Where do the body’s axes come from? In Cognimed they are not imposed — they are the low eigenmodes of the embryo’s own electrical geometry.
The operator. Cells are coupled by gap junctions into an electrical syncytium. That coupling defines a graph Laplacian — the embryo’s own diffusion operator — and its lowest eigenmodes are smooth standing patterns over the tissue: a head-to-tail mode, a back-to-belly mode, and a left–right mode whose node is the midline. These are the body axes. The anterior–posterior mode matches the real axis in the mouse atlas at r ≈ 0.96, and the frame is grown from the embryo’s own connectivity, never borrowed from the atlas.
The face and the organs. The same construction on the face yields the eigenframe on which facial features are placed — GWAS facial-shape variation is low-rank in exactly this basis — and each organ repeats the trick internally: the heart’s first eigenmode is its apex-to-base activation axis, the gut’s is the oral-to-aboral peristaltic axis. Organs and limbs are placed at the antinodes of the body-scale modes, addressed by the HOX code on the anterior–posterior mode (derived from single-cell Hox expression, Spearman 0.81).
The amphibian threshold. The left–right eigenmode exists only if the body has medio-lateral width: a thin, convergent-extension-collapsed body has no such mode and grows no limbs — a fish. Widen the body (a single Wnt-PCP knob) and the mode enters the spectrum, and bilateral limbs appear at its antinodes — a tetrapod. The fish-to-tetrapod transition is a geometric threshold, with the limb genes unchanged.
The frameless case is instructive: a tissue without this electrical frame is a teratoma — all the parts, no geometry. See the papers, especially Papers 4, 6 and 9.