Derived Dynamics of the Flag Universe: Validated Staircase Action, a Matter Theorem, Forced Cosmology, and Observer-Held Time (INDYNA Research Note 25)

We construct and validate the (3+1)-dimensional dynamics of the closed bimetric "flag universe" of INDYNA-STATIK (Notes 23–24). A globally ordered Freudenthal staircase with a shared bimetric hinge rule satisfies the product-spacetime criterion exactly (S/2dt=S3 to 10-10, dt-independent). Three theorems follow. (i) Matter theorem: the force holding the curved equilibrium r* in the edge dynamics is exactly f=φ2δrad, the radial edge deficit doubled by the golden bimetric factor 1+φ=φ2; numerically δrad coincides digit-for-digit with the string tensions of the earlier Model A. Matter is the distance from flatness: the pure edge world is in equilibrium exactly on the unit sphere (δrad(1)=0, flat embedding). (ii) Forced cosmology: for every natural thread matter (tracking strength λ<1) and in both potential conventions, the unheld homogeneous sector spirals (complex frequency pair, Monte-Carlo robust), with doubling time 0.28 anchor units and an ℓ=2 shear collapse at finite deformation; the unstable sector is exactly ℓ=1⊕ℓ=2 (translation and shear), while ℓ=0 breathing is the only stable homogeneous direction. (iii) Observer-held time: pinning antipodal probe pairs renders the sector real; three pinned pairs are minimal and—in mixed configurations containing corner and mid nodes—fully positive, with tones ω2=3.85, 1.51, 1.11. Time, in this universe, is what observation holds still. Part of the INDYNA Notes series (Notes 16–34). All numbers reproduce from the INDYNA law register (master data record, doi:10.5281/zenodo.21891088). Licence CC-BY-4.0.