The Complete Periodic Table of the Emergence Canvas Model: Combinatorial Ontology and Modular Mathematics

This document presents the complete periodic table of the Emergence Canvas Model. The table combines two layers of structure: (1) the combinatorial ontology—all 255 non-empty subsets of the eight primitives, organized by Level and Status—and (2) the modular mathematics—the time-averaged product A_S = \prod_{i \in S} f_i for each connected subgraph, which determines the numerical value of each physical quantity. The eight primitives are: · Dynamic: Order (O, 1/5), Amplitude (Am, 1/3), Acceleration (Ac, 1/2), Polarity (P, 1/7)· Property: Chirality (C, 1), Dimension (D, 3), Angle (An, \pi/2), Charge (Ch, q_s \in \{1,2,3\}) The active fractions 1/2, 1/3, 1/5, 1/7 are the reciprocals of the first four primes \{2,3,5,7\}, forced by the synchronization condition that adjacent primitives share sign-change points. These are the same primes that appear in Euler's product formula for the Riemann zeta function—a connection that is not coincidental. What the table contains: The table enumerates all 255 non-empty subsets of the eight primitives, organized into eight Levels by subset size. Of these, 76 induce connected subgraphs of the 4-sunlet graph and represent irreducible physical structures. The remaining 179 are disconnected and factorize into independent components. Each entry is assigned a Status: · ANCHOR: Fixed by the framework's own derivations· GAP-FILLED: A slot the framework needs, identified as missing—these are the predictions· COMPOSED: Generated by the compositional rule For connected subgraphs, the time-averaged product A_S is computed. This product determines the numerical value of the physical quantity corresponding to that entry. The table includes exact algebraic expressions (e.g., \pi/60, 1/210, 3q_s\pi/2) with decimal approximations where appropriate. Key connected subgraphs and their physical meanings: Combination A_S Physical Meaning\{C, D\} 3 Parity\{C, An\} \pi/2 Spinor double cover (S=1/2)\{An, Ch\} q_s\pi/2 Weinberg angle\{O, Am, D\} 1/5 3D Space; CKM \lambda\{O, Am, Ac\} 1/30 Momentum\{Am, Ac, P\} 1/42 Generation 2 fermion\{O, Am, Ac, An\} \pi/60 Angular momentum\{O, Am, Ac, P\} 1/210 Generation 3 fermion\{C, D, An, Ch\} 3q_s\pi/2 Complete property structure Why this matters: The Standard Model contains 19+ free parameters. The Emergence Canvas Model reduces these to a combinatorial ontology and a modular mathematics. The periodic table is the unified reference for the framework: it shows what can be built (the combinations) and what each building produces (the numerical values). The GAP-FILLED entries are the predictions—structures that must exist based on the combinatorics. The modular math provides the numerical predictions for each entry. The table is exhaustive and forms the periodic table of the Emergence Canvas Model—a solid milestone that organizes all known and predicted structures of the framework. Keywords: canvas model, emergence, periodic table, combinatorial ontology, modular mathematics, 4-sunlet, primitives, gauge coupling unification, fermion generations, time-averaged product, falsifiable predictions, Physics OS