Routing and memory in the three-dimensional mirror model on K-lattice
Abstract
We study numerical observables relevant to delocalization in the three-dimensional Manhattan mirror model, also known as the K-lattice. Our principal experiment separates the locations of transmitting boundary channels from the routing between them. We derive an exact conditional comparison that preserves all transmission and reflection aperture sets, and find a statistically resolved deficit of physical transmission relative to this comparison. Nearby transmitting channels are themselves suppressed relative to a uniform subset with the same cardinality. A second experiment resolves the contribution of repeated vertices by their return age. The squared norm of the signed old-memory remainder is consistent with an inverse-square-root decay over the measured range. Annular experiments quantify decreasing continuation losses, while an initially apparent history dependence fails independent replication. Finally, a periodic configuration has a connected auxiliary contact graph but only finite routing cycles. These results identify estimates on reflection routing and adaptively selected revisit charges that may assist a rigorous proof. They do not establish an infinite-volume delocalized phase.
Related
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BibTeX
@misc{gu2026routing,
title = {{Routing and memory in the three-dimensional mirror model on K-lattice}},
author = {Jian Gu and Paul Schaeffer and Qin Hao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23244},
eprint = {2609.23244},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23244},
}
RIS
TY - UNPB
TI - Routing and memory in the three-dimensional mirror model on K-lattice
AU - Jian Gu
AU - Paul Schaeffer
AU - Qin Hao
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2609.23244
UR - https://arxiv.org/abs/2609.23244
AB - We study numerical observables relevant to delocalization in the three-dimensional Manhattan mirror model, also known as the K-lattice. Our principal experiment separates the locations of transmitting boundary channels from the routing between them. We derive an exact conditional comparison that preserves all transmission and reflection aperture sets, and find a statistically resolved deficit of physical transmission relative to this comparison. Nearby transmitting channels are themselves suppressed relative to a uniform subset with the same cardinality. A second experiment resolves the contribution of repeated vertices by their return age. The squared norm of the signed old-memory remainder is consistent with an inverse-square-root decay over the measured range. Annular experiments quantify decreasing continuation losses, while an initially apparent history dependence fails independent replication. Finally, a periodic configuration has a connected auxiliary contact graph but only finite routing cycles. These results identify estimates on reflection routing and adaptively selected revisit charges that may assist a rigorous proof. They do not establish an infinite-volume delocalized phase.
ER -