Canvas Combinatorics: A Synthesis of the Combinatorial, Processes, and Dynamics Tables

This document presents the complete specification of the Emergence Canvas Model—a unified framework in which all physical phenomena emerge from wave dynamics on a pre-geometric canvas, governed by eight primitive concepts and four dynamical pillars. The specification takes the form of three tables, each presented as a self-contained Part with its own abstract, derivations, and conclusions. Part 1: The Combinatorial Table classifies all physical structures by which of the eight primitives they contain. The 2^8 - 1 = 255 non-empty subsets of the primitives generate every particle, field, interaction, and property of spacetime in the Standard Model, plus three predicted right-handed neutrinos. A compositional rule generates the physical interpretation for each entry. The table is complete, self-auditing, and makes specific falsifiable predictions. Part 2: The Dynamics Table specifies, for each of the 255 entries, which of the Four Pillars governs its evolution, the specific form of the governing equation, its conservation laws, its interaction products, and its emergent physical quantities. The Pillars are distributed across the entries: Pillar I (the Unified Wave Equation) governs the continuous dynamics of all fields; Pillar II (the Threshold Condition) governs discrete particle formation; Pillar III (the Eigenvalue Equation) governs spectral organization; and Pillar IV (the Feed Equation) governs attractor-driven parameter fixation. Part 3: The Processes Table specifies which entries can interact, what selection rules govern those interactions, and what the products are. The central result is a primitive conservation law: gauge interactions cannot change the primitive composition of a physical structure; only threshold crossings can. Five selection rules, derived from the Four Pillars, correctly predict all observed Standard Model processes and forbid unobserved ones (\mu \to e\gamma, proton decay, right-handed charged currents). Part 4: Synthesis describes how the three tables work together to form the complete specification of the model's predictions. The Combinatorial Table tells you what exists. The Dynamics Table tells you how each structure behaves. The Processes Table tells you how structures interact. Together, they constitute the operating system of physical reality—the Physics OS. Why this matters: The Standard Model of particle physics contains 19+ free parameters. Cosmology adds 6+ more. These numbers are inputs, not predictions. The Emergence Canvas Model reduces these to: · Zero free dimensionless parameters in the Machine· One dimensionful parameter (the Planck scale, as unit of measurement)· Two cosmological boundary conditions (the age of the universe and the initial fluctuation amplitude) This document provides the complete combinatorial classification of what exists, the complete dynamical specification of how each structure behaves, and the complete set of selection rules governing how they interact. It is the canonical reference for the Emergence Canvas Model. All claims carry explicit status labels. All derivations are step-labeled. Open problems are honestly acknowledged. The framework is presented as a research programme with specific, falsifiable predictions, not as a finished Theory of Everything. Keywords: canvas model, emergence, unified framework, combinatorial classification, dynamical pillars, particle physics, Standard Model, gauge couplings, fermion generations, dark matter, cosmology, Physics OS