The Theory of the Board: A Discrete Causal Geometry for Emergent Physical Law

The Theory of the Board (TT) proposes a discrete causal-combinatorial foundation for physical law. Starting from a locally finite directed acyclic graph (DAG) endowed with fairness and entropic dominance, the theory derives structural constraints on emergent fields, symmetry sectors, and informational geometry.

This version presents formal stability results, including:

• A combinatorial stability theorem leading to a unique binary sector under coarse-graining (supporting a two-dimensional local state space);

• An informational-geometric derivation of complex structure from Fisher metric and non-degenerate symplectic form;

• Rational relations among gauge couplings under minimal symmetry embedding;

• A geometric classification argument linking compact complex surfaces to a minimal tripartite topological sector.

All results are stated under explicit structural hypotheses. This work is intended as a foundational program and a mathematically structured preprint for open scientific discussion.