cabibboProjection
cabibboProjection supplies the integer exponent -3 for the golden-ratio projection that enters the Cabibbo mixing angle V_us. Researchers deriving CKM elements from ledger geometry in Recognition Science cite this constant when assembling the RSBridge. The definition is a direct literal assignment with no computation or auxiliary lemmas.
claimThe golden projection exponent for the Cabibbo angle is the integer $-3$.
background
The RSBridge module derives CKM mixing angles from geometric counts on the cube dual and the φ-ladder rather than treating them as free parameters. V_us is obtained from the projection φ^{-3} minus a radiative term proportional to α, while V_cb equals 1/24 from the edge-dual count and V_ub equals α/2. The supplied upstream correction factor 1/(φ N) supplies the finite-N adjustment used in related quantum-channel calculations.
proof idea
Direct definition that assigns the literal integer -3. No lemmas or tactics are invoked; the body is a one-line constant declaration.
why it matters in Recognition Science
This definition supplies the missing exponent in the geometric CKM derivation. It is invoked by the theorem mixingAngles_geometric_origin, which simultaneously records edgeDualCount = 24 and confirms the projection exponent equals -3, thereby recovering the observed V_us ≈ φ^{-3} - (3/2)α. Within the Recognition framework the constant closes the φ-ladder step for first-to-second generation mixing and feeds the full RSBridge structure that replaces arbitrary CKM parameters with ledger geometry.
scope and limits
- Does not derive the exponent -3 from the T0-T8 forcing chain.
- Does not compute the numerical value of any mixing angle.
- Does not incorporate higher-order radiative corrections.
Lean usage
have h : cabibboProjection = -3 := rflformal statement (Lean)
50def cabibboProjection : ℤ := -3
proof body
Definition body.
51
52/-- The radiative correction coefficient -/