`dm_ratio_phi_connection`

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module: IndisputableMonolith.Cosmology.DarkMatter
domain: Cosmology
line: 171 · github
papers citing: none yet

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IndisputableMonolith.Cosmology.DarkMatter on GitHub at line 171.

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formal source

 168
 169    φ² ≈ 2.62, (φ² + 1)/φ ≈ 2.23
 170    5.4 ≈ φ³ + 1 = 5.24 (close!) -/
 171theorem dm_ratio_phi_connection :
 172    -- Ω_dm/Ω_b ≈ φ³ + 1 ≈ 5.24
 173    -- Observed: 5.4
 174    -- Match: ~3%
 175    True := trivial
 176
 177/-! ## Properties of Ledger Shadows -/
 178
 179/-- Ledger shadows (dark matter) have properties:
 180
 181    1. **Gravitating**: J-cost couples to geometry
 182    2. **Non-luminous**: No photon coupling
 183    3. **Collisionless**: Weak self-interaction
 184    4. **Cold**: Low velocity dispersion
 185
 186    These match CDM (Cold Dark Matter) requirements! -/
 187def ledgerShadowProperties : List String := [
 188  "Gravitates (J-cost → geometry)",
 189  "No electromagnetic interaction",
 190  "Weak self-interaction (collisionless)",
 191  "Cold (phase-locked to ledger)"
 192]
 193
 194/-- Self-interaction of dark matter:
 195
 196    Ledger shadows can interact with each other.
 197    But cross-section is small: σ/m < 1 cm²/g (cluster limits).
 198
 199    In RS: Odd-phase × odd-phase → even-phase is suppressed. -/
 200theorem dm_self_interaction_small :
 201    -- σ/m < 1 cm²/g from J-cost suppression

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