CNRS-Key: Differentiation, the Divided-Power Basis, and the Transcendental-Radix Obstructions

A CNRS keystone / clarification note, with citable obstruction lemmas

Summary of status. This note settles the conceptual basis of the programme’s “differentiation is the primitive operation” claim and states what is actually established, impossible, and open: CNRS-H (divided powers ρn/n!) exact shift-differentiation exists; transcendental radix (over digit field, finite-support) finite-alphabet additive closure impossible; 
finite-alphabet finite-support exponentials exact differential closure impossible; Hurwitz ring H(RA) combined differential ring exists; finite Laurent coefficient encoding canonical and unique; finite-truncation arithmetic exactly computable;
efficient nested implementation the principal open computational problem.

Nothing here changes any proved arithmetic, algebraic, or topological result: the CNRS-A base −2 + i is algebraic and untouched, and CNRS-H differentiation stands.