The Standing and the Flowing: What Holds in Three Dimensions, What Flows in Four (INDYNA Research Note 48)

With the stored slab matrices of the three four-dimensional flag doubles (tesseract, 24-cell, 600-cell) we complete the linear dynamics of the model and record what it decides. (i) The dynamical self-observation of Note 46 is computed: condensed onto the 24 vertices of the observer inside the 600-cell double, the observer breathes with a real frequency, ζ_self = 0, identically for the rational and for every golden 24-cell; the viscosity 8.45% belongs to the observer alone. (ii) All three doubles are autonomously unstable: the tesseract only through its viscous pair, the 24-cell and 600-cell through a purely imaginary type mode whose radius pattern is, to ±½, inner types against outer types — the eversion direction. (iii) A theorem: a role exchange that is a symmetry of the double cannot change Floquet multipliers; accordingly every linear holding mechanism built from symmetric exchanges (body chain, isoclinic steps, torus-knot ordering, the five 24-cells) leaves the eversion growth untouched, while the three-dimensional double holds exactly (max|μ| = 1) and keeps holding under eversion with scale change. (iv) Driven lock-in of the dual pairs damps the eversion rate strongly (8.25 → 3.31 along the diagonal) and the driven branches fold before any drift–form crossing; the fold’s null direction is the eversion mode to 91%. (v) Reading these results with the model’s own laws — inversion is time — the four-dimensional golden world does not fail to hold: it flows; the observer alone does not flow. (vi) Two simple readings of the fine-structure constant fail (Larmor with the clock; every product of two constants of the chain), and a pre-registered test of the constellation resemblance fails; the place of α is narrowed to the dynamics of the eversion with scale change. (vii) From the model of July 2026 a Hopf threshold ω_c = ω_breath|ω_tip| follows: 5.12 for the 600-cell (below its clock 5.5431), 10.14 for the 24-cell; the planned multi-spin computation is its test (Ledger 40). Computational status clarification, 28 September 2026: the multi-spin scan has not started; Part C branch continuation is running and Part B code is prepared. Ledger 40 remains a prediction, not a completed numerical confirmation. The supplied original PDF and TeX are preserved unchanged; their phrase “now running” is a manuscript-era statement superseded by this status clarification.