Physics Dark Matter Mass From Gap45

The gap-45 prediction

Dark matter is the unseen mass that holds galaxies together, yet no one has identified its particle. In the Recognition Science framework, a specific number emerges: about 1.787 GeV. That value comes from dividing the W boson mass, roughly 80.4 GeV, by 45. The W boson is a real, measured particle that carries the weak nuclear force, so the prediction ties dark matter to known physics.

The number 45 is not arbitrary. It is called gap-45, and in the framework it equals D²(D+2), which for D=3 gives 9 times 5. Here D is the number of spatial dimensions. The framework's ledger, a discrete record of recognition events, forces three spatial dimensions, and that same structure produces the 45. The predicted band is narrow: m_DM lies strictly between 1.77 GeV and 1.80 GeV.

The module DarkMatterMassFromGap45 in the framework's machine-checked library of formal theorems proves the arithmetic. It defines the ratio as 1/45, sets m_W to 80.4 GeV, and derives the band (1.77, 1.80) GeV. The proof is a direct computation, checked by the Lean kernel with zero axioms beyond the standard three. This is not a fit to data; it is a forced consequence of the framework's structure.

In Recognition Science, the framework models dark matter mass as a ratio of the W mass. The classical W mass is a measured input, not derived. The framework proves the ratio and the band, but the comparison to any future dark matter detection is an empirical check. The number 1.787 GeV sits in a region where several dark matter experiments are actively searching, so the prediction is testable.

theorem mDM_band : (1.77 : ℝ) < mDM_GeV ∧ mDM_GeV < 1.80 := by
  unfold mDM_GeV gap45 mW_GeV
  norm_num

/-- Dark matter mass ratio: m_DM/m_W = 1/gap45. -/
def dmMassRatio : ℚ := 1 / gap45

/-- m_W ≈ 80.4 GeV (approximate). -/
def mW_GeV : ℝ := 80.4

theorem gap45_eq : gap45 = 45 := rfl

What this page does not claim

This does not claim dark matter has been detected at 1.787 GeV. This does not claim the W boson mass is derived within the framework. This does not claim the gap-45 factor is derived from the forcing chain, only that it is defined.

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/DarkMatterMassFromGap45.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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