Quantum Mechanics from the Constraint Axiom: A Derivation from Octonionic Algebra

The complete mathematical structure of quantum mechanics is derived from first principles, tracing all fundamental results to the constraint axiom via octonionic algebra. Without postulates, empirical fitting, or measurement assumptions, the following results are established: (1) Quantum states must reside in a complex Hilbert space over the complex numbers. (2) The canonical commutation relation between position and momentum follows from octonionic non-commutativity together with holographic information bounds. (3) The Heisenberg uncertainty principle arises as a mathematical theorem from the Cauchy–Schwarz inequality. (4) The Schrödinger equation emerges from time translation symmetry. (5) Spin one-half arises from the structure of the relevant Clifford algebra. (6) The Pauli matrices originate from the quaternion subalgebra contained within the octonions. (7) The Born rule appears as the unique probability measure on complex projective space. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/