IndisputableMonolith.RecogSpec.RSBridge
RSBridge supplies geometric constructions from the 3-cube to CKM mixing angles inside Recognition Science. It defines cubeEdges as the 12 edges together with dual counts, cabibboProjection, radiativeCoeff, and the V_xx_from_bridge maps that link the φ-tier ledger to observable parameters. The module is cited by derivations of mixing angles and g-2. Its content is a set of definitions and short equalities that connect the rich ledger to bridge geometry.
claimCube edge count equals 12. Projections from dual edge counts on the 3-cube yield Cabibbo angle and CKM elements $V_{us}$, $V_{cb}$, $V_{ub}$ via the φ-ladder ledger.
background
The module sits inside RecogSpec and imports Constants (where τ₀ equals one RS tick), Core, and RSLedger. RSLedger supplies the rich ledger in which particle masses occupy discrete rungs on the φ-ladder and mass ratios arise from generation torsion rather than explicit φ-formulas. Core supplies the underlying specification language. The bridge geometry uses the 3-cube whose 12 edges and dual counts furnish projections for mixing angles.
proof idea
This is a definition module. It introduces cubeEdges as the edge count of the 3-cube, states edgeDualCount together with its equality lemma, then defines cabibboProjection and radiativeCoeff, and assembles the RSBridge object and the three V_xx_from_bridge functions.
why it matters in Recognition Science
The module feeds BridgeDerivation, which derives the canonical mixing-angle payload CkmMixingAngles and g-2 from RSBridge geometry with mixingAngles = { vus := V_us, vcb := V_cb, vub := V_ub }. It supplies the geometric step that converts the φ-ladder ledger into CKM parameters inside the Recognition framework.
scope and limits
- Does not derive the full CKM matrix or its phases.
- Does not produce numerical values for mixing angles.
- Does not connect directly to the mass formula or generation torsion.
- Does not address g-2 or radiative corrections beyond the defined coefficient.
used by (1)
depends on (3)
declarations in this module (19)
-
def
cubeEdges -
def
edgeDualCount -
theorem
edgeDualCount_eq -
def
cabibboProjection -
def
radiativeCoeff -
structure
RSBridge -
def
V_cb_from_bridge -
theorem
V_cb_canonical -
def
V_cb_real -
def
V_ub_from_bridge -
def
V_us_from_bridge -
def
canonicalRSBridge -
theorem
canonicalRSBridge_edgeDual -
theorem
canonicalRSBridge_alpha -
theorem
canonical_V_cb -
theorem
canonical_V_ub -
theorem
canonical_V_us -
theorem
mixingAngles_geometric_origin -
theorem
V_cb_approx