In continuum lattice gauge theory, a Wilson loop is a path-ordered exponential of a gauge connection — an abstract bookkeeping object computed via functional integration. In the Holographic Circlette (TCH) discrete substrate built on the bipartite tensor network Z3 ⊗Q3, the analogous object is a literal product of Pauli operators along a discrete path on the parity-check graph of the [8,4,4] code. We argue this is more than a formal analogy: the framework’s discrete Wilson strings are quantum Markov chains in a precise technical sense, with the Boltzmann survival relation M(c) = exp(φF(c)/2) of 14, §5.2 doubling as a mass formula and as a Markov-chain per-tick transition probability. Taking this seriously yields four specific predictive targets that follow from the same machinery the framework already uses to compute ρ(770) and the nucleon mass: (i) the strong-force string tension σ as a finite spectral calculation on the [8,4,4] code; (ii) a rigidity theorem forbidding 3D anyons from the discrete Pauli algebra; (iii) a glueball mass ladder from the spectra of closed cycles on the simple-cubic gauge web; (iv) a strict prediction that the framework’s vacuum topological entanglement entropy is exactly zero, distinguishing the framework from string-net condensate and toric-code models. Update 2026-05-25: All four targets are now closed. The Markov-chain framing established here drove a subsequent three-paper glueball trilogy 10–12 producing six canonical structural theorems and a Capstone Master Formula mdressed N = (2N−1)ΛQCD +Nshared(t−δ)ΛQCD (with t= 1/3 analytic and δ≈0.155 universal) that reproduces the complete LQCD lightest-glueball spectrum — five canonical JP C channels (0++ ,0−+ ,1+− ,1−− ,2++) — to within 3% precision from substrate topology alone (Target 3 closure). The string-tension calculation √σ = (4/3)ΛQCD ≈442.7 MeV matches the LQCD consensus √σQCD ≈440 MeV to 0.6% from the same substrate-level F2 combinatorics (Target 1 closure, ANCHOR §7.17). The No-3D-Anyons Rigidity Theorem is rigorously established via stabilizer-code error-propagation, Pauli-commutator braiding reduction, and the Pati-Salam 2D-Majorana mechanism (Target 2 closure, ANCHOR §7.16). The vacuum topological entanglement entropy γTEE = 0 follows directly as a corollary of the framework’s classical-product-state vacuum at 14, §4.3 (Target 4 closure). The closure exceeded all original target framings: a single paper exploring the Markov-chain reframing yielded four LQCD-precision substrate-level predictions and three rigorous theorems. We close with the open structural problem of whether the discrete Wilson string admits a continuous master-equation limit at long wavelengths — a candidate route to recovering the continuum Yang–Mills functional integral as an emergent description
David Elliman (Mon,) studied this question.