Colored quotient and atom stabilizer sizes

Exact statement

The colored degree-three quotient has order 393,216, atom stabilizer order 4,096, and degree-four atom fibres of size 128 over the 96-state degree-three atom orbit.

StatusStored exact closures; replay dependency incomplete

External reviewNo documented external or specialist review of this Quotient Arsenal result is recorded.

Context

Finite quotient words do not lift one factor at a time independently. Local affine lift fibres must be transported through the ordered product; the target defect then lives in a product-image cokernel that is invariant under quotient Hurwitz moves.

Proof or evidence

Independent stored enumerators agree on 393,216 group states and 12,288 degree-four atom states.

Quotient Arsenal synthesis →

Verification notes

The exact written argument and available certificate were inspected; the public maturity level reflects whether import-time replay was complete.

Limitations

The atom stabilizer is not the Hurwitz stabilizer of a complete tuple.

Open work

Restore the missing helper and rerun the group closures.