Transport Papers T14b. Simulating the Dark Towers: Methods, Assumptions and Tests of the Unit-Ball Composition

T14b of the Transport Papers, a companion note to T14 (Dark Matter and the Arrow of Time). Version 1.0. 36 pages. Epistemic status: Tier C. The dark-matter paper T14 fixes how much matter each dark tower holds. By its unit-ball rule the mirror carries 18.6 percent of the dark matter, the three-dimensional towers 49.7 percent and the five-dimensional towers 31.6 percent. This note sets out the assumptions, equations, code and results of the tests of those amounts. Quanta confined to a sheet scatter in two dimensions; per unit of the mass gravity sees, their cross-section is a length times the sheet spacing. At composite strength the three-dimensional towers' matter is a fluid, eight to thirteen orders of magnitude above the cluster bound, whatever its confinement scale. A tree-gravity, multi-species smoothed-particle code, with the sheet fluid's pressure confined to its planes, follows a Bullet-like merger and a cluster's assembly. As T14 writes it, the composition fails both tests: 68 percent of the dark matter collides, with randomly oriented sheets the subcluster dissolves from the lensing map, and halos reach about 0.4 of the cold-dark-matter ellipticity. If the odd towers' matter is collisionless, only the mirror collides; the subcluster keeps a lensing peak on its galaxies, its gas trailing, at the cost of a puffier subcluster and halos about 0.8 as elliptical. A semi-analytic Milky Way model with helium-star feedback excludes the mirror's proton-only branch; its helium branch fits at the Sun under some normalisations, and in the bulge only if the bulge holds over twice the mirror's proportional share of its dark mass. Two films, the code and a verification script accompany the note. Position in the series: Within the series it relies on T14, and refers to T12 for the gauge charges of the minimal massive composite. It proves nothing about the series' algebra and changes no derived result of T14; it says which of T14's physical statements the simulations and the Galaxy model support and which they do not. The series is surveyed in T17, The Transport Programme, whose status table records every paper's tier and check count. Verification: verify_T14b.py checks the note's computational identities and derived numbers (60 checks in eight parts, all passing at deposit). Algebraic identities are checked in exact rational arithmetic; evaluations with physical constants, transcendental functions and integrals in double precision, with the tolerance stated beside each check. It imports GA.py, the series' shared library, deposited alongside so the record is self-contained. Run with a bare Python 3: python verify_T14b.py. Supplement: T14b_supplement.zip holds everything needed to rerun the simulations, the Galaxy model, the films and the figures: the simulation code tpsim.c (tree gravity and multi-species SPH), the initial-condition, measurement, Galaxy-model and figure scripts, the run outputs the note quotes, the two films, a README and requirements.txt. It needs Python 3.10 or later with numpy, scipy and matplotlib, a C compiler with OpenMP (gcc), and ffmpeg for the films; on Windows, use WSL 2. Section 14 of the note, "Running the code", gives full instructions; python code/reproduce.py figures --deposited redraws the note's figures from the deposited outputs in seconds. Films: merger_three_ways.mp4 ("Galaxy clusters in collision", https://www.youtube.com/watch?v=0SvmSwInN0c) and bullet_moment.mp4 ("The Bullet moment", https://www.youtube.com/watch?v=KQnZUVR7bCk), both also in the supplement. Files: T14b_simulations.pdf; T14b_simulations.tex; the ten figure files the source includes (T14b_fig_sigma.pdf, T14b_fig_fraction.pdf, T14b_fig_merger.pdf, T14b_fig_retention.pdf, T14b_fig_halo.pdf, T14b_fig_galaxy.pdf, T14b_fig_Tc.pdf, T14b_fig_neff.pdf, T14b_film1_still.png, T14b_film2_still.png); verify_T14b.py; GA.py; T14b_supplement.zip; LICENSE-CODE.txt. Licence: the paper (PDF and LaTeX source), its figures, the films and the run outputs are CC BY 4.0. The code files in this record, including those in T14b_supplement.zip, are additionally released under the MIT licence; see LICENSE-CODE.txt. Authorship and disclosure. The founding idea of the series is the author's: that division by zero in a Clifford algebra should be read not as a prohibition but as a transport into a higher-dimensional algebra, and that the transported division need not be accompanied by an inverse operation. The direction of investigation and the critical review of the results are likewise the author's. The mathematical development and the drafting of the text were carried out in extended collaboration with Claude Fable 5 (Anthropic), an AI system.