The unbounded fractional authoritative camera
The unbounded fractional authoritative camera is a version of the fractional authoritative camera that can be used with fractions > 1
.
Most of the reasoning principles for this version of the fractional authoritative cameras are the same as for the original version. There are two difference:

We get the additional rule that can be used to allocate a "surplus", i.e. if we have the authoritative element we can always increase its fraction and allocate a new fragment.
✓ (a ⋅ b) → ●?{p} a ~~> ●?{p + q} (a ⋅ b) ⋅ ◯?{q} b

At the cost of that, we no longer have the
◯?{1} a
is an exclusive fragmental element (cf.frac_auth_frag_validN_op_1_l
).