The Emergence Canvas Model: A Mathematical Model Generating Physics

scale-setting constant, interaction strengths, particle thresholds, and cosmological parameters. The Dynamics Table assigns each entry its governing Pillar, with each Pillar grounded in specific primitives. The Processes Table specifies selection rules, with the central Primitive Conservation Law: gauge interactions cannot change dynamic primitive content; only threshold crossings can add or remove primitives. Cross-referencing the three tables generates the complete physical specification of every structure. The gauge coupling ratios g_2^2/g_1^2 = 2/3 and g_3^2/g_1^2 = 2/\pi are determined by the active fractions. Three fermion generations follow from the internal space dimension n=3, with an exponential mass hierarchy parameter \beta = 1/6 and integer mode numbers that are sums of three squares. The Higgs field is the trace mode of the threshold tensor. The cosmological constant is \Omega_\Lambda = 3/(3+\sqrt{2}) \approx 0.680 from the horizon information bound. The strong CP angle vanishes identically. Proton decay, \mu \to e\gamma, and right-handed charged currents are absolutely forbidden. Numerical predictions are tested against experimental data. Gauge coupling running from the Planck scale to M_Z agrees within 0.3–5% (two-loop corrections bring \alpha_3 within 1%). Fermion mass ratios across three generations are predicted to 13–22% accuracy using integer mode numbers. The cosmological constant agrees at 0.7%. The Weinberg angle at M_P is \sin^2\theta_W = 3/5 = 0.6. Gravitational wave dispersion is modified with coefficient \alpha \approx 0.96. Dark matter emerges as an entropic effect with acceleration scale a_0 = cH_0/(8\pi\log 2). The 4-sunlet maps onto the algebraic core of multiple established frameworks. All derivations are step-labeled. All claims carry explicit status labels distinguishing derived results from fitted parameters and open problems. The paper concludes with a complete catalog of open problems and their identified solution paths. Why this matters: The Canvas Model provides a unified mathematical foundation for all of physics. It derives the gauge group SU(3)×SU(2)×U(1), three generations of fermions, the Higgs mechanism, the cosmological constant, and the Einstein field equations from a small set of postulates. It resolves the strong CP problem, the hierarchy problem, the cosmological constant problem, and the measurement problem. It predicts specific numerical values for gauge couplings, fermion mass ratios, and the dark energy density. The 4-sunlet structure maps onto the algebraic core of spacetime algebra, twistor theory, noncommutative geometry, causal fermion systems, loop quantum gravity, causal sets, string theory, holographic quantum gravity, the amplituhedron, and entropic gravity—establishing the Canvas Model as the common mathematical core of fundamental physics. Keywords: emergence, canvas model, unified framework, gauge coupling unification, fermion generations, cosmological constant, strong CP problem, hierarchy problem, measurement problem, 4-sunlet, active fractions, threshold condition, synchronisation, meta-time, string theory, loop quantum gravity, amplituhedron, entropic gravity