The Shadow: A Cosmology of the Plenum

The Shadow: A Cosmology of the Plenum develops a deterministic, arithmetic-firstcosmological ansatz in which the physical universe \( M \) is interpreted as ameasure‑zero shadow cast by a richer underlying structure \( V \), the plenum. The central engine is the operator \[\large J = 1 + \zeta_5\] whose action on a six‑axis register generates the symbolic dynamics, projection geometry,and statistical partitions that appear in physics as matter, space, and quantum behaviour. Core claims - Dark matter is geometric, not particulate. The visible fraction arises from Thue–Morse pair statistics: \[ \large f_{\mathrm{vis}} = \frac{1}{6}, \qquad f_{\mathrm{dark}} = \frac{5}{6} \] giving a universal dark‑to‑visible ratio \[ \huge \frac{f_{\mathrm{dark}}}{f_{\mathrm{vis}}} = 5. \] - Spatial dimension \( d = 3 \) is derived from the eigenstructure of the projection \[ \Large L^{T} L = I - \frac{1}{5} 11^{T}, \] where three eigenvalues carry full weight and the trace direction is suppressed by the order of \( \mathbb{Z}_5 \). Space is the kernel of the trace map, not an assumed arena. - Relativity emerges from rendering constraints: \[ c = 1 \text{ edge/tick}, \] time dilation from reduced Lapse \( N_x \), and length contraction as projection distortion. - Quantum phenomena arise from deterministic chaos on \( V \). The Born rule is a Kähler‑measure normalization: \[ P[\psi(z)] = \frac{|\psi(z)|^2}{\int |\psi|^2}. \] - Baryon fraction appears as a regulator identity: \[ \Omega_b \approx \frac{\pi^2}{200}. \] The manuscript proposes that the universe is not a zoo of particles but a theatre ofshadows cast by a single arithmetic operator. Space is the remainder after subtractingobservation; matter is the event‑trace of a deeper plenum; and nine major physicalphenomena emerge from one operator with no adjustable parameters. Simplizis.