Volume I (G): Axioms and Gravitational Evidence — The Being Tax, the Causal Skeleton, the Tiling Scaffold, and Gravitational Dimensional Collapse

The axiomatic foundation of the Network Emergent Architecture (N.E.A.) framework. The universe is modeled as a discrete causal graph governed by two rigid axioms: global conservation of a generalized enthalpy Q and the principle of least action. Each node is subject to a finite computational bandwidth, B=1, which imposes an irreducible "Being Tax" and mandates a universal 1D Skeletal Connectivity. We prove that the canonical enthalpy decomposition Q = U + pV emerges from spectral localization via the inverse participation ratio, without additional postulates. The C8 cubic tiling is identified as the unique spatial scaffold in three-dimensional Euclidean space, with the photon serving as the sole fundamental interaction carrier. Gravity is the inter-cell stitching mode of this photon on the C8 scaffold. Its long range and extreme weakness follow from a single geometric fact: the cube successfully tiles space, diluting the stitching rent across an infinite translational symmetry group. In low-density environments, the stitching density drops, causing local tiling failure and a gravitational dimensional collapse from q=2 (Newtonian) to q approaching 1 (MOND-like). We validate this dimensional collapse model on 138 SPARC galaxies and a blind test on UGC 128, reproducing galaxy rotation curves without dark matter. The work also presents discrete graph experiments on Rindler horizons, anisotropic transport, sparse graph limits, and holographic area laws, demonstrating gravity as an emergent, dimension-dependent phenomenon. Dark matter is reinterpreted as a geometric artifact. No new particles are required.