# Section 12: Significance and remaining scope

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## 12 Significance and remaining scope

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The results give explicit routes from a complete coherent forcing to a physical derivative form and then to every admitted coordinate current. The inverse-lift argument handles a form-dual residual through its temporal regularity. The window argument handles changing input directions without discarding the operator response. The ordered resolvent formulas retain source interactions and physical weights without a false commutation. The Coulomb example discharges these questions in a definite electron–oscillator parent, including the source graph and the feedback-modified input.

The distinctions in the hypotheses are productive. They identify whether a calculation still needs a residual derivative, a physical form floor, a spectral coefficient, endpoint dressing, a source moment, or a common-domain propagation argument. They also expose specific invalid substitutions: a tiny collision tail does not make a Coulomb residual differentiable in space; a source-only truncation does not suppress propagated high-sector response; a reference invariant is not the physical current metric; and a shifted spectral floor is not an actual spectral gap.

A physical record application must still supply its original wave and actual law, the complete Hamiltonian/current constitution, an earned flow, a decoder and a whole retention interval. The current estimates can then enter its guard or moving-surface argument with the relevant length scales and original-law factor. No common apparatus joining all four portfolio papers has been inferred. Finite material sources, microscopic current reductions, preparation warrant and attainable control errors remain separate research questions.



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#### Funding.

 This research was conducted independently without external funding.



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#### AI assistance and verification.

 AI systems assisted with mathematical drafting, literature comparison, algebraic and numerical checks, and manuscript preparation. The author remains responsible for the arguments and presentation. This assistance does not constitute independent scientific validation.



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#### Independent review and collaboration.

 The author welcomes independent mathematical review of the common-form and domain arguments, computational replication of the explicit spectral and current bounds, and physical collaboration on complete source/control models and faithful retained records.