What is the in-between state of a u-quark capturing an electron? Try to picture it and you'll know it doesn't make sense.
Even two points trying to superimpose don't make sense.
Those formulas for i, j, k aren't the only values that satisfies i^2 = j^2 = k^2 = -1, in fact any point on the unit sphere would. So we have: i can be = j can be = k which contradicts the proof that they are always distinct.
From the above we can conclude they are commutative, contradicting a consequence of the axioms.
So it doesn't matter that I can't substitute +/-sqrt(-1) for i, j, k.
Lemma: |i| = |j| = |k| is consistent with the axiom: i^2 = j^2 = k^2. Then the i, j, k cannot be distinct except where the sign on any two may differ.
Proof:
Assume i^2 = j^2 = k^2
Do the operation: drawing the square root to both sides of the equation:
sqrt(i^2) = sqrt(j^2) and sqrt(j^2) =...
We have the equation: i^2=j^2=k^2=ijk=-1. Now solve the first three equations and substitute the result into the fourth. We get:
ijk = (+/-sqrt(-1))(+/-sqrt(-1))(+/-sqrt(-1)) = +/-sqrt(-1) not = -1.
Now the story is that you cannot make this substitution which is contrary to Mathematical rules.
If you say the tau changed into energy and the energy changed into the particles, I say this can't happen because neither of the three have a corresponding anti-particle.
That formula you quoted is illegal as a tau-antineutrino was not also created. It you insist on it, you must explain it that the tau-neutrino was part of the tau: that is ridiculous. My formulas respects the "only particle-antiparticle creation" rule.
My formulas are too elegant to be untrue.