Canvas Model: The Architecture of the Primitives (Preliminary Observations — A Working Note)

This working note presents preliminary observations on the structure of the eight primitive tethers of the Canvas Model. The threshold factor framework assigns a dimensionless factor to each dynamic primitive: Amplitude (1/5), Order (1/3), Acceleration (π/2), and Polarity (1/X). The first three are universal across all sectors. The Polarity factor is sector-dependent. Key observations: 1. Wavelength classes from the Unified Wave Equation. The UWE contains four terms: two smooth source terms (Amplitude: b\Phi_0, Order: av), one smooth second-derivative term (Acceleration: c\,d^2\Phi/dv^2), and one discontinuous term (Polarity: d\,\operatorname{sgn}(\Phi)). The Polarity term is a step function — it jumps at every zero crossing, flipping from +1 to -1 instantaneously — and therefore operates at half the wavelength of the smooth terms. This allows it to mix with short-wavelength property primitives (especially Charge) to produce sector-dependent effects. 2. Internal/external expression framework. The eight primitives are not independent. They are four concepts, each expressed internally (as property primitives describing the canvas structure) and externally (as dynamic primitives governing canvas behavior): Concept Internal Expression External ExpressionScale Dimension (P6): 3 Amplitude (P2): 1/5Sign Charge (P8): 1, 2, 3 Polarity (P4): 1/XGeometry Angle (P7): π/2 Acceleration (P3): π/2Direction Chirality (P5): +1 Order (P1): 1/3 3. Consequences of the architecture: · Three threshold factors are universal (1/5, 1/3, π/2)· One threshold factor is sector-dependent (Polarity, 1/X)· Mixing angles (CKM, PMNS) are geometric in origin· Charges carry signs because Polarity provides the binary ± structure that Charge inherits· The Polarity Domain transition is the crossover between long-wavelength and short-wavelength regimes Status: This working note is observational and preliminary. It documents patterns that have been noticed in the Canvas Model's structure. It does not yet constitute rigorous derivations from first principles. The observations are intended to guide further investigation and to organize existing knowledge. Why this matters: The architecture of the primitives explains why some parameters of the Standard Model are universal and others are sector-dependent. It shows that the eight primitives are not independent postulates but two sides of four fundamental concepts. This is a significant simplification of the theory's ontology, reducing the effective number of independent primitives from eight to four. Keywords: canvas model, primitives, threshold factors, wavelength hierarchy, Unified Wave Equation, internal/external expression, preliminary observations, working note, architecture