The Tetractys is the triangular figure of ten dots arranged in four rows (1+2+3+4=10) — the Pythagorean symbol of cosmic completeness. The Pythagoreans swore their most solemn oath by it. It encodes: point, line, plane, solid (the four dimensions); the musical ratios (octave, fifth, fourth); and the progression from unity to manifest reality. Hex 15 (Modesty) is the only hexagram where every line is favorable — a state of such perfect equilibrium that nothing needs to be added or removed. This is the Tetractys as lived principle: completeness that does not display itself. Hex 63 (After Completion) is the Tetractys as structure: water over fire, every line in its correct place. Both describe what 'ten' meant to the Pythagoreans — not a quantity but a quality of wholeness.