Perfect resource placements in dense Eisenstein--Jacobi (EJ) networks partition the network into hexagonal radius-$t$ service cells. This paper studies local repair of such placements after resource failures. For one failed resource, we prove that one replacement cannot cover the failed hexagon and two always suffice, giving $ρ_{\mathrm{EJ}}(t)=2$ for all $t\ge1$. Among minimum-size repairs, the sharp minimum-overlap formula $Ω_{\mathrm{EJ}}(t)=t^2$ follows from the three-strip geometry of EJ balls. For two failed resources, independent repair gives a four-replacement upper bound, but unlike the Gaussian case EJ repair is not always additive: two infinite neighboring displacement families admit three-replacement repairs, proved optimal by a two-ball impossibility argument. Additive behavior is established algebraically via endpoint-rigidity and diagonal-corridor theorems. For $q$ failed resources, independent canonical repair gives a universal $2q$ upper bound, exact when failed cells are pairwise more than $4t$ apart. Dense cluster subadditivity is proved for infinite four-fault and six-fault families with exact repair numbers four and five, giving savings of four and seven over independent repair. An exact inclusion--exclusion identity governs repeated coverage for arbitrary multi-fault repairs. An audit over 19,400 instances confirms widespread subadditivity. EJ local repair is structurally distinct from the Gaussian case: the one-fault overlap is quadratic, two-fault repair can be non-additive, and clustered repairs reuse replacement balls across multiple failed cells.

翻译：在稠密的爱因斯坦-雅可比（EJ）网络中，完美资源放置将网络划分为半径为$t$的六边形服务单元。本文研究了资源故障后此类放置的局部修复问题。针对单个资源故障，我们证明了一个替换单元无法覆盖故障六边形，而两个替换单元始终足够，由此得到对所有$t\ge1$有$\rho_{\mathrm{EJ}}(t)=2$。在最小规模修复中，由EJ球的“三带”几何结构可得精确的最小重叠公式$\Omega_{\mathrm{EJ}}(t)=t^2$。对于两个资源故障，独立修复给出四个替换单元的上界，但与高斯情形不同，EJ修复并非总具有可加性：两个无限邻接位移族允许三个替换单元的修复，并通过两球不可能性论证证明其最优性。通过端点刚性与对角线走廊定理，从代数角度确立了可加行为。对于$q$个资源故障，独立规范修复给出通用$2q$上界，当故障单元两两间距超过$4t$时该上界精确。针对无限四故障和六故障族，证明了稠密簇次可加性，其精确修复数分别为四和五，相较于独立修复节省了四个和七个替换单元。针对任意多故障修复的重复覆盖，建立了精确的容斥恒等式。对19400个实例的审计证实了广泛的次可加性。EJ局部修复在结构上区别于高斯情形：单故障重叠呈二次型，双故障修复可能非可加，且聚类修复会在多个故障单元间复用替换球。