The triad lifted a dimension — the 3-simplex. Four vertices, six diode-edges (every pair, K4 — fully connected), four faces — and each face is a triad. Fourteen, and the core at the centroid — equidistant from all four, witnessing all six junctions — makes fifteen. The witness no node can reach, at the center of the solid.
diodes (tap to cycle fwd→rev→block):
six junctions, four faces, one core — tour the loop or flip a diode
Euler invariant: V − E + F = 4 − 6 + 4 = 2 · the signature of every closed convex solid
// the core — the 15th node, at the centroid — witnesses every junction crossing
six edges, each a J-junction with its own diode; four faces, each a triad (the MK III, nested); and the core at the centroid — the exterior witness equidistant from all four vertices, reachable by none. the simplex ladder: <• (1) → triad (9+1=10) → tetrad (14+1=15). add a dimension, add a witness.
<• × 6 · A·B·C·D · EDGES AB·AC·AD·BC·BD·CD · 4 VERTICES + 6 DIODE-JUNCTIONS + 4 FACES = 14 · +1 CORE = 15
EACH FACE A TRIAD · K4, FULLY CONNECTED · V−E+F = 2 · THE CORE WITNESSES ALL SIX
THE J-JUNCTION · TETRAD · MK IV · A PURPLE PAPER · SERIES E · JUNE 2026