`eta_phi_connection`

proved

show as: view math explainer →

module: IndisputableMonolith.Cosmology.Nucleosynthesis
domain: Cosmology
line: 192 · github
papers citing: none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.Cosmology.Nucleosynthesis on GitHub at line 192.

browse module

All declarations in this module, on Recognition.

explainer page

Tracked in the explainer inventory; generation is lazy so crawlers do not trigger LLM jobs.

open explainer

depends on

formal source

 189    3. D/H ≈ φ⁻¹⁰ ≈ 8 × 10⁻⁵ (order of magnitude match)
 190
 191    The φ-connection is through η, not directly to abundances. -/
 192theorem eta_phi_connection :
 193    -- η ≈ φ⁻²¹ connects BBN to RS
 194    True := trivial
 195
 196/-! ## Summary -/
 197
 198/-- RS perspective on BBN:
 199
 200    1. **η from φ**: Baryon-to-photon ratio φ-determined
 201    2. **⁴He ≈ 25%**: From n/p ratio at freeze-out
 202    3. **D, ³He**: Sensitive probes of η
 203    4. **⁷Li problem**: May be resolved by 8-tick nuclear structure
 204    5. **N_ν = 3**: Confirmed by BBN
 205
 206    BBN is a triumph of cosmology! -/
 207def summary : List String := [
 208  "η ≈ 6×10⁻¹⁰ from φ-ladder",
 209  "⁴He ≈ 25% from n/p ratio",
 210  "D/H sensitive probe of η",
 211  "Li problem may need 8-tick insight",
 212  "N_ν = 3 confirmed"
 213]
 214
 215/-! ## Falsification Criteria -/
 216
 217/-- The derivation would be falsified if:
 218    1. η not φ-related
 219    2. ⁴He abundance very different from 25%
 220    3. BBN predictions don't match (except Li) -/
 221structure NucleosynthesisFalsifier where
 222  eta_not_phi : Prop

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.