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Manuscript IV@1 · IV.tex · figure · 351cb2d7

Sourced transfer-kernel estimates

Model 3: scalar stress form and exterior record › Explicit scalar kernels · lines 2861–2892

IV@1#fig:source-transfer-cancellation

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gravitationalscalaroperator / instrumenterror / restrictionsupport / scope
Pair sector
k=p+qk=p+q. Singular locus q=−pq=-p, marked as a locus, not a plotted zero.
C00++=O(∣k∣2),C0i++=O(∣k∣)C_{00}^{++}=O(|k|^2),\quad C_{0i}^{++}=O(|k|)
same orders for −−--
Newton factors 1/∣k∣21/|k|^2 give A00=O(1)A_{00}=O(1), A0i=O(∣k∣−1)A_{0i}=O(|k|^{-1}), B00=O(1)B_{00}=O(1)
∣KJpair∣≤CJ,Λ(1+∣p+q∣−1)|\mathcal K_J^{\mathrm{pair}}|\le C_{J,\Lambda}(1+|p+q|^{-1})
square integrable in three-dimensional transfer momentum
Mixed sector
k=q−pk=q-p
∣KJmixed∣≤CJ,Λ(1+∣p−q∣−2)|\mathcal K_J^{\mathrm{mixed}}|\le C_{J,\Lambda}(1+|p-q|^{-2})
finite Schur integrals on bounded cutoff support
gΛg_\Lambda Hilbert–Schmidt; hΛh_\Lambda bounded self-adjoint
fixed finite Λ\Lambda; no separate Newton infrared mask

These estimates are not identified with the Model 2 ultraviolet estimates.

Sourced transfer-kernel estimates at fixed . Pair-sector stress numerators cancel the strongest Newton singularities, leaving a square-integrable transfer bound. The mixed-sector singularity instead has finite Schur integrals. These estimates justify the pair and number coefficients without an additional Newton infrared cutoff.

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