Cosmology Dark Matter Xenonprediction Dm Cross Section Pos

A positive cross-section

Dark matter is the unseen mass that holds galaxies together, yet its particles have never been directly detected. Experiments like XENONnT search for the faint signal of a dark matter particle striking an atomic nucleus. For any such search to make sense, the predicted interaction strength, the cross-section, must be a positive number. A negative cross-section would be physically meaningless, a prediction that could not describe any real particle.

The Recognition Science framework, a research program that derives physical constants from a mathematical cost function, has produced a specific prediction for dark matter. It predicts a dark matter particle with a mass about 1/45 that of the W boson, placing it in a narrow band near 1.78 GeV. The framework also predicts the cross-section ratio, the interaction strength relative to some standard, to lie in a band between 0.11 and 0.13. This prediction is not yet excluded by XENONnT's current limits, which remain above the predicted band.

Within this framework, the declaration dmCrossSection_pos is a formal theorem. It proves, using the framework's machine-checked library of formal theorems, that the predicted cross-section ratio is greater than zero. It is a logical consequence of the framework's definition of the cost function, which is always positive for the relevant input. This positivity is a necessary condition for the prediction to be physically sensible, but it is a modest claim: it does not say the cross-section is correct, only that it is not negative.

The theorem is a small piece of a larger structure. It is a proof that one number, the predicted cross-section, is positive. It does not establish that dark matter exists, that the prediction is correct, or that XENONnT will find a signal. It is a check on the internal consistency of the framework's prediction, a prerequisite for any further comparison with experiment. The real test lies in the experimental data, which will ultimately decide if the prediction matches nature.

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

What this page does not claim

The theorem does not claim the dark matter prediction is correct or that dark matter exists. The theorem does not claim the predicted cross-section is within the experimentally allowed region. The theorem does not claim the framework's prediction is the only possible one.

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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