Cosmology Dark Matter Xenonprediction Dark Matter Xenoncert

The certified prediction

Dark matter is the unseen mass that holds galaxies together, but no one has yet detected a particle for it. One candidate mass range comes from a specific theoretical framework, and that framework has now produced a formal certificate: a machine-checked proof that its predicted dark matter mass and interaction strength fall inside a narrow, testable band. The certificate is a compact object that bundles three facts: the predicted mass ratio, the positivity of the cross-section, and the claim that the cross-section lies below a stated upper bound.

The mass prediction is expressed as a ratio. The framework sets the dark matter particle mass at 1/45 of the W boson mass, the heavy particle that carries the weak nuclear force. With the W mass known from experiment, that ratio translates to a dark matter mass of about 1.78 GeV, roughly twice the mass of a proton. The second prediction concerns the cross-section, a measure of how often a dark matter particle would interact with ordinary matter. The framework predicts this interaction strength falls in a band between 0.11 and 0.13 in its natural units.

The certificate proves three things formally. First, the mass ratio is exactly 1/45. Second, the cross-section ratio is positive. Third, the cross-section ratio is less than 0.13. The proof that it is less than 0.13 uses the known value of the golden ratio, which in this framework is the unique self-similar scaling constant. The certificate does not prove the cross-section is greater than 0.11; that lower bound is stated in the documentation but is not part of the formal certificate.

What does this mean for experiment? The XENONnT detector, a tank of liquid xenon deep underground, searches for dark matter by watching for the faint flash of light when a particle bounces off a xenon nucleus. As of the certificate's writing, XENONnT has not yet reached the sensitivity needed to test the framework's prediction at 1.78 GeV. The predicted cross-section band lies below the current exclusion limit, meaning the experiment has not ruled it out. The certificate itself does not claim the prediction is correct, only that the framework's own numbers are internally consistent and formally derived.

In Recognition Science, this certificate is a step toward a testable cosmology. The framework derives its constants from a single cost function, and the dark matter prediction follows from that derivation. The certificate is a formal object, checked by a machine, that packages the prediction so it can be compared against data. The next step is experimental: if XENONnT or another detector reaches the predicted band and finds nothing, the framework's dark matter model would be falsified. If it finds a signal at 1.78 GeV, the framework would have made a precise, testable prediction that survived.

/-- Predicted DM mass / W mass = 1/45. -/
noncomputable def dmMassRatio : ℝ := 1 / 45

/-- Cross-section ratio is positive. -/
theorem dmCrossSection_pos : 0 < dmCrossSectionRatio :=
  Jcost_pos_of_ne_one phi phi_pos phi_ne_one

/-- The prediction is not yet excluded: cross-section is in J(phi) band. -/
theorem dmCrossSection_in_band : 0 < dmCrossSectionRatio ∧ dmCrossSectionRatio < 0.13 := by
  constructor
  · exact dmCrossSection_pos
  · unfold dmCrossSectionRatio
    rw [Constants.Jcost_phi_val]
    linarith [phi_lt_onePointSixTwo]

structure DarkMatterXENONCert where
  dm_mass_ratio : dmMassRatio = 1 / 45
  cross_section_pos : 0 < dmCrossSectionRatio
  cross_section_band : 0 < dmCrossSectionRatio ∧ dmCrossSectionRatio < 0.13

What this page does not claim

The certificate does not prove the cross-section is greater than 0.11. The certificate does not claim the dark matter prediction is experimentally confirmed. The certificate does not derive the dark matter mass from first principles; it states the ratio as a definition.

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/DarkMatterXENONPrediction.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.

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