Randomized theoretical model explores high-fidelity Turing machine encoding in holographic systems, suggesting efficiency for nonvolatile storage.
The PV‑crystallographic hypercomputer architecture of Emmerson~{EmmersonPVHPC}requires two capabilities that were left as open assumptions: (i) embedding auniversal Turing machine (UTM) into a bulk probe inside an AdS (oreffective‑cone) temporal‑compression chamber, and (ii) reading out the haltstate on the boundary with fidelity arbitrarily close to unity at the finiteexternal deadline. This paper supplies a complete, rigorous mathematicalsolution to both. We work within the holographic quantum error‑correcting code formalism,exemplified by the HaPPY perfect‑tensor network. The bulk is a negativelycurved tensor network whose boundary is a one‑dimensional spin chain. Abulk Turing probe is defined as a designated set of bulk logicalindices that realize a universal Turing machine, with an infinite tapeextending along the radial direction and a finite‑state head. Theholographic map encodes the entire tape and head state into the boundarywith built‑in quantum error correction. A special halt tensorinside the network encodes the answer: if the simulated program halts, alocal operation toggles the halt tensor from \(|0\) to \(|1\);otherwise it stays at \(|0\). On the boundary, the halt state becomes a logical qubit protected by aholographic code of distance \(D\). We define the crystallizationlatch as a boundary operator \(\) that measures this logical qubit. Bychoosing the network size appropriately, the effective error per measurementis exponentially small in \(D\). Consequently, for any desired targetfidelity \(1-ε\), there exists a finite tensor network and afinite readout region such that the boundary latch yields the correct haltpredicate with probability at least \(1-ε\). The proper time ofthe probe diverges as its location approaches the conformal boundary,implementing the infinite proper‑time condition exactly. The construction isfully explicit and does not rely on any new physics beyond the standardholographic duality. Thus we complete the missing link in the PV‑crystallographic hypercomputer,establishing that a bulk universal Turing machine with high‑fidelityboundary readout is mathematically consistent and can be engineered withinthe known framework of AdS/CFT.
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Parker Emmerson (Yaohushuason) (2026) studied this question.
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