A baguette is a rectangle with its corners intact, and corners are where emerald fails. The stepped emerald cut exists specifically because beryl coloured by chromium is brittle and internally fractured, and clipping the corners removes the points at which a stone is most likely to chip when a setter applies pressure. Cutting emerald as a baguette puts those points back. At 37 mm the problem sharpens rather than eases: each stone carries less material at its corners than the equivalent baguette on the 41 mm version of the same reference, while the pressure required to seat it in a channel does not fall in proportion. A smaller emerald baguette is therefore a more delicate object than a larger one, and this reference sets them across the dial, the bezel and a full bracelet. It is the most demanding stone in the ten-piece anniversary gem set to execute, and the smaller case is the harder of its two sizes.
The case is 37 mm across and 10 mm thick in white gold, with the octagonal bezel gem-set in baguette-cut emeralds. The plain 37 mm selfwinding Royal Oak of the same generation runs to 9.1 mm, so the setting adds nine tenths of a millimetre, less than the one and one tenth it adds at 41 mm, since shallower channels serve smaller stones. The eight hexagonal screw positions remain in place, breaking the continuous run of stones at fixed points the setting accommodates rather than overrides. The dial is white gold set with baguette-cut emeralds across its whole surface, with no applied hour-markers. The stones are the dial. The white gold Royal Oak hands are the only element above them. The bracelet carries the same setting to the clasp, tapering from the case and closing on an AP folding clasp. Emerald returns less light than any other stone in the set, because the internal fracturing that gemmology calls the garden interrupts the path light takes through the crystal, and the result is a dense saturated green rather than a bright one. Across the smaller stones of a 37 mm setting that density reads as a deep continuous field, closer to a lacquered surface than to a mosaic of gems.
The function set is hours, minutes and centre seconds. There is no date. Cutting an aperture through a continuous stone surface would break the setting at the point where an unbroken run matters most, and on emerald in particular a cut edge introduces stress precisely where the material is weakest. Centre seconds keeps the three hands on a single axis and avoids the second circular interruption a small seconds subdial would require. Time is read from hand position against the case, since the dial offers no markers. Emerald is dark enough that the white gold hands separate cleanly from it in almost any light, an advantage this reference shares with the ruby and blue sapphire versions and not with the pale stones in the set at either size.
The Royal Oak is the collection Audemars Piguet is built on, and the 37 mm anniversary references step through three degrees of setting. The 15550 is plain at 9.1 mm, the 15551 carries a diamond-set bezel over an unset dial at the same height, and this reference sets dial, bezel and bracelet and reaches 10 mm. Ten stones were used: emerald, tsavorite, ruby, blue sapphire, tanzanite, blue topaz, amethyst, pink tourmaline, yellow chrysoberyl and orange spessartite. Each was issued at 37 mm here and at 41 mm at reference 15514, giving twenty references on one construction across two sizes. Green is one of only two colours represented twice, in emerald and tsavorite, which makes those two the single direct within-colour comparison the set offers, and tsavorite appears again in one of the non-anniversary graded dials while emerald appears in neither. That leaves the 37 mm and 41 mm single-stone references as the only two ways Audemars Piguet issued emerald in this case, where tsavorite can be had three ways.
This reference suits a collector who wants the oldest stone in the set and accepts the terms it comes with. Emerald has been mined and valued for thousands of years, it is recognised instantly in a way tsavorite is not, and it carries associations that no recently discovered material can manufacture. Against that it is the most fragile choice among the ten in practice, less because of where it sits on the hardness scale than because of how it breaks, and a 37 mm bracelet set in emerald is an object to be worn with attention rather than without thought. Anyone weighing this against the tsavorite version is choosing between the older stone and the brighter one, and at the smaller size the difficulty of the emerald build is part of what is being bought. The anniversary designation ties production to the occasion rather than to an open catalogue run.