The Crossing Taxonomy: How the Four Dynamic Primitives Generate All Threshold Phenomena in the Canvas Model

The Canvas Model has four dynamic primitives: Order (P1), Amplitude (P2), Acceleration (P3), and Polarity (P4). Each primitive alone generates a fundamental waveform and a corresponding first-order threshold crossing type. Pairs of primitives generate six second-order crossing types. Together, these ten crossing types account for every physical quantity in the Standard Model: the fermion mass hierarchy, the neutrino mass ordering, the absolute Yukawa scale, CP violation, and the baryon asymmetry. This paper presents the complete taxonomy of threshold crossing types in the Canvas Model. First-order crossings are pure manifestations of single primitives: · Sequential crossing (P1) determines neutrino mass ordering· Amplitude crossing (P2) sets the absolute Yukawa scale· Acceleration crossing (P3) governs dynamics· Polarity crossing (P4) distinguishes matter from antimatter Second-order crossings combine two primitives: · Mass crossing (P2 × P3) produces the Yukawa hierarchy· Activation count crossing (P1 × P3) determines synchronization times· Asymmetry crossing (P3 × P4) generates CP violation· Angle crossing (P1 × P2) governs 2D synchronization· Sequence asymmetry (P1 × P4) determines matter/antimatter ordering· Magnitude asymmetry (P2 × P4) sets the baryon asymmetry scale All ten crossing types are generated by the unified wave equation Φ(v) = av + bΦ₀ + cΦ̈ + dπ(v) with appropriate weights. The first-order types set a single weight to unity. The second-order types set two weights to unity. No new primitives are introduced. Quantitative results derived from the primitives with zero free parameters: The mass crossing gives all six quark and charged lepton mass ratios within factors of 1.2–2.8 of observation. The activation count crossing gives synchronization times τ₃ = 1, τ₂ ≈ 3.1, τ₁ ≈ 385. The sequential crossing gives the atmospheric neutrino splitting within 6% and the correct solar splitting sign. The amplitude crossing shows the absolute Yukawa normalization is a counting fraction of order unity. The asymmetry crossing establishes the CP violation mechanism with asymmetry parameter α = (π−2)/(π+2). What this paper achieves: The crossing taxonomy completes the link between the foundational primitives and the observable Standard Model. Every physical quantity traces to a specific crossing type, and every crossing type traces to a specific combination of primitives. The Canvas Model is unified not only in its axioms but in its mechanisms: all threshold phenomena are crossings, and all crossings are primitive pairs. Why this matters: The Standard Model of particle physics contains nineteen experimental inputs. The Canvas Model reduces these to zero free dimensionless parameters in its laws. The crossing taxonomy shows how every parameter arises from a specific combination of the four dynamic primitives—a complete, bottom-up derivation of the observable particle spectrum from foundational axioms. Keywords: canvas model, crossing taxonomy, threshold phenomena, dynamic primitives, fermion masses, CP violation, neutrino mass ordering, unified framework, emergence