From the First Triangle to an Error-Correcting Lattice: Simulations of a Growing Bell-Pair Network

In the Selection-Stitch Model (SSM), space is a lattice of Bell pairs that builds itself by two local rules: stitch adds a node in a triangle’s plane, and lift adds one above or below it, both at exact close-packed sites, so that every bond has the same length. From one tetrahedron, stitch generates only the face-centered cubic (FCC) lattice spanned by its edges, so FCC order is a closure property of the rules; the simulations measure the defects that growth adds. In 688 simulations of up to 1.2×106 nodes, with the bare rule, about 98% of cluster nodes four or more layers below the surface are FCC. Slabs grown on one close-packed sheet form twin domains and are 84–92% FCC; on a three-layer ABC substrate they grow as one variant. Read as a quantum state, the grown network has an entanglement entropy that counts the bonds crossing a boundary. Node parity checks with local repair turn it deterministically into a state of the FCC stabilizer code. Its distance is at most three, so it protects the lattice locally, cell by cell; checks are intact around 96% of cluster nodes three or more layers deep. The error-correcting lattice emerges from the postulate “what exists is what can persist”: only checked bonds of equal length persist, and the triangle is the smallest network whose bonds check one another.