The Mandelbrot Set as a Roadmap: Black Holes, Push-Back Points and the Model G Atom

The Mandelbrot set read as a roadmap: the big heart is one black hole, the round bulbs are smaller black holes pushed out onto its rim and glued on at one point, the swirls between them push back onto the black holes they came from, and the whole is finite at the Planck length. Each part is set against the mathematics of the set: one attracting cycle per component, so new black holes are born on the rim with beats that multiply; Misiurewicz points, dense on the edge, as the push-back points; external rays sorting the two, odd denominators to the black holes and even to the swirls, balancing one for one at the first two levels and 4 to 1 by level 10; the heart 78.2% of the area, the bulbs on it 19.5%, everything smaller 2.3%; hydrogen's levels in step with the bulbs 1/n running into the cusp; and the four readings of the Riemann work, shape, time, speed and temperature, on the map, with speed and temperature both giving π at the neck. The Model G atom, in the 3D incompressible Navier–Stokes fluid, is tested against the map in sealed, pre-registered rounds (SHA-256 fingerprints written before any run). It takes the map's first doubling, with the gap squared straight in the push; it enters it with a jump where the map opens from nothing (round 241: one steady value at push 0.0666, a pair already 0.23 wide at 0.0667); at one push it holds two ways of beating, the start and its stir choosing (rounds 237, 238); and it returns to one steady value. Across the atom rounds 324 of 617 sealed predictions hold. The deposit carries the paper in English and in Thai, each in colour and in black and white (PDF), with its Markdown, LaTeX and Word (English in Arial 16, Thai in TH SarabunPSK 16), seven figures with English and with Thai labels, the full working of every Model G round (The Toroid Field: the Maths), every script that works out the numbers and draws the figures, five complete sealed rounds with their models, read-outs, fingerprints and every run's results, the pre-registrations of the six rounds running, and the web pages in English and Thai.