Editing Openai/6935580c-34e4-8001-9136-7bbdf1499790 (section)

=== If you want, I can: ===
* Attempt to formalize and axiomatize the premises (P1)–(P3) and explore known candidates (Colombeau algebra, nonstandard models, ultrafunctions) to see whether any known construction satisfies all required properties (and where they fail).
* Work out the Picard series terms in explicit integral form and show in detail how termwise differentiation and energy identities pass to the limit under your axioms.
* Try to construct such an extended algebra (this is a deep research project and I will be explicit about which parts are conjectural).
* Translate the conditional proof into a fully written manuscript suitable for peer review that clearly separates which statements are assumptions and which follow.

Tell me which of these you want next and I will proceed (bearing in mind the distinction between proving the conditional argument vs constructing the extensions themselves).