What holds us entranced by the woman’s entrancement is the carefully choreographed clash of pattern, pigment and texture that fix her in this alluringly stylised elsewhere. The work is a vibrant inventory of Klimt’s own cultural obsessions, from flowing Chinese robes to the floating lyricism of Japanese woodcuts, both of which the artist collected and turned to for inspiration. Klimt’s home, according to the Austrian expressionist Egon Schiele, whom Klimt mentored, was furnished with “a large number of Japanese prints covering the walls” and “a huge wardrobe, which held his marvellous collection of Chinese and Japanese robes”. The rich silk of the young woman’s green and gold striped robe, her porcelain complexion blushed with rouge, her chestnut curls, and the imagined flutter of the fan’s vermillion leaves, all form a riot that is invigorated further by the chaos behind her.

This flattened background, which recalls the smooth dimensionalities of Japanese woodblocks and painted Chinese porcelain, could as easily be ornate wallpaper as the immaterial fabric of the daydreaming young woman’s imagination. Here we find floating a mystical phoenix (or , a symbol of grace and virtue in Chinese mythology) with fabulous emerald fangled feathers, as if fledged from the mystery of her mind. Opposite the phoenix, standing on the right of the canvas, boasting breast feathers of resplendent ultramarine, stands a long-legged crane, an emblem of wisdom and immortality, while all around the unreal air explodes with bright bursts of pink lotus flowers, signifying the immutability of beauty.

Lady with a Fan is among the very few portraits by Klimt, a leading figure of the Vienna Secession art movement, to be owned privately. It was last sold in 1994, when it fetched $11.6m (£9m). Thirty years later, it is expected to command nearly seven times that, likely becoming one of the most expensive portraits ever to come to auction. If Sotheby’s achieves the price it is asking, £65.5m ($83.4m), Klimt’s final painting will soar past René Magritte’s L’empire des Lumières, which sold for £59.4m ($75.6m) in 2022; Alberto Giacometti’s Walking Man I, which set the record for any work of art sold at auction in Europe when it went in 2010 for £65m ($83m); and Claude Monet’s Le Bassin aux Nymphéas, which sold for £40.9m ($52m) in 2008.

Set side-by-side with Klimt’s better-known works, such as The Kiss and Portrait of Adele Bloch-Bauer I, Lady with a Fan reveals how far the artist had travelled creatively in the decade before his death. Gone is the audacious glitter of gold leaf that exalted his sensual subjects into secular icons. Far looser and more expressive in its brushstrokes, Lady with a Fan relies for its intensity on the blurring of textures, both material and psychological, as everything bleeds into a single scintillating substance. Intensifying that sense of unfixable fluidity are moments in the painting where the bare weave of linen canvas is still visible – unpainted patches that have led some to suspect that work was still unfinished. But this is a painting whose very power issues from flux and fragmentation. Its unfinishedness is what completes it.