Signature Algebra: Axiom System and Core Implications — An Exploratory Proposal

This preprint presents Signature Algebra — a self-consistent algebraic axiom system whose core prohibition is the ban on cloning an operator, formulated mathematically as non-left-distributivity. Starting from this prohibition, together with several explicitly labelled physical hypotheses, the theory derives the layered structure of space (N=4 uniqueness), the inevitability of warped geometry, and an algebraic formulation of the Pauli exclusion principle. The logarithmic joint-depth function provides a purely derived geometric origin for chemical screening constants and bond-angle trends. A zero-parameter prediction of the Li₂ dissociation energy (deviation -7.6%) is given, and the complete derivation chain for the ζ parameters is presented with honest labelling of the empirical components at each step. The paper is positioned as an exploratory proposal: it asks what physical structures would be forced into existence if no-cloning is the deepest prohibition of the universe. All assumptions and boundaries are honestly labelled.