Resonant Detachment: A Mechanism for Particle Generation in the Emergence Canvas Model

This paper proposes a mechanism for particle generation in the Emergence Canvas Model based on resonant detachment. When two open waves on the 2D canvas intersect above threshold, a closed loop can form. We show that the detachment probability is maximized when the canvas frequency spectrum resonates with the natural frequency of the primitive subset, where the natural frequency is the inverse of the least common multiple of the individual primitive periods. The resonance condition selects exactly the 15 dynamic-only connected subsets of the 4-sunlet. These correspond to the four bosons (single primitives), six dynamic pairs (including the Generation 1 fermion mass threshold), four dynamic triples (including the Generation 2 fermion), and one dynamic quadruple (the Generation 3 fermion). The property primitives (P5–P8) act as modifiers on these fundamental resonances. The resonance spectrum: Dynamic subset lcm Resonant harmonic Physical meaning{P3} 2 105 Acceleration boson{P2} 3 70 Amplitude boson{P1} 5 42 Order boson{P4} 7 30 Polarity boson{P2,P3} 6 35 Gen 1 fermion mass threshold{P1,P3} 10 21 Momentum{P3,P4} 14 15 CP violation base{P1,P2} 15 14 Space field{P2,P4} 21 10 —{P1,P4} 35 6 Time field{P1,P2,P3} 30 7 Momentum + Order{P2,P3,P4} 42 5 Gen 2 fermion{P1,P3,P4} 70 3 New particle (~520 GeV){P1,P2,P4} 105 2 New particle (~346 GeV){P1,P2,P3,P4} 210 1 Gen 3 fermion The mass hierarchy follows from the resonant harmonic: Gen 3 (n=1) is heaviest, Gen 2 (n=5) is intermediate, Gen 1 (n=35) is lightest. The bare lcm scaling is modified by additional suppression factors (harmonic mode overlaps, Polarity domain shifts), which are identified as Tier 2 corrections. Why this matters: The Emergence Canvas Model derives the Standard Model from eight primitive concepts and four dynamical pillars. However, the model lacks a mechanism to determine which of the 76 connected subsets correspond to stable particles. Connectivity alone establishes combinatorial irreducibility but not physical stability. The return-map architecture identifies the detachment law \mathcal{B}_{ij} as the central missing piece: the function that determines when and how intersecting open waves detach to form closed loops. This paper proposes resonant detachment as the specific mechanism for the detachment law. The resonance hypothesis provides a selection rule, a mass hierarchy, and a unification of Standard Model factors as products of dynamic resonance factors and property modification factors. What this paper is: A physically motivated conjecture with substantial supporting evidence. The resonance mechanism is presented as a candidate for the detachment law that the Canvas Model requires. The mathematical structure is developed in detail: the lcm spectrum, the beat envelope analysis, the coherent accumulation argument, and the modifier role of property primitives. What this paper is not: A completed derivation. Five specific mathematical problems are identified that must be solved for rigorous foundation: linearization of the UWE around the attractor, derivation of the energy functional, coupled dynamics at the intersection, the canvas frequency spectrum, and quantum threshold crossing. These are well-posed and solvable within the existing framework of the Canvas Model. If confirmed, the resonance mechanism would complete the detachment law and unlock the full generative power of the Canvas Model—transforming it from a decomposition framework into a particle generation engine. Keywords: resonant detachment, canvas model, emergence, particle generation, lcm spectrum, 4-sunlet, fermion generations, mass hierarchy, threshold crossing, beat envelope, detachment law, unified framework