Arithmetic Positivity and Absolute Hodge Classes: Why HR Positivity Does Not Strengthen Deligne's Absoluteness

DRAFT version. This is an advanced draft and remains subject to revision. The paper establishes a boundary result for arithmetic positivity and absolute Hodge classes; it does not claim a proof of the Hodge conjecture or of Deligne's question. We introduce arithmetic positivity conditions (AP1–AP3) inspired by the Hodge–Riemann bilinear relations and prove that APp(X) = AbsHodgep(X): the AP conditions are automatically satisfied by all absolute Hodge classes. This is a negative result — the Hodge–Riemann framework does not strengthen Deligne's absoluteness criterion. Version 1.3 keeps that boundary theorem explicit and updates the bibliography and internal Zenodo references after a source audit; AP', AP'', and…