TAGC — Mathematical Formalisation of L1

This paper presents a rigorous mathematical formalisation of Level L1 of the TAGC programme (Theory of Gravity Anchored by Complexity). Starting from the primitive concept of a Fundamental Informational Unit (UIF) with four binary constitutive capacities (Existence, Differentiation, Relation, Persistence), we define the constitutional space C = F242 containing the sixteen constitutional configurations. We then prove that a saturated connected subgraph G16 – a subgraph that contains all sixteen configurations – emerges with probability 1 under the dynamics of relational steps. No external selection mechanism is needed; the result follows solely from the ontological primitives. The formalisation is self-contained and does not rely on any empirical input. All mathematical objects used (probability spaces, graphs, connectivity, XOR difference) are standard and are cited where appropriate. This work completes the formalisation of the L1 layer of TAGC and provides the rigorous foundation for the subsequent transitional liminal regime LT and the emergence of quanta.