Turning Inside Out Without Closing: The Eversion Spiral, Time as Scale, the Domino Cascade, the Field Equation and the Golden Ladder (INDYNA Research Note 40)

Abstract

This note collects the exact results and the tests of register entries L464–L529, which prepared the gravitational candidate of Note 39 and the four-dimensional dynamics of Note 41. (1) In the model the Einstein coupling is a pure number, G_model = φ²/8π; the physical problem is the bridge of 10⁻⁶³ between a laboratory anchor and the Planck scale. (2) Dual eversion D, point reflection P and Galois conjugation σ generate a four-group; the rational polytopes close after two eversions, the golden ones only after four, passing through the star polytopes of density 7 — the shape returns, the scale does not: a spiral. Particle–antiparticle mass equality fixes that σ changes shape, not scale. (3) Time is the scale: the edge-to-core ratio of the universe is the Hubble time in Planck ticks, and instantaneous overlay predicts Ġ/G = 0, consistent with lunar laser ranging, while every delay known to the register is excluded. (4) A single law—no vertex closer than an edge—drives eight rigid triangles from the cuboctahedron to the icosahedron (rotation exactly 22.2388°, parameter 1/φ²), breaks into the octahedron, and repeats in 4D (24-cell → 600-cell) and 8D (E₈). (5) The field equation 4π − Σθ = 0 of the vertex action on the 62-node flag double reproduces the home and the matter ratios without input; the form sector is 157 times stiffer than the drift. (6) On the golden ladder M(g) = A₁ + gA₂ the ratio of form to drift is a quotient of Fibonacci and Lucas numbers; spin 1 and spin 2 are degenerate on the first rung. We also state a distinguishing neutron prediction for icosahedral quasicrystal approximants and list all tests of this range that failed.