canonicalRSBridge_alpha
The theorem states that the alpha exponent carried by the canonical recognition bridge on any RSLedger equals the locked value alphaLock = (1 - 1/phi)/2. Workers deriving CKM angles from ledger geometry cite it to fix the fine-structure input. The proof is a one-line reflexivity that follows from the bridge definition.
claimFor any RSLedger $L$, the fine-structure exponent of the canonical recognition bridge on $L$ equals the locked constant $(1 - 1/phi)/2$.
background
RSBridge supplies the geometric structure that turns ledger counts into CKM mixing angles. The module derives V_ub from alpha/2, V_cb from the 24 edge-dual count, and V_us from a phi-ladder projection with radiative correction. alphaLock is the canonical locked fine-structure constant defined as (1 - 1/phi)/2.
proof idea
The proof is a one-line reflexivity that matches the alphaExponent field of canonicalRSBridge L directly to alphaLock.
why it matters in Recognition Science
It anchors the fine-structure constant inside the bridge used for all three CKM angles. The result closes the step from ILG self-similarity to observable couplings and supports the geometric derivation of mixing parameters rather than their free assignment.
scope and limits
- Does not derive the numerical value of alpha from first principles.
- Does not include higher-order radiative corrections beyond the lock.
- Applies only to the canonical bridge construction on an RSLedger.
formal statement (Lean)
122@[simp] theorem canonicalRSBridge_alpha (L : RSLedger) :
123 (canonicalRSBridge L).alphaExponent = alphaLock := rfl
proof body
Term-mode proof.
124
125/-! ## Canonical Mixing Angle Values -/
126
127/-- V_cb = 1/24 for canonical bridge -/