all_profiles

The module derives generation torsion values ${0,11,17}$ as the unique values compatible with the 8-tick Hamiltonian cycle on the 3-cube $Q_3$, projected onto the $\varphi$-ladder through the Recognition Composition Law. RCL forces independent couplings to add in the ladder exponent; the Gray cycle partitions $Q_3$ into active and passive subcells by CW level.

A coupling profile records which nontrivial CW levels participate in surface coupling. Vertices (level 0) are already coupled by the Hamiltonian cycle; the interior (level 3) is unavailable for surface coupling. That leaves edges (CW-dim 1) and faces (CW-dim 2), each on or off, hence four Boolean pairs.

Separately, the CW boundary prerequisite (faces attach along edges) will later restrict admissible profiles to a downward-closed subset; this definition itself only names the ambient finite set.

Definitional list: the four constructors of CouplingProfile written out in order (neither, edges only, faces only, both). No lemmas or tactics.

Feeds all_profiles_complete, which proves every coupling profile appears in the list, so case analysis on profiles is exhaustive and finite. That exhaustiveness is the bookkeeping step before CW lower-set filtering and the variational ground-state argument that force torsion into ${0,11,17}$.

In the module chain this sits between (B) the 8-tick partition of $Q_3$ and (C) the CW boundary prerequisite: one must first name all surface-coupling states before discarding those that couple faces without edges. Landmark contact is T7 (eight-tick octave on $2^3$ vertices) and the RCL additive torsion channels that turn those discrete profiles into ladder exponents.