For the first time the former "Cartan Convention" is displayed correctly:

                                q_λ^a q_a^λ = 4                                 (12)

But any remark about the wrong former version q_λ^a q_a^λ = 1 (e.g. in the GCUFT book vol.1) is missing, and no word about the designation "Cartan Convention", it's a "normalisation" now.

However, already "Definition" (11)

                                R q_λ^a = ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)                                 (11)

is inadmissible : Equ. (11) is to be satisfied for all pairs of indices a,λ = 0,1,2,3. Therefore Equ. (11) represents 4×4 = 16 (sixteen) definitions of R, and nobody tells us

why these different definitions of R should agree.

Thus, the conclusion

. . . and multiply both sides of eq. (11) by q_a^λ to obtain

                                R = ¼ q_a^λ ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)                                 (13)

is inadmissible. This value of R cannot fulfil the 16 equations (11) in general. Myron should check that by plugging the expression (13) into the definitions (11) (by hand *⁾ or by computer algebra). He should tell us the result.

There is no ECE Lemma.

*) Applying his New Math (handling of Eqs. (22 - 23)) Evans would probably execute the following "self check" by hand:

Plugging R (eq.(13)) into eq.(11) yields

                                R q_λ^a = [¼ q_a^λ ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)] q_λ^a

                                          = [¼ q_a^λq_λ^a] ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)

                                          = [¼ 4] ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)

                                          = ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)

and so he feels fully justified.

Really! So he did!!! In the handwritten document http://www.atomicprecision.com/blog/wp-filez/acheckpriortocoding5.pdf we read

. . .

i.e.

                o q_α^a = ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)                                                       (8)

Now define

                R = q_a^λ ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)                                                       (9)

and use the famous EC (= Evans Convention)

                q_λ^aq_a^λ = 1 (!!!)                                                                                 (10)

to find by using the eqs. (8-10)

                o q_λ^a =₍₈₎ 1 · ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)
                                =₍₁₀₎ [q_λ^aq_a^λ] · ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)
                                =_(?) q_λ^a · [q_a^λ ∂^μ (Γ^ν_μλq_ν^a − ω^a_μbq_λ^b)]
                                =₍₉₎ R q_λ^a                                                         (11)