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To determine whether individual grid fields inherit the rotational symmetry of their macro-scale hexagonal lattice, the authors evaluated within-field angular structure using harmonic decomposition on experimental recordings alongside matched synthetic controls. Across biological cells and observation-matched Burak–Fiete continuous-attractor networks, individual firing fields exhibited no selective sixfold angular modulation, quantitatively matching locally circular reference profiles instead. This decoupling of local field morphology from global lattice geometry establishes strict microstructural constraints for mechanistic models of spatial representation.
Global hexagonal coordination does not imprint on individual grid fields: single firing fields remain strictly circular rather than sixfold-modulated, ruling out local microstructural leakage even in continuous-attractor architectures.
The firing fields of a grid cell form a hexagonal lattice, yet each field's intrinsic geometric structure remains unclear: Are individual grid fields radially symmetric or do they exhibit (weak) sixfold modulation inherited from the global lattice? To address this question, we quantified the within-field angular structure using harmonic analysis and per-cell matched simulations that preserved sampling statistics, field scale, and lattice geometry after correction for global elliptic deformation. We found that, across the investigated cells, the sixfold harmonic power fraction was consistent with values from matched locally circular reference fields. Experimental fields further showed substantially less sixfold modulation than matched simulations with an imposed local sixfold component, demonstrating sensitivity to sixfold structure at that level. This conclusion was supported by a complementary sixfold regression metric, harmonic leave-one-out sensitivity analyses, and robustness checks across radial-window choices, smoothing, and simulated background-noise levels. An observation-matched Burak--Fiete continuous-attractor network likewise showed no selective local sixfold enhancement despite its globally periodic grid structure, and this conclusion persisted when grid scale and relative field width were matched more closely to the experimental regime. These results suggest that the global hexagonal lattice organization need not be accompanied by detectable local sixfold angular modulation of individual firing fields, placing quantitative constraints on grid-field microstructure and mechanistic models of grid formation.