numerator cancellations, while mixed signs can retain a locally integrable inverse-square transfer singularity. The symmetric kernel sums the pair contributions rather than multiplying their singularities.

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