Gauge-energy preservation under congestion-controlled network repair
Abstract
We study preservation of finite gauge-energy flows under local network repair after Bernoulli edge failures. A macroscopic demand network records terminal pairs to be routed, while a microscopic physical network contains local backup routes, bypasses and shared corridors. We prove a deterministic gauge-energy repair theorem: if the usable demand network ℬ♯ carries a finite Φ-energy flow θ, then the repaired physical network H carries a lifted finite Φ-energy flow Θ with ℰΦH(Θ) ≤ L βΦ(K) ℰΦℬ♯(θ), where L bounds route length, K bounds routing congestion, ℰ marks energy, and βΦ is the gauge dilation constant. We then convert this comparison into probabilistic repair criteria: finite-dependent local repair is handled via domination by product measures, and random repair lengths via a variable-cost formulation compatible with chemical-distance estimates. As a main application, we prove a finite-dependent local bypass theorem: any macroscopic network whose supercritical percolation cluster supports a finite gauge-energy flow remains gauge-energy stable after bounded-range local reinforcement, provided the local repair probability is sufficiently high. This yields reinforced lattice and wedge-type examples and provides a potential-theoretic framework for random network repair beyond tree-like or edge-disjoint constructions.
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BibTeX
@misc{sun2026gaugeenergy,
title = {{Gauge-energy preservation under congestion-controlled network repair}},
author = {Zhenyuan Sun and Dayue Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39587},
eprint = {2609.39587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39587},
}
RIS
TY - UNPB
TI - Gauge-energy preservation under congestion-controlled network repair
AU - Zhenyuan Sun
AU - Dayue Chen
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39587
UR - https://arxiv.org/abs/2609.39587
AB - We study preservation of finite gauge-energy flows under local network repair after Bernoulli edge failures. A macroscopic demand network records terminal pairs to be routed, while a microscopic physical network contains local backup routes, bypasses and shared corridors. We prove a deterministic gauge-energy repair theorem: if the usable demand network ℬ^♯ carries a finite Φ-energy flow θ, then the repaired physical network H carries a lifted finite Φ-energy flow Θ with ℰ^Φ_H(Θ) ≤ L β_Φ(K) ℰ^Φ_ℬ^♯(θ), where L bounds route length, K bounds routing congestion, ℰ marks energy, and β_Φ is the gauge dilation constant. We then convert this comparison into probabilistic repair criteria: finite-dependent local repair is handled via domination by product measures, and random repair lengths via a variable-cost formulation compatible with chemical-distance estimates. As a main application, we prove a finite-dependent local bypass theorem: any macroscopic network whose supercritical percolation cluster supports a finite gauge-energy flow remains gauge-energy stable after bounded-range local reinforcement, provided the local repair probability is sufficiently high. This yields reinforced lattice and wedge-type examples and provides a potential-theoretic framework for random network repair beyond tree-like or edge-disjoint constructions.
ER -