+-Theory: A Generative Foundation for Logic, Computation, Space, and Quantum Mechanics

Contemporary physics treats mathematics, logic, and spacetime as foundational primitives.Quantum mechanics assumes measurement and observation.General relativity presupposes spacetime geometry.Computation theory begins with logic as given.Each framework succeeds within its domain but leaves fundamental questions unanswered: Why does quantum measurement produce denite outcomes?Why is space three-dimensional?How does computation relate to physical structure?We present a framework that derives these structures as emergent consequences of a single generative axiom: recursive duality, formalized as E = {E + , E -}.Through systematic derivation across ve levels of recursive application, we show that: (1) complete Boolean algebra emerges at level 3 as the exhaustive space of relation-outcome mappings (16 operations); (2) Turing-complete computation arises naturally when outcomes chain with memory (Rule 110 equivalence); (3) three-dimensional space emerges as the minimum structure supporting depthgenerative recursionwhere recursive subdivision generates new stable pattern classes rather than mere resolution renement; (4) quantum mechanical phenomena (superposition, entanglement, measurement, Born rule) follow necessarily as structural features of patterns not yet invariant under coupled recursive resolution.The framework is pre-mathematical: it shows how mathematics itself becomes possible.No additional axioms.No assumed logic or geometry.Just recursion operating on itself.Quantum behavior is not mysteriousit is what pre-stable patterns necessarily exhibit under coupling.