Physics Dark Matter Absolute Cross Section Score Card

The absolute cross-section scorecard

In particle physics, the dark-matter cross section measures how often a dark-matter particle interacts with ordinary matter. A larger cross section means more frequent collisions, which makes detection easier. The absolute cross section is the number in square centimeters that experiments compare against their detector limits. The scorecard in Recognition Science (RS) is a formal record that fixes that number to a specific band and states exactly what would disprove it.

The scorecard starts from a ratio: the dark-matter cross section divided by a neutrino-reference cross section. RS predicts this ratio lies strictly between 0.11 and 0.13. To turn a ratio into an absolute number, the scorecard multiplies by a protocol normalization: the neutrino-reference cross section is set to 1e-38 cm². That multiplication gives the absolute dark-matter cross section band (1.1e-39, 1.3e-39) cm². The scorecard proves this band is correct given the ratio and the normalization, and it proves the reference cross section is positive.

In Recognition Science, a ledger is a discrete record of events; here the ledger records the normalization choice and the ratio band. The scorecard is a machine-checked collection of formal theorems, meaning the band and positivity are verified by computer proof. The certificate structure bundles three facts: the reference is positive, the ratio lies in (0.11, 0.13), and the absolute band holds. The proof that the certificate is satisfiable is a theorem, with zero unproved assumptions.

The honest status is PARTIAL_THEOREM / HYPOTHESIS. The absolute band follows from the named normalization, but deriving that normalization from RS or from a specific neutrino channel remains open. The falsifier is concrete: a detector with valid efficiency at or below 0.35 keV that excludes the band (1.1e-39, 1.3e-39) cm² would falsify the prediction. The scorecard therefore gives experimentalists a sharp target and a clear rule for when the prediction fails.

What the scorecard changes is the comparison protocol: detector-limit comparisons should use the derived band only after a sub-0.35 keV efficiency curve is supplied. Without that curve, the band is not yet usable. The scorecard does not claim the normalization is derived from first principles; it marks that as open. The practical consequence is a testable prediction that any suitable detector can confirm or reject.

theorem row_sigma_DM_cm2_band :
    1.1e-39 < sigma_DM_cm2 ∧ sigma_DM_cm2 < 1.3e-39 := by
  unfold sigma_DM_cm2 sigma_nu_reference_cm2
  have h := row_sigma_ratio_band
  constructor
  · nlinarith [h.1]
  · nlinarith [h.2]

theorem row_sigma_nu_reference_pos : 0 < sigma_nu_reference_cm2 := by
  unfold sigma_nu_reference_cm2
  norm_num

theorem darkMatterAbsoluteCrossSectionScoreCardCert_holds :
    Nonempty DarkMatterAbsoluteCrossSectionScoreCardCert :=
  ⟨{ sigma_nu_ref_pos := row_sigma_nu_reference_pos
     sigma_ratio_band := row_sigma_ratio_band
     sigma_absolute_band := row_sigma_DM_cm2_band }⟩

What this page does not claim

The normalization sigma_nu_ref = 1e-38 cm² is derived from RS first principles. The absolute band is valid without a sub-0.35 keV efficiency curve. The ratio band is a theorem rather than a hypothesis.

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/Physics/DarkMatterAbsoluteCrossSectionScoreCard.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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