Microscopic Foundations of an Entanglement Tapestry

We specify a background-independent microscopic theory for an entanglement tapestry: an infinite pre-geometric graph of unlabeled nodes connected by entanglement threads. Nodes carry no intrinsic properties. The physically meaningful degrees of freedom reside on the threads. Each thread is taken to be a qubit. A three-term many-body Hamiltonian — a valence potential, a local swapping term, and a combinatorial frustration term — generates the dynamics. The valence potential favors a preferred coordination {\boldsymbol{v}}_{\ast }. The integer value of {\boldsymbol{v}}_{\ast } is not derived here; it remains a free parameter. When a concrete continuum expression is required we use the illustrative value {\boldsymbol{v}}_{\ast }=4.The new content is not a new gravitational action. It is an explicit state space, a dynamical law, and a staged continuum pathway from that Hamiltonian to an effective metric. An Einstein-like equation is obtained by varying a covariant continuum action in which the Einstein–Hilbert term is introduced as an effective gravitational sector, not derived from the graph measure. A tensor-network blocking on a two-dimensional square lattice is used only as a proof of principle that the leading linear coefficient in the beta function is extractable once a blocking rule is fixed. No thermodynamically controlled numerical value of that coefficient is reported. High-density patterns admit an entanglement bound of Ryu–Takayanagi type from thread counting across relational cuts; saturation is not claimed for generic states. The continuum description is of closed-time-path type, which avoids a local wrong-sign kinetic term for a single propagating field. A complete stability analysis of the model’s continuum kernels is left open.This paper does not derive a preferred integer {\boldsymbol{v}}_{\ast }, an Einstein–Hilbert term from the microscopic measure, or a reduced vault–forge master equation. Those problems are stated where they arise and are left open.