darkSector
plain-language theorem explainer
The darkSector definition enumerates the odd indices in the eight-tick cycle as the dark sector. Cosmologists modeling non-luminous matter within Recognition Science cite it to separate gravitationally active but electromagnetically invisible components. The definition is a direct list assignment of indices 1, 3, 5, 7.
Claim. The dark sector consists of the odd phases in the eight-tick cycle, namely the indices $1,3,5,7$ in the set of eight phases.
background
The eight-tick cycle from Foundation.EightTick partitions phases as $k$ for $k=0$ to $7$, with each phase given by $kπ/4$. The module Cosmology.DarkMatter treats this cycle as the temporal projection of the phantom sector, where odd phases form ledger shadows that remain invisible to photons. Photons are phase-0 excitations, so only even phases exchange phase-0 quanta.
proof idea
Direct definition that assigns the list of odd indices in the Fin 8 type. It draws on the phase definition from EightTick to label these indices as the invisible sector.
why it matters
This definition supplies the concrete odd phases for the COS-010 dark-matter mechanism. It supports sibling results such as omega_dm and dm_baryon_ratio by isolating the non-luminous ledger configurations. It aligns with the eight-tick octave (T7) and the phase-mismatch suppression noted in the module for null-detection consistency at the 1.79 GeV scale.
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