Geometric Compression in Monte Carlo Reactor Physics: Structural Coherence as a Dimensionless Multi-Dimensional Invariant

Monte Carlo neutron transport calculations for Small Modular Reactor (SMR)safety analysis require large simulation campaigns that impose signicant computa-tional costs on certication timelines and budgets. We demonstrate that the struc-tural coherence metric Wij of the LESE-EIA framework derived analytically asthe xed point of a dissipative entropic ow equation is simultaneously dimen-sionless and multi-dimensional: it maps spaces of arbitrary dimension to a scalar in(0, 1] while preserving structural topology. This dual property implies a geometriccompression of order ∼ 107× from the original neutron ux space to the naturalsemantic dimension of the framework. As a direct consequence, the number of in-formationally independent simulation states is xed by geometry rather than bydataset size. Applied downstream of OpenMC on the PWR-SMR-2026-01 dataset(555 control rod misalignment states, 245,000 mesh cells per state), 10% of simula-tions (55 states, sampled blindly and uniformly) achieve 98.4% anomaly detectionrecall across the full state space. The remaining 90% are redundant by geometricconstruction, not by empirical approximation. Applied upstream of OpenMC, thesame geometric principle enables optimal simulation campaign design before anyMonte Carlo calculation is performed, yielding direct savings in time and computa-tional cost. Simultaneous upstream and downstream deployment provides maximalcoverage: optimal campaign selection followed by full structural monitoring. Thethreshold W∗ = e−1 ≈ 0.3679 is derived analytically and requires no calibration onreactor data.