structureFormation
plain-language theorem explainer
Dark matter ledger shadows in Recognition Science drive structure formation by decoupling early at z around 10^6, permitting linear growth of perturbations during the radiation era. Baryons subsequently collapse into the resulting halos after recombination near z 1100, enabling galaxies to assemble on observed timescales. Cosmologists working in the eight-tick parity framework cite this sequence to account for the required matter density without extra particles. The declaration is a direct list literal with no reduction steps.
Claim. The sequence of dark matter driven structure formation is DM decouples early ($z sim 10^6$), DM perturbations grow as $delta propto a$, baryons fall in after $z sim 1100$, galaxies form in DM halos.
background
The COS-010 module treats dark matter as the temporal projection of the sigma=0, Z nonzero phantom sector, realized as odd-phase orbits within the 8-tick parity cycle. Upstream, the EightTick.phase definition supplies the discrete angles k pi over 4 for k in Fin 8, periodic with period 2 pi, while the Wedge.phase supplies the unimodular complex number exp(i w). These phases underwrite the ledger-shadow picture in which gravitationally active entries remain electromagnetically decoupled, consistent with the observed Omega_dm approximately 0.27 and the requirement that galaxies form in time.
proof idea
The declaration is a direct definition that assigns a four-element list of strings. It references the phase constructions from EightTick and Wedge only for contextual parity, with no tactic steps or lemma applications inside the body.
why it matters
This definition fills the structure-formation step of the COS-010 paper proposition on non-luminous ledger configurations. It anchors the T7 eight-tick octave within cosmology and supplies the qualitative mechanism that resolves the galaxy-formation timeline. No downstream theorems are recorded, leaving open its quantitative link to the phi-ladder mass formula and the alpha band.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.