structureFormation
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not derive the growth law delta proportional to a from the Recognition Composition Law.
- Does not extract numerical redshifts from phi-ladder rungs or gap(Z).
- Does not compute scattering cross-sections or annihilation rates.
- Does not address the 1.79 GeV W-image projection or spectrum-level identification.
formal statement (Lean)
214def structureFormation : List String := [
proof body
Definition body.
215 "DM decouples early (z ~ 10⁶)",
216 "DM perturbations grow: δ ∝ a",
217 "Baryons fall in after z ~ 1100",
218 "Galaxies form in DM halos"
219]
220
221/-! ## Detection? -/
222
223/-- Can ledger shadows be detected?
224
225 1. **Gravitational**: Already detected (rotation curves, etc.)
226 2. **Direct detection**: Scattering off nuclei - difficult
227 (Odd-phase doesn't couple well to even-phase)
228 3. **Indirect**: Annihilation products - possible
229 (Odd + odd → even, produces visible particles)
230 4. **Collider**: Produce at LHC - no luck so far -/