Cosmology Dark Matter Xenonprediction Dm Mass Ratio

The predicted mass ratio

The dark matter mass ratio is a number that appears in a specific physical prediction. In the Recognition Science framework, the ratio of the dark matter particle mass to the W boson mass is defined to be exactly 1/45. This is not a measurement; it is a definitional choice, a fixed number that the framework's internal structure suggests. The W boson is the heavy particle that carries the weak nuclear force, one of the four fundamental forces. The framework predicts this ratio, and from it, a dark matter mass in the range of 1.77 to 1.79 GeV, which is roughly twice the mass of a proton.

The framework also defines a related quantity, the dark matter cross-section ratio, which describes how likely dark matter is to interact with ordinary matter. This ratio is set to the value of the framework's cost function at the golden ratio, J(φ), which falls in a band between 0.11 and 0.13. This cross-section band is the target for experiments like XENONnT, a detector deep underground that searches for dark matter particles scattering off xenon atoms. As of the latest data, XENONnT has not yet reached the sensitivity needed to test this specific prediction at a dark matter mass of 1.78 GeV. The prediction is therefore still alive, though untested.

In the machine-checked library, the definition dmMassRatio is a formal statement that the ratio equals 1/45. A separate theorem proves that the cross-section ratio is positive and lies below 0.13, which is the upper edge of the predicted band. These are formal facts, verified by the computer. What this does not claim is that dark matter has been discovered, that the mass ratio is measured, or that the framework's prediction is correct. It only establishes what the framework's internal logic says the ratio should be, and that this specific value has not yet been excluded by experiment.

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

/-- DM cross-section ratio at J(φ). -/
noncomputable def dmCrossSectionRatio : ℝ := Jcost phi

/-- 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]

What this page does not claim

This does not claim dark matter has been discovered. This does not claim the mass ratio has been measured; it is a definitional prediction. This does not claim the prediction is correct, only that it has not yet been excluded.

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)

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