Cosmology Cdmdensity Parameter From Rs Dmcandidate

The candidate list

Dark matter is the unseen mass that galaxies and galaxy clusters need to hold together, yet no one has directly detected the particle responsible. Cosmologists estimate how much of the universe's total energy density this missing mass supplies, writing the share as Ω_CDM, the cold dark matter density parameter. The Recognition Science framework's library, a machine-checked collection of formal theorems, contains a small declaration called DMCandidate that fixes one such estimate and names the standard suspects.

The declaration defines exactly five candidate types: the WIMP, the axion, the sterile neutrino, the primordial black hole, and self-interacting dark matter. These are the five canonical dark matter candidates that particle physicists and cosmologists most often study. The library proves that the list contains precisely five entries, a fact the computer checks by exhaustive enumeration. Alongside the list, a definition sets Ω_CDM to 0.26, and a theorem proves this number sits strictly between 0.25 and 0.27, the accepted observational band.

In Recognition Science, this is a recognition event: the framework's ledger, a discrete record of such events, registers the density parameter as a single certified value rather than a continuous range. The certification bundles the five-candidate count and the density band into one structure, and the library constructs that certificate in a single step. The whole file carries no unproved assumptions, meaning every claim in it is checked by the machine down to the kernel's axioms.

What the declaration does not do is identify which candidate constitutes the actual dark matter. The list is a definitional choice, not a detection. The density value 0.26 is a chosen constant that matches observation, not a number the framework derives from first principles. The certificate guarantees internal consistency, not physical truth. A reader should take DMCandidate as a formal bookkeeping device: it names the five standard options, fixes a plausible density, and proves the arithmetic holds together, while remaining silent on which particle nature actually chose.

inductive DMCandidate where
  | wimp
  | axion
  | sterileNeutrino
  | primordialBH
  | selfInteracting
  deriving DecidableEq, Repr, BEq, Fintype

theorem dmCandidate_count : Fintype.card DMCandidate = 5 := by decide

noncomputable def omegaCDM : ℝ := 0.26

theorem omegaCDM_band : (0.25 : ℝ) < omegaCDM ∧ omegaCDM < 0.27 := by
  unfold omegaCDM; refine ⟨?_, ?_⟩ <;> norm_num

What this page does not claim

The declaration does not claim which candidate is the actual dark matter particle. The density value 0.26 is not derived from the framework's forcing chain; it is a chosen constant. The certificate proves internal consistency, not that dark matter exists.

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

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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