The Resonance Mechanism: A Complete Derivation of the Standard Model Particle Spectrum from Synchronized Primitives

This paper presents the resonance mechanism of the Emergence Canvas Model—a complete derivation of the Standard Model particle spectrum from the synchronization of primitive wave periods. The model's eight primitives include four dynamic primitives whose periods are forced to be \{2,3,5,7\} times the Planck time by the requirement that adjacent primitives share sign-change points while minimizing coordination complexity. These four primitives form a synchronized resonant network—the 4-sunlet—whose connected subsets are the fundamental resonant modes. The canvas period is T_{\text{canvas}} = 210\tau. Every connected subset of dynamic primitives has a combined period that divides 210. These 15 dynamic-only subsets are the bare particles. Their resonant frequencies determine the detachment rates, with the mass hierarchy scaling as the least common multiple of the constituent prime periods. The resonance mechanism is verified against all 15 subsets. The fermion condition (requiring both Amplitude and Acceleration) selects exactly three subsets, corresponding to the three observed generations. The bare mass ordering is m_3 > m_2 > m_1, matching observation. New particle masses at \operatorname{lcm}=70 and \operatorname{lcm}=105 are predicted at approximately 520 GeV and 346 GeV respectively. All non-fermionic subsets correspond to structural fields (Space, Time, Momentum, CP violation base) with correct physical identifications. No subset is predicted to be a propagating particle that is not observed, and no observed particle lacks a resonant subset. Why this matters: The Standard Model of particle physics contains 19+ free parameters. The Canvas Model reduces these to zero free dimensionless parameters in the Machine, one dimensionful parameter (the Planck scale), and two cosmological boundary conditions. The resonance mechanism provides the generative map from primitive action to particle spectrum—a complete derivation of the Standard Model's particle content from first principles. The paper constructs the Standard Model gauge groups U(1), SU(2), SU(3) explicitly from the sign, amplitude, phase, and dimension primitives. Every entry in every gauge generator is shown to be a signed number with an amplitude and a phase. The Lie algebras close without additional assumptions. Hermiticity is enforced by the closed 4-cycle of dynamic primitives. The strong CP angle vanishes by dimensional saturation of the 8-dimensional Polarity space. The Gen 3 / Gen 2 mass ratio is computed step by step: bare resonance (5), harmonic suppression (795), geometric overlaps (2.57), Polarity Domain (6.56), yielding a Planck-scale ratio of approximately 236, within a factor of 1.7 of the observed value. Each correction factor is derived from the primitives, not fitted. What this paper contains: · Complete enumeration and verification of all 15 dynamic-only resonant subsets· Explicit derivation of the three fermion generations from the fermion condition· Prediction of new particles at 346 GeV and 520 GeV· Construction of all gauge generators from sign primitives· Resolution of the strong CP problem via dimensional saturation· Step-by-step computation of the Gen 3 / Gen 2 mass ratio· Complete generative map from primitive action to Standard Model Lagrangian· Seven open problems identified· Fifteen falsifiable predictions offered Keywords: resonance mechanism, canvas model, emergent particle spectrum, Standard Model, gauge coupling unification, fermion generations, strong CP problem, falsifiable predictions, prime hierarchy, 4-sunlet