One-Octonion Brane-Bulk Framework — Foundations Synthesis: Emergence of Special Relativity, General Relativity, Quantum Mechanics, and Quantum Gravity

A full-read, math-verified, honestly-delimited synthesis showing how the kinematics of special relativity, the dynamics and measurement structure of quantum mechanics, and general relativity at tree level emerge from a small set of postulates of the One-Octonion Brane-Bulk Framework: G2 = Aut (O), the auxetic brane (Poisson ratio nu = -1), the Planck action floor, and mass-energy equivalence. The Minkowski signature, Lorentz boosts, light cone, and relativistic dispersion are forced by the H+ quaternion sector. The Schroedinger equation is derived parameter-free as the continuum limit of Planck-lattice mode evolution, with the imaginary unit identified as the brane-bulk separator e7. The Born rule's quadratic form, normalization, and counting measure are derived to the standard of statistical mechanics. General relativity is recovered at tree level (Einstein vacuum, fixed 8πG4, Noether conservation, non-associativity to Lambda, one-quarter horizon entropy), and quantum gravity is characterized as a finite, falsifiable lattice theory. The document is explicit about what is forced, what is derived, what remains an axiom (notably nu = -1), and records the routes that were tested and refuted. Six falsifiable predictions are listed. Verification: 29/29 symbolic and numerical checks (verifyQMGRₘasterᵥ2). Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.