EAS Association Geometry: A Cyclic PL Three-Manifold and Scale-Relative Riemannian Construction, with Conditional Lorentzian, Spin, and Finite U (1) Interfaces

This paper is archived as a speculative research work. This paper establishes an exact finite geometry in an explicitly selected EAS association sector. On a finite nonempty modeled domain satisfying association closure, distinct non-self targets, fixed-assignment noninterference, and directed all-pairs reachability, fixed completed rank-three association records determine ordered paths and a dimensionless shortest-path metric. In the cyclic sector $$X_n=\mathbb{Z}/n\mathbb{Z}, \qquad A_n(i)=(i+1,i+2,i+3), \qquad n\geq7,$$ the four-point supports $\sigma_i=\{i,i+1,i+2,i+3\}$ form a compact connected orientable PL three-manifold with torus boundary, face vector $(n,3n,3n,n)$, and homotopy type $S^1$. After a positive scale $s$ is supplied, the maximal cells become regular Euclidean tetrahedra and glue to a complete geodesic piecewise-Euclidean metric. A compatible smooth Riemannian realization exists, but no preferred smooth metric is selected. These finite combinatorial and scale-relative Riemannian results are the paper's principal contribution. Downstream results are stated separately and conditionally. A selected cyclic presentation convention supplies an ordered history carrier, but not a Lorentzian sign or history scale. Once those data and a smooth spatial metric are supplied, the product carrier supports an ultrastatic Lorentzian metric, two absolute Spin structures, and one absolute $\mathrm{Spin}^c$ class. Admitted completed-support reports admit a unique linear, cyclically invariant, unit-normalized scalar compression, interpreted as a finite charge-facing class. Admitted recurrent-wave complex lines, positive amplitude forms, and unique unitary comparison maps define a finite Hermitian $U(1)$ connection. Continuum reconstruction, Maxwell–Dirac theory, and QED remain conditional interfaces rather than consequences of primitive association data.