Cosmology Baryogenesis Staging Relic Product H Surv H Ind Discharged General

The relic product

In cosmology, a relic is a particle population left over from the early universe. The Recognition Science framework's ledger, a discrete record of events, models how such populations evolve. A key question is what final density a relic will have, given how many particles survive and whether their channels are independent.

The theorem relic_product_hSurv_hInd_discharged_general establishes a specific relationship. It states that if each survival amplitude is exactly 1/phi, where phi is the golden ratio, and if the number of transient channels is 44 with independence confirmed, then the relic product equals phi raised to the power -44. This is a formal statement in the machine-checked library of formal theorems, meaning the calculation is verified.

The number 44 appears throughout the framework's baryogenesis staging, a module that tracks how baryon number might be generated. The theorem connects this count to a specific density value. The proof relies on a chain of definitions and prior theorems, including the definition of the forced relic composition and the uniqueness of the transient rank.

This result is a formal derivation, not a measured value. It does not claim that the universe's baryon asymmetry is actually explained by this number. The theorem's conditions, such as the survival amplitude being exactly 1/phi, are assumptions. The framework models a scenario; it does not assert that this scenario is the one realized in nature.

The theorem's value is in showing a logical connection within the framework. If the stated conditions hold, the relic density follows. This provides a target for further work, but it is not an empirical prediction. The framework's own documentation emphasizes that it holds small, honest theorem targets to prevent faking the missing mechanism of baryogenesis.

theorem D_forced_eq_relic_composition
    (channelIndependence : ℕ → Bool)
    (survivalAmplitude : ℕ → ℝ)
    (transientChannelCount : ℕ)
    (hSurv : ∀ i, survivalAmplitude i = 1 / phi)
    (hCount : transientChannelCount = 44)
    (hInd : channelIndependence transientChannelCount = true) :
    D survivalAmplitude transientChannelCount
      (channelIndependence transientChannelCount) = D_forced :=
  relic_product_eq_phi_neg_44 channelIndependence survivalAmplitude
    transientChannelCount hSurv hCount hInd

What this page does not claim

This theorem does not claim that the baryon asymmetry of the universe is explained by this number. The theorem does not assert that the survival amplitude is 1/phi in the real universe. The result is a formal derivation, not a measurement or an empirical prediction.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Cosmology/BaryogenesisStaging.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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