Numerical Identity Units and the Projection Non-Identity Principle

The ontological base. It separates three layers — value, representation, object — and states the Projection Non-Identity Principle: a scalar read-out π_v(𝔑)=x is not the whole numerical information object. 'Every number is one' is rewritten as 'each identified object is one identity-preserving unit', explicitly not the number 1 and not 1=2=3. Scalar equality splits objects into fibers (equivalence classes), and adding an observable can only refine them (Propositions 1–3). The seven axioms and the statements labelled 'theorem' are direct consequences of these definitions.